By the
A M U SE M E NT S
sa m e
IN
3 s 6d
.
A ut/z or
M AT H E M A T I C S
.
"
TH E
AN T ER BU R Y
PU Z Z L E S
AND O TH E R CU R I O U S P R O BL E M S
H E N R Y E R N E ST D U D E N E Y
AU T H O R O F
“A M U SE ME NTS
I N M ATH E M ATI C S ,
TH O M A S
Fulle r So lutio n s
N E L SO N
LO ND O N E D I N BU R G H
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I
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ED ITI ON
S E C ON D
(With So me
E TC
919
an d
Addi tional
AN D
,
No te s)
S O N S, L T D
AN D N E W YO R K
.
C O N TE N TS
PR E FA C E
I N T R O D U C TI ON
TH E C AN TE R BU R Y P UZZ LES
P UZZ LI N G TI M E S A T SO LVAM H ALL C A STLE
TH E M E RR Y M ON K S O F R I D D LE W E LL
TH E STR AN G E E S C A P E O F TH E K I N G S JESTE R
TH E S Q U I R E S C H R IST M AS P UZZ LE P A R T Y
AD V E N T U R ES O F TH E P UZZ LE C L U B
TH E PR O FE SS O R S P UZZ LES
M IS C ELL AN E OU S P UZZ LES
S O L U TI ON S
I N D E!
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P R E F AC E
WH E N prep aring this new edition for the press m y first inclin a
tion was to withdr aw a few puz z les that appe ared to be o f in
fe ri o r interest an d to substit ute others for them
But on second
thoughts I decided to let the book st and in its origin al form an d
add extended sol utions an d some short note s to cert ain problems
th at h ave in the p ast involved me in corre spondence with inter
e ste d re aders who desired addition al inform ation
I h ave also provided— wh at was cle arly needed for reference
an index
Th e very n ature an d form of the book p re vented an y
sep aration of the p uz z les into cl asse s b ut a c ert ain amount o f
cl ass ific ation will be fo und in the index Th us for ex ample if the
re ader h as a predilection fo r problems with Moving Co unters or for
Magi c Sq u are s or for Combin ation an d Gro up P uz z les he will find
th at in the index the se are bro ught together for his c onvenience
Though the proble ms are q ui t e di fferent with the exc eption
of j ust one or two little v ari ations o r extensions from tho se in
my book A musements i n M athemati cs e ac h work being c omplete
in it s elf I h ave tho ught it wo uld help the re ader who h appens
to h ave both books before him if I m ade o c casion al references
t h at wo uld dire c t him to s ol utions an d an aly se s in the l ater book
c al c ul ated to el ucid ate m atter in thes e p ages Thi s c ourse h as
F o r the s ake
al so obvi ated t h e nece s sity of my repe ating my s elf
of brevity Amusements i n M athemati cs is th ro ugho ut referred to
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as
A in M
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HE NRY
THE AU TH O R S
J u ly
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C L U B,
2, 1 9 1 9
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E
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DU DE NE Y
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I N T R O D U C TI O N
The M i ll
will remember that when
ever Mr Tullive r found himself confronted b y an y little diffic ult y
he was accustomed to m ake the trite rem ark
It s a p uz z ling
world
There c an be no denying the fact th at we are surrounded
on every h and by posers some of which the intellec t of man h as
m astered an d m any of which may be s aid to be impossible of
solution Solomon himself who may be suppos ed to h ave been
as sh arp as most men at solving a pu z z le h ad to a dmit
there
be three things whi ch are too wonderful for m e yea four which
I know not the way of an e agle in the air the way o f a serpent
upon a n ick
the way o f a ship in the midst o f the se a and the
way o f a man with a m aid
P robing into the secrets o f N ature is a p as sion with all m en
only we se lect diff erent lines o f rese arch Me n h ave spent long
lives in such attempts as to turn the b aser met als into gold to
discover perpetu al motion to find a c ure for cert ain m align ant
dise ases an d to n avigate the air
F rom morning to night we are being perpetually bro ught face
Those
to face with puz z les
But there are p uz z les an d puz z les
th at are usu ally devised for recre ation an d p astime m ay be roughly
divided into two cl asses : P uz z les th at are b uilt up on some inter
esting or informing little principle ; an d puz z les th at conce al no
principle wh atever— s uch as a picture c ut at random into little
bits to be put together again or the j uvenile imbecilit y kn own as
the rebus or pict ure puz z le
Th e former species may be
s aid to be ad apte d to the amusement of the sane man o r wom an ;
the l atter c an be confidently recommen de d to the feeble minded
R E AD E R S
of
the F loss
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I N T R O D U CT I O N
12
Th e
curious propen s ity for propoun di ng p uz z les is not peculi ar
to an y r ace or to an y period of h i story
It is simply inn a te in
every intelligent m an wom an an d child th at h as ever lived tho ugh
it is always showing it self in di fferent forms ; whether the indi
vid ual be a Sphinx of Egypt a S am son of Hebrew lore an Indi an
f akir a Chi nese philosopher a m ah atm a of Tibet or a Europe an
m athem atici an m ake s little di fference
Theologi an scienti s t an d artis an are perpet ually eng aged in
attempting to solve p uz z les while every g ame sport an d p astime
is built U p of problems of gre ater or les s di ffic ul ty Th e spon tane
o us q u estion asked b y the C hi ld of his p arent
by one c yclist of
another while t aking a brief rest on a stile by a cricketer d u ring
the luncheon hour or b y a y achtsm an l az ily sc an ning the hori z on
is freq uently a problem of considerable d i ffi culty
In S hort we
are all propo unding p uz z les to one another every d ay of o ur lives
withou t always knowing it
A good puz z le S ho uld dem and the exercise of o ur best wit and
ingenuit y an d although a knowledge of m athem atic s an d a cert ain
fam i li ari t y with the methods of logic are often of gre a t servi c e
in the sol ution of these things y et it sometimes h appen s th at a
kind of n at ur al c unning an d s agacity is of c on s ider able val ue
F o r m any of th e best problems c annot be s olved by an y f amili ar
schol astic methods b ut mus t be att ac ked on entirel y origin al
lines This is wh y after a long an d wide experience one find s
th at p arti c ul ar pu z z les will sometimes be solved more re adily by
persons poss ess ing only n at ural ly alert fac ul ties th an by the better
ed uc ated Th e be st pl ayers of s uc h p uz z le g ames as c he ss an d
dr aughts are not m athem atici ans tho ugh it i s j ust po ss ible th at
often they m ay h ave undevelope d m at hem ati c al mind s
It is extraordin ary wh at fas c in ation a good p uz z le h as for a
gre at m any people We know the t h ing to be of trivi al i mpor
t ance yet we are impelled to m aster it an d when we h ave s uc ceeded
the re is a ple as ure an d a sense of s at i sfaction th at are a q uite su f
ficien t rew ard fo r o ur trouble even when there is no priz e to be
Wh at is thi s mysterious ch arm t hat m an y find irresistible
wo n
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I N TR O D U C T I O N
1
3
Wh y do we like to be pu z z led
The curious thing is th at direct ly
the enigm a is solved the in terest generally vanishes We have
done it and that is en ough But why did we ever attempt to
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nswer is s imply th at it gave us ple asure to see k the solution
—
that the pleasure was all in the s e e ldng an d finding for their own
sak es A good puz z le like virtue is it s own reward Man loves
to be confronted by a mystery an d he is not entirely h appy u ntil
he h as solved it We never like to feel o ur ment al inferiority to
those around us Th e s pirit of rivalry i s inn ate in man ; it stim u
l ates the s m allest c hi ld in pl ay or ed uc ation to keep level with his
fellows an d in l ater life it t urns men into gre at di scoverers in v e n
tors orators heroes artists an d (if they have more m ateri al aims)
Th e
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In st art ing o n a tour through the wide re al m of Pu z z ledom we
do well to remember th at we s h all meet with points of interest of
I sh all t ake adv ant age of this v ariety
a very v aried ch ar acter
”
P eople often m ake the mi st ake o f confining themselves to one
little corner of the re al m an d thereby mis s opport uni ties of new
ple as ures th at lie within t heir re ac h around them On e person
will keep to acrostic s an d other word p uz z les another to m athe
m atic al br ain racke rs an o t h e r to C hess p roblems (which are merely
p uz z les on the ches s bo ard an d h ave little practic al rel ation to the
game o f ches s) an d so on This is a mist ake bec ause it restricts
one s pleasures an d neglects th at v ariety whi ch is so good for the
brain
And there is re ally a practic al utility in p uz z le solving R e g
ul ar exercise i s s uppo s ed to be as nec e s sary for the brain as for the
body an d in both c ases it is not so m u c h wh at we do as the doing
of it from whi c h we derive benefit Th e d aily wal k rec ommended
by the doctor for the good of t h e body or the d aily exerci se for
the brain m ay in it s elf appe ar to be so much was te of time b ut
it i s the tru e st econom y in the end Albert Smith in one of his
de scribes a wom an wh o was convin c ed th at she
am using novels
This may be a very rare
suff ered from co bwigs o n the brain
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I N T R O D U C TI ON
14
complaint but in a more met aphoric al sense m an y of us are very
apt to suffer from ment al cobwebs an d there is nothing equ al to
the solvin g of puz z les and problems for sweeping them away They
keep the brain al ert stimul ate the im agin ation and develop the
reasoning fac ulties And not only are they useful in this indirect
way b ut they often directly h elp us by te aching us some little tricks
wrinkles that can be applied in the affairs o f life at the most
an d
unexpected tiIn es an d in the most unexpected ways
There is an interesting p as sage in praise of pu z z les in the qu aint
letters o f F itz osbo rn e Here is an extract
The ingenio us
st udy o f m aking an d solving puz z les is a science undoubtedly o f
most necessary acquirement an d deserves to m ak e a p art in the
m edit ation o f both sexes It is an art indeed th at I would re c o m
mend to the encouragement of both the Universities as it aff ords
the easiest and shortest method of conveying som e o f the most
useful principles o f logic
It was the m axi m of a very wise prince
th at he who knows not how to di ssemble knows not how to reign
an d I desire yo u to receive it as mine th at
he who knows no t how
to riddle knows not how to live
How are good puz z les invented
I am not referring to acrostics
an agr am s ch ar ades an d th at sort of thing but to puz z les th at
cont ain an origin al ide a Well you c annot invent a good pu z z le
to order anymore th an you c an invent anything else in that m anner
Notions for p uz z les c ome at strange times an d in strange w ays
The y are suggested by something we se e or hear an d are led up
to b y other pu z z les that come under o ur notice It is useless to
I will s it down an d invent an origin al puz z le bec ause there
s ay
i s no way of cre ating an ide a you can onl y m ake use of it when
it comes
Yo u may think this is wrong bec ause an expert in
these things will m ake scores of puz z les while another person
equal l y clever c annot invent o n e to s ave his life as we s ay
Th e expl an ation is very simple
The expert knows an ide a when
he sees one an d is able by long experience to j udge of its val ue
F ertility like facilit y comes b y practice
Sometimes a new an d most interesting ide a is suggested by the
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I N T R O D U CTIO N
15
‘
blunder o f somebody over another pu z z le A b oy was given a
pu z z le to solve by a friend but he misunderstood what he h ad to
do and set abo ut attempt i ng wh at mos t likely everybod y would
have told him was impossible But he was a bo y with a will and
he stu c k at it for s ix months o ff and on until he act ually succeeded
When his friend s aw the sol ution he said This is not the puz z le
—
I intended you misunderstood me—b ut you h ave found out
so mething m uch gre ater l
And the pu z z le which that boy acci
dent ally discovered is now in all the old pu z z le books
P uz z les c an be m ade o ut of al mo st an ything in the h ands o f
the ingenious person with an idea Coins m atches c ards counters
bits of re or string al l come in useful An immense number of
u
z
l
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r
e
O
been
m
a
de
u
t
f the letters of the alph abet an d from
o
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i
p
those nine little digits an d cipher I z 3 4 5 6 7 8 9 an d o
It S hould always be remembered th at a very simple person may
—
a
propound problem th at can only be solved by clever he ads if
at all
A chi ld asked Can God do everyt hing P
On receiving
an affirmfl i ve reply s h e at once s aid :
Then can He m ake a
stone so heavy th at He c an t lift it
Man y wide awake grown
up people do not at onc e see a s atisfactory answer Yet the diffi
cult y lies merely in the absurd though cunning form of the ques
tion which reall y am o unts to asking Can the Almight y destroy
His o wn o mnipotence ?
It is somewhat simil ar to the other ques
tion
Wh at would h appen if an irresistible moving bod y c ame
in cont act with an immovable body ?
Here we have siIn ply a
contradiction in terms for if there existed such a thing as an im
movable body there could not at the s ame tiin e exist a moving
body that nothing could resist
P rofessor Tynd all used to invite children to ask him puz z lin g
q ue stions an d some of them were very h ard n uts to crac k On e
child asked him why th at p art of a towel that was dipped in water
was of a d arker colour th an the dr y p art
How m any readers
co uld give the correct reply ? Many people are s atisfied with the
most ridiculo us answers to p uz z ling que stions If you as k Why
c an we s ee thro ugh gl ass ?
nine people o ut o f ten will reply
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I N T R O D U CT I O N
6
Q
B ec ause it is tr ansp arent ; which is of c ourse simply another
Bec ause we c an s e e thro ugh it
Way o f s aying
P uz z les h ave such an infinite variety th at it is sometimes very
diffi cu lt to divide them into distinct clas ses They often so merge
in ch aracter th at the best we c an do is to sort them into a few
bro ad types Let us t ake three o r four ex amples in illustration
o f wh at I me an
First there is the ancient R iddle th at draws upon the im agin a
tion an d pl ay o f fancy R eaders will remember the riddle of the
Sphinx the monster o f B oeoti a wh o propo unded enigm as to the
inh abit ants an d devo ured them if they failed to solve them It
was s aid th at the Sp hinx would destroy herself if one of her riddles
It was this
Wh at anim al walks
was ever corre c tly answered
o n four legs in the morning two at noon an d three in the evening
It was expl ained by (Edipus who po inted o ut th at man walked o n
his h ands an d feet in the morning of life at the noon o f life he
walked erect an d in the evening of h i s d ay s he s upported his
i nfirm i ties with a stic k
When the Sphi nx he ard this expl an ation
sh e d ashed her he ad against a rock an d immedi atel y expired
This
shows th at p uz z le solvers m ay be re ally us eful on occ asion
Then there i s the riddle propo unded by S am son
It i s perh aps
the first pri z e competition in thi s line on record the pri z e being
thirt y sheets and thirty c h anges of g arments for a correct sol ution
The riddle was this
Out of the e ater c ame forth me at an d o ut
o f the strong c ame forth sweetness
A honey
Th e answer was
comb in the body of a de ad lion
To d ay t hi s sort of riddle s ur
vives in s uch a form as
Why does a c hicken cross the ro ad ?
to whi ch most people give the an swer
To get to the other side ;
though the corre ct reply is
It h as
To worry the ch au ffe ur
degenerated into the con undrum whi c h i s usually b ased on a mere
pun F o r ex ample we h ave been asked from o ur infancy When
an d here ag ain the answer us u ally f urni shed
is a door not a door
When it is a j ar is not the correct one It sho uld be When
it is a negress (an
There is the l arge class o f Letter P u z z les which are b ased on
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I N TR O D U C T I O N
17
the little peculi ariti es o f the langu age in which they are written
such as an agr ams acrostics word squares an d ch arades I n this
class we also find p alindromes o r words an d sentences th at re ad
b ac kwards an d forwards alik e Thes e m ust be very ancient indeed
if it be tru e th at Ad am introd uced himself to Eve (in the Englis h
l angu age be it noted) with the palindromic words
Madam I m
Adam to which his consort replied with th e m odest pal indrome
Eve
Then we h ave Arithmetic al P uz z l e s an immense cl ass full o f
diversity These range fro m the puz z le th at the al gebr ai st fin ds to
be nothing but a simple equ ation quite easy o f di rect solution
up to the profoundest problems in the elegant dom ain of the theory
o f numbers
Next we h ave the Geometric al P uz z le a favourite and very
an cient br an ch o f which is the p uz z le in dissection req uiring some
pl ane figure to be c ut into a cert ain number of pieces that will
fit together and form anoth er figure Mos t o f the wire p uz z les sold
in the streets and to y shops are concerned with the geometry of
po sition
But the se classes do not nearly embrace all k inds of puz z les
even when we allow for those th at belong at once to several of the
cl asses There are m an y in genious mech anical pu z z les th at you
cannot cl assi fy as they st and quite alone : there are pu z z les in
logic in ches s I n draughts in c ards an d in dominoes while every
conj urin g trick is nothing b ut a pu z z le the solution to whi ch the
performer tries to keep to himself
There are puz z les th at loo k e as y an d are e asy puz z les th at loo k
e asy an d are di ffi cult puz z les th at loo k di fii cult an d are di ffic ult
an d puz z les th at look difficult an d are e asy an d in e ach cl ass we
may o f course h ave degrees of e asine ss an d diffi c ult y Bu t it does
not follow th at a p uz z le that h as conditions th at are e asily under
st ood b y the merest chi ld is in it self e asy Such a p uz z le might
however look simple to the uninformed an d only prove to be a
very h ard nut to him after he h ad act ually t ackled it
if we write down nin et e en ones to form the number
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2
I
I N T R O D UCTIO N
8
then ask fo r a n umber (other th an
I o r itself) th at will divi de it witho ut rem ainder the conditions
are perfectly simple but the t as k is terribl y di fficult
Nobody in
the world knows yet whether that number h as a divisor o r not
If yo u c an find one you will h ave succeeded in doing somethi ng
!
th at nobody else h as ever done
Th e n umber composed o f seventeen ones
111
h as onl y these two divisors
an d
and their discovery is an exceedingl y he avy t as k
Th e only
number compo sed only o f ones th at we know with cert ainty to
h ave n o divi s or is I I Such a number is o f course c alled a prime
number
Th e m axim th at there are al way s a right way an d a wrong way
o f doin g anyt hi ng applies in a very m arked degree to the solving
Here the wrong way consists in m aki ng aimles s tri al s
o f puz z les
—
without method hoping to hit on the answer by accident a proces s
th at general ly results in our getting hopelessly ent angled in the trap
th at h as been artful ly l aid for us
Occ as ion ally however a p roblem is o f such a character th at
though it may be solved immedi atel y by tri al it is very difficult
But in most c ases the latter
t o do b y a process o f p ure re ason
method is the only one that gives an y real pleasure
When we sit down to solve a pu z z le the first thing to d o is to
m ake sure as far as we can that we underst and the conditions
F o r if we do not underst and wh at it is we h ave to d o we are not
very li kely t o succeed i n doing it We al l know the story o f the
If a herring and a half cost
man who was asked the question
three halfpence how much wifl a do z en herrings cost ?
After
several uns uccessful attempts he gave it up when the propo under
expl ained to him that a doz en herrings wo uld cost a shilling
I was worki ng
He rri ngs l excl aimed the other apologetic al l y ;
it o ut in h addoc k s l
It sometimes requires more care than the reader might Suppose
so to word the conditions of a new pu z z le th at they are at once
See foo tn o te o n pag 1 9 8
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I N TRO D U CTIO N
20
He then amended his defini tion by s ayin g th at the actu al see ing
all sides was not essenti al but yo u went in such a wa
th
t
given
a
y
S ight y ou co uld see all sides Upon which it was suggested that
con sequently y ou could not walk around a man who h ad b e en shut
up in a bo x ! And so o n Th e whole thi ng is am us ingly stupid
an d if at the st art y ou very properly
decline to admit any but
a simple an d correct definition of
to go around there i s no
puz z le left an d yo u prevent an idle and often he ated argument
When y ou have gras ped your conditions always se e if you cannot
simplify them for a lot o f c o nfusio n is got rid of in this way Man y
people are pu z z led over the old question o f the man wh o whi le
pointing at a portrai t s ays Brothers an d sisters h ave I none but
th at m an s father is m y father s son
Wh at rel ation did the man
in the picture bear to the speaker
Here you simplify by s aying
th at m y father s so n must be either myself o r my brother
But since the spe aker h as no b rother it is cle arl y m yself
Th e
st atement simplified is thus nothing m ore th an Th at m an s father
is myself and it was obviousl y his son s portrait Yet people fight
over t hi s question b y the hour
There are m y steries th at h ave never been solved in m any bran ches
of Pu z z ledom Let us consider a few in the world of numbers
little t hi ngs the conditions o f which a c hi ld c an underst and though
the gre atest minds c annot m aster Everybody h as he ard the t e
m ark
It is as h ard as squ aring a circle though m an y people
h ave a very h az y notion o f what it me ans If you have a circle of
given di ameter and wish to find the side o f a squ are th at sh all con
t ain ex actly the s ame are a y ou are confronted with the problem
Well it c annot be done with exactitude
o f sq u aring the circle
c
a
a
ll
a
a
l
tho
gh
we
get
nswer
ne
r
enough
for
pr
cti
purposes
u
c
n
an
a
a
(
)
bec au se it is not possible to say in exact n umbers wh at is the ratio
o f the di ameter to the circumference
But it is only in recent times
th at it h as been proved to be impossible for it is o ne t hi ng no t to
be able to perform a c ert ain fe at but q uite another to prove that
it c annot be done O nl y uni nstructed cranks now waste their tim e
in trying to s quare the Circle
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I NT R O D U C T I O N
21
Again we c an never me as ure ex actly in n um bers the di agon al of
If you h ave a window p ane ex actly a foot on every s ide
a squ are
there is the dist ance from c orner to corner st arin g yo u in the face
yet yo u c an never s ay in ex act n umbers wh at is the length of th at
di agon al Th e simple person will at once suggest th at we might
t ake our di agon al firs t s ay an exact foot an d then construct o ur
s q uare
Yes y ou c an do thi s but then you can never s ay exactly
wh at is the length of the side You c an h ave it whi ch way y ou
like but yo u c annot h ave it both ways
All my re aders know wh at a m agic squ are is Th e numbers
I to 9 c an be arr an ged in a squ are o f nine cells so th at all the
columns and rows and e ach of the di agonals will add up 1 5 It is
quite e asy ; an d there is only one wayof doing it for we do not count
as di fferent the arr angements obt ained by merely turning round the
square an d reflecting it in a mirror Now if we wish to m ake a
m agic squ are of the I 6 numbers 1 to 1 6 there are j ust 880 di fferent
ways of doing it again not counting revers al s an d reflections This
But how m any m agic
h as been fin ally proved of recent ye ars
squ are s may be formed with the 2 5 numbers I to 25 nobody knows
an d we sh all h ave to extend o ur knowledge in cert ain directions
before we c an hope to solve the pu z z le But it is surprising to find
th at ex actly
such squ ares may be formed of one p artic ul ar
restricted kind only— th e bordered square in which the inner square
of nine cells is itself m agic And I h ave S hown how thi s number
may be at once doubled b y merely c onverting every bordered squ are
—
b y a simple ru le— into a non bordered one
Then v ain attempt s h ave been m ade to construct a m agic squ are
by wh at i s c alled a knight s tour over the c hes sbo ard numbering
e ac h squ are th at the knight vi sits in succession 1 2 3 4 etc an d
it h as been done with the exception o f the two di agon als whi ch so
far h ave b affled all e fforts
But it is not cert ain th at I t c annot
be done
Though the contents o f the present volume are in the m ain
entirely origin al some very few old frien ds will be found ; but these
will not I trust prove unwelcome in the new dress th at they h ave
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I N TRO D U CTIO N
22
received The pu z z les are o f every degree o f d iffi cult y and so
varied in ch ar acter th at perh aps it is not too m uch to hope th at
—
every true pu z z le lover will find ample m ateri al to interest and
po s sibly instruct In some c ases I h ave de alt with the methods of
solution at considerable lengt h b ut at other times I h ave reluct antly
felt obliged to restrict myself to giving the b are answers Had the
f ull solutions an d proofs been given in the c ase of every puz z le
either h alf the problems would h ave h ad to be omitted or the si z e
o f the book gre atl y incre ased
And the pl an th atll h ave adopted
has its adv ant ages for it le aves scope for the m athem atic al e u
Even in those c ases where
th us iast to work out his o wn an al y sis
I h ave given a general formul a for the solution o f a puz z le he will
find great interest in verifying it for himsel f
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CHANCE GATH E R ED
comp any of pilgrims o n their way to
the shri ne of S aint Thom as aBecket at Canterb ury met at the
o ld Tab ard I nn l ater c alled the Talbot in So uthw ark an d the host
proposed th at they should beguile the ride by e ach telling a t al e
to hi s fellow pilgrim s This we all know was the origin of the
immort al Canterbury Tales of o ur gre at fourteenth c entury poet
Geoffrey Ch aucer Unfort un at ely the t al es were never completed
an d perh aps th at i s why the q u ain t an d c urious
Cante rb ury
devised and propo unded by the s ame body of pilgrim s
P u z z les
were not also recorded b y the poet s pen This is gre atly to be
regretted since Ch auc er who as Lel and tells us was an ingenio us
m athem atici an an d the author of a learned tre atise on the astro
In
labe was pec uli arly fitted for the p ropo undi ng o f problem s
pre senting for the first time some of thes e old world posers I will
not stop to expl ain the S ingul ar m anner in which they c ame into
my posse ssion b ut proceed at once witho ut unnece ss ary pre amble
to give my re aders an Opportunity of solving them an d testing
their quality There are cert ai nly far more di fficult p uz z le s ext ant
b ut di ffi culty an d in terest are two qu alities o f p uz z ledom that d o
not necessarily go together
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CA N TE R B URY P U ZZ L E S
T HE
24
I
.
—The
Reve
’
s
P uz z le
.
wily m an and something o f a schol ar As
an d
There was n o auditor could o f hi m win
Ch aucer tells us
there could n o man bring hi m in arre ar
The poe t also noticed
This he did that
th at ever he rode the hindermost o f the route
he might the better without interruption work o ut the fanciful
problems and ide as that p assed through his active brai n Wh en the
The R eve was
a
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pilgrims were stopping at a wayside t avern ,a number of cheeses of
vary
ing siz es c aught his alert eye ; and c alling for four stools he told
the comp an y th at he wo uld Show them a p uz z le o f his o wn th at
would k eep them amused during their rest He then pl aced eight
chees es o f gr aduating si z es on one of the end stools the sm allest
C heese being at the top as cle arly s hown in the illustr ation
Thi s
is a riddle q uoth he th at I did once set before my fellow town s
men at Baldeswe ll th at is in Norfolk an d by S aint Jo c e there was
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T HE
C A N T ER B U R Y P U ZZLES
25
in an am ong them that could rede it aright And yet it is withal
full eas y for all th at I do desire is th at by the moving of one cheese
at a ti me from o ne stool u nto another y e S h all remove all the cheese s
to the stool at the other end without ever putting an y cheese o n one
that is sm aller th an itself To him th at will perform this feat in the
least num be r o f moves that be pos s ible will I give a dr aught o f
the best that o ur good host can provide
To solve this p uz z le in
th e fewes t possible moves first with 8 then with I O an d aft erw ards
with 2 1 cheeses is an interesting rec reation
no
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The
gentle P ardoner th at straight was come from the court
begged to be excused ; but the company would no t sp are
o f Ro m e
F riends and fellow pil grims
o f a truth the
said he
hi m
riddle that I h ave m ade is but a poor thing but it is the best that
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I
Bl ame my l ack of knowledge of such
able to devise
m atters if it be not to your liking
But hi s invention was very
well received He prod uced the accompanying pl an and said that
it represented sixt y four towns through which he had to pass
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THE C AN T E R B U R Y PUZZ L ES
26
d uring
some o f his pilgrim ages and the lines conn e cting them were
roads He expl ained th at the pu z z le was to st art from the l arge
black town an d visit all the other towns once an d once only in
fift e e n straight pilgrim ages Try to trace the route in fifteen
strai ght li nes with your pencil You may end where you like but
note th at the omission of a little ro ad at the bottom is intentio nal
as it s ee ms th at it was impossible to go tha t way
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3
—The M i ller s
’
.
P uz z le
.
Th e Miller
next took the comp any aside and showed them
nin e s ac ks of flour th at we re st anding as depicted in the sketch
s aid he while that I do se t ye
No w hearken all an d some
the riddle o f the nine s ac ks of flour And m ark y e m y lords and
m asters th at there be single s ac ks o n the out side p airs next unto
them an d three together in the middl e thereof B y S aint Benedict
it doth so h appen th at if we do b ut multiply the p air 28 by the
sing le on e 7 the answer is 1 96 which is o f a truth the number
shown by the sa c ks in the middle Yet it be not tru e th at the other
p air 34 when so multiplied by its neighbour 5 will also m ake 1 96
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Wherefore I do beg y ou gentle sirs so to pl ace anew the nine sac ks
wit h as little trouble as possible that e ach pair when thus multi
plied by its sin gle neighbo ur sh all m ake the n umber in the middle
As the Miller h as stipul ated in e ffect th at as few b ags as possible
s h all be moved there is only one answer to this pu z z le which e v ery
body sho uld be able to solve
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—
e
h
T
4
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K night s P uz z le
’
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worthy man was as Ch aucer tells us
gentle knight and In m any a noble arm y
This
,
,
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a
h ad
very perfect
he been : At
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THE C A N TER B U RY PUZZLES
28
remembered one o f hi s riddles th at might be new to her fellow
“
pilgrims : Why is a b ung th at h ath been m ade fast in a barrel
like unto another bung th at is j ust f alling out of a b arrel ?
As
the compan y promptly answered t hi s e as y conundrum the l ady
went o n to say th at when sh e was one d ay se ated sewing in her
private ch amber her so n entered
Upon receiving s aith she
the p arent al comm and D ep art my so n an d do not disturb me I
he did reply I am of a truth thy so n but thou art not m y mother
and un til thou h ast shown m e how this maybe I sh all not go forth
Thi s perplexed the comp any a go od deal b ut it is not lik el y to give
th e reader much diffi cult y
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6
Th e
,
P erh aps
was
H ost s P uz z le
’
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puz z le o f the whole collection c aused more j ollity o r
found more entert aining than that produced b y the Host o f
no
T HE C A N TE R BU RY P U ZZLES
29
Tab ard who accompanied the part y all the way He
called the pilgrim s together an d spoke as follows
My merry
m as t ers all no w th at it be m y turn to give your brains a twist
will S how ye a little piece of craft that will try your wits to their
And y et methinks it is but a simple m atter when the
ull bent
doing o f it is m ade clear Here h e a c ask of fine London al e and
in m y hands do I hold two measures—o ne of five pints an d the
other o f three pints P ray show how it is possible for me to put a
true pint into e ach o f the me asures
Of course no other vessel or
article is to be used an d no m ar king of the me as ures is allowed
It is a knott y little problem and a fascin ating one A good m an y
persons to d ay will find it by no means an e asy t ask Yet it c an
be done
—
l
er
o
x
e
n
or
d
s
P
u
z
z
h
e
k
O
l
e
T
C
f
f
7
Th e silent an d tho ughtful Clerk of Oxenford of whom it is re
corded th at Every fart hi ng th at his friends e er lent In books an d
learni ng was it always spent was prevailed upon to give his
the
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pu z z le He said
O ft times of late h ave I given
m uch thought to the study o f thos e strange t alism ans to ward o ff
th e plag ue an d such evils th at are y clept m agic squares an d the
secret o f such thi ngs is very deep an d the numb er o f such squ ares
a
.
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T HE C A N TE R B U R Y P UZZ L ES
0
3
trul y great But the sm all riddle th at I did mak e y ester eve for
the purpose o f this comp any is not so h ard th at any may n ot fin d
it o ut with a little p atience
He then prod uced the squ are shown
in the illustration and s aid th at it was desired s o to cut it into fo ll l
pieces (b y cuts al ong the lines ) th at they would fit together ag ain '
an d f orm a perfect m agi c sq u are in which the four columns the
four rows an d the two long di agon al s S ho uld ad d up 3 4 It will
be found that this is a j ust sufficiently e asy puz z le for most people s
t astes
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8
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—The
Tapi s er s P uz z le
’
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c ame forward the Tapiser who was o f course a m aker o f
t apestry an d must no t be confounde d with a t apster who draws
an d sells ale
He produced a be autiful piece of t apestry worked in a simple
ch equered p attern as shown in the di agr am
This piece o f
Then
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quoth he hath one hundred an d sixt y nine sm all
squares an d I do desire yo u to tell me the m anner o f cutti ng the
t apestry into three pieces that shall fit together and m ake o ne
whole piece in sh ape of a perfect square
More over sin ce there b e d i v ers way s o f so doi ng I do wis h to
tapestry
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sirs
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T HE
CA N TE R B URY P UZZLES
:
3
know that way wherein two of the pie ces s h all together cont ain as
m uch as possible of the rich fabric
It is clear that the Tapiser
intended the cuts to be m ade al ong the lines di viding the squares
onl y an d as the m ateri al was not bo th sides alike no piece may be
reversed but c are must be observed that the chequered pattern
matches properly
”
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—
T
l
ie
9
.
Carpeuter s P uz z le
’
.
Th e Carpenter
produced the c arved wooden pill ar that he is
seen holding in the ill ustration wherein the knight is propo unding
his knotty problem to the goodly company (No
an d s poke a s
follows
There dwelleth in the city of London a cert ain schol ar
that is le arned in astrology an d other st range arts Some few d ays
gone he did bring unto me a piece of wood th at h ad three feet in
length one foot in bre adth an d one fo ot in depth an d did desire
that it be c arved an d m ade into the pi ll ar th at you do now behold
Also did he promise cert ain p ayment for every c ubic inch of wood
c ut away by the carving the reof
Now I did at first weigh the block and found it truly to cont ain
thirty po unds where as the pillar doth now weigh b ut twenty po unds
Of a truth I have therefore c ut a way o n e c ubic foot (which is
to say one t hi rd) of th e three cubic feet of the block ; b ut
this scholar with al doth hold th at payment m ay not thu s be fairly
m ade by weight since the he art of the block m ay be heavier or
perch an c e m ay be more light th an the outside How then m ay
I with ea se satisfy the schol ar as to the quantity of wood th at hath
been cut away
This at fir st sight looks a di ffi c ult question b ut
it is so absurdly simple th at the method employed by the carpenter
should be known to everybody to d ay for it is a very useful little
wrinkle
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10
The P uz z le of the S quire s Yeoman
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says of the Squire s Yeoman who formed one o f hi s
party of pilgrims A forester was he t ruly as I guess an d tell s us
that Hi s arrows droo ped not with feathers low And in his h and
he b are a mighty bow
When a h alt was made one day at a
Ch aucer
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T HE
2
3
CA N TER BU RY P U ZZLES
wayside inn be arin g the old sign o f the Chequers this yeom an
consented to give the company an exhi bition of his skill Selecting
nine good arrows he said Mark ye good sirs how that I shall
shoo t these nin e arrows in such m anner that e ach o f them sh all
lodge in the mi ddl e o f o ne o f the squ ares that b e upon the sig n o f
the Chequers an d yet o f a truth sh all no arrow be in line with
an y other arrow
Th e di agr am will show ex actly how he did
this an d no two arrows will be fo und in line horiz ont ally vertically
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di agon ally
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the Yeoman sai d
Here then is a riddle for
ye R emove three of the arrows each to o ne of its neighbouring
s qu ares so th at the ni ne sh all yet be so pl a ced th at none there of
m ay be in line with another
By a neighbouri ng squ are is
me ant o ne th at adj oins either l ater ally or di agon all y
or
.
Then
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11
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The Nuu s P uz z le
’
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I trow there be n ot o n e among ye quoth the N un o n a later
oc casion
th at doth not know th at m any monks do oft pass the
time in play at cert ain g ames albeit they be not lawful for them
These games such as cards an d the g ame o f Chess d o they cun
nin gly hide from the abbot s e y e by p utting them away in holes
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T HE CA N TE R BU R Y PUZZ L E S
33
th at they have c ut o ut o f the very hearts o f gre at books that be
upon their shelves Shall the nun therefore be gre atl y blamed if
she do likewise ? I will show a little riddle game that we do
sometimes pl ay among ourselves when the good abbess doth h ap
to be away
Th e Nun then produ ced the eighteen c ards that are shown in
the illustration She expl ained that the puz z le was so to arrange
the cards in a p ack that by pl acing the uppermost one o n the t able
a
a
t
l
cing
the
next
one
the bottom o f the pa ck the n ext o ne on the
p
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,
,
t able the next at the bottom of the pack an d so on until all are
on the t able the eighteen cards sh all then read CANTE R BURY
P I LG R I MS
Of course e ach card must be pl aced o n the t able
to the immedi ate ri ght o f the o ne that preceded it It is easy
enough if you work b ackwards but the rea der shoul d try to arrive
a t the required order without doing this o r u sing an y actu al cards
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12
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The M erckant s P uz z le
’
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the Merch ant the poet writes
F orsooth he was a worth y
He was thoughtful f ull o f schemes and a good
man withal
m anipul ator of figures
His reaso ns spake he eke full solemnly
On e morning when
Sounding alway the increase of hi s winning
they were on the ro ad the Knight an d the Squire who were
ri di ng beside him reminded the Merchant th at he h ad not yet
propo unded the pu z z le th at he owed the company He thereupon
said Be it so
Here then is a riddle in numbers that I will set
before this merry compan y when next we do m ake a halt There
be thi rty of us in all ridin g over the common t hi s morn Tru y we
Of
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T H E C A N TER BU R Y P UZZ L ES
34
one an d one in wh at they do call the Single file o r two an d
two or three an d th ree or five an d five or six an d six o r ten an d
t en o r fifteen an d fifteen or all thirty in a row
In no other way
m ay we ride so th at there be no l ac k of equ al n umbers in the rows
Now a p art y of pilgrims were able thu s to ride in as m any as sixty
m ay ride
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four different ways P rithee tell me how m any there must perfore
have been in the comp an y
Th e Merchant Cle arly re
sm allest number o f persons th at could so ride in the sixt
ways
1 3 — The M an of Law s P uz z le
.
”
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’
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Sergeant of the Law was full ri c h of excellence Di screet
he was an d o f gre at reverenc e
He was a very busy man b ut
like m any o f us to d ay he seemed bu sier th an he was
He was
t alki ng o ne evening of prisons an d prisoners and at len gth m ade the
following rem arks :
And that which I have been sayin g doth
Th e
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CA N TER BU R Y PUZZLES
T HE
6
3
of cloth m ay be cut into four several pieces each o f the same siz e
It is not
an d S h ape an d e ach piece be aring a lion an d a c astle
,
”
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,
orded that an ybod y m astered this puz z le though it is quite
possible o f solution in a satisfacto ry m ann er No cut may p ass
through any p art o f a lion o r a castle
rec
,
.
.
15
—
The
.
Cook s P uz z le
’
.
We fin d th at there was a coo k among the comp any ; and his
se rvices were no doubt at times in gre at request
F o r he co uld
roast and seethe an d broil an d fry And m ak e a mortress and well
b ake a pie
One night when the pilgrims were seated at a country
hostelry about to begin their repast the coo k presented himself
at the he ad o f the t able th at was presided over b y the F r anklin and
s aid Listen awhile my m asters whi le that I do ask ye a riddle
an d b y S aint Moden it is o n e th at I c annot answer m y self with al
There be eleven pilgrims se ated at this board o n which is se t a
warden pie an d a ve nison past y ea ch o f which may truly be divided
into four parts an d no more Now m ar k y e five o ut o f the eleven
pi lgrims c an e at the pie b ut will no t touch the p ast y while four
,
,
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”
.
,
,
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,
,
,
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,
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,
,
,
,
T HE
CA N TER BU RY P UZZLES
3 7
will eat the p asty b ut turn away from the pie Moreover the two
th at do rem ain be able an d willing to e at o f either By m y hal i
dame is there any th at c an tell me in how m an y different ways the
good F ranklin may choose whom he will serve
I
j ust
.
,
.
,
c aution the re ader th at if he is not c areful he wi ll find when he sees
t h e ans wer th at he h as m ade a mist ake of fort y as all the comp any
did with the exception of the Cler k of Oxenford wh o got it right
by accident thro ugh p utting down a wrong figure
Strange to s ay while the company perplexed their wits about
this riddle the cook pl ayed upo n them a merry j est In the midst
of their deep thinking an d hot disp ute wh at should the cunning
kn ave do but stealt hi ly t ake away both the pie an d the past y
Then when hunger m ade them desire to go on wi t h the rep ast
fin din g there was nought upon the t able they c alled cl amorously
for the cook
My m ast ers he explained
seeing you were so deep se t in
t h e riddle I did t ake them to the next room where others did eat
them with relish e re they h ad grown cold There be e xcellent
bread and cheese in the p antry
,
,
,
,
,
.
,
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.
,
,
,
.
,
,
,
,
.
”
.
T HE
8
3
16
CA N TE R B URY P U ZZ L ES
.
—The
S ompn our s P uz z le
’
.
Sompnour or Summoner who according to Ch aucer
j oined the p art y of pilgrims was an officer whose dut y was to
summon delinquents to appe ar in ecclesi astic al co urts In l ater
times he bec ame known as the app aritor Our particul ar indi
vidual was a somewh at q uaint though worthy man
He was
Th e
,
,
,
,
,
.
.
.
hireling and a kind ; A better fellow should a m an not
find
In order that the re ader may underst and his appe arance
in the picture it must be expl ain ed th at his peculiar he adge ar is
duly recorded b y the poet
A garl and h ad he set upo n hi s head
As gre at as if it were for an ale st ake
One e v ening te n o f the comp any stop p ed at a vill age i nn and
a
.
,
,
.
-
.
C A N T E R B U R Y P UZZ LE S
T HE
39
equested to be put up for the night b ut mine host could only
a ccommoda te five of them
Th e Sompnour s ugge sted that they
sho uld draw lots an d as he h ad h ad experien c e in such m atters in
the s ummoning of j uries an d in other ways he arranged the comp any
in a circle an d propo sed a count o ut
Being of a chivalro us
n at ure his little plot was s o to arr ange th at the men s ho uld all fall
o ut an d le ave the l adies in po ss e s s i on
He therefore gave the Wife
of B ath a number an d di rected her to co unt ro und an d ro und the
circ le in a clockwise di rec tion an d the pers on on whom th at number
fell was immedi ately to step o ut of the ring Th e c ount then began
afres h at the next person
But the l ady mi sunderst o od her i n
stru cti o n s an d selected in mist ake the n umber eleven an d st arted
the count at herself As wi ll be found this resulted in all the
women falling out in turn inste ad of the men for every eleventh
pe rson withdr awn from the ci r c le i s a l ady
Of a truth it was no fault of mine
said the Sompno ur next
Can a n y
d ay to the compan y
an d herein i s methi nks a rid dl e
tell me what n umber the good Wife s ho uld h ave used with al and at
whi c h pilgrim s h e sho ul d h ave begun her count s o th at no other
Of cours e
th an the five men s ho uld h ave been co unted o ut ?
t h e point is to find the sm alles t n umber th at wi ll h ave the desired
effect
r
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17
—The M ouk s
’
.
P uz z le
.
Th e Monk
that went with the p art y was a gre at lover o f sport
Greyhounds he h ad as swift as fowl of flight Of riding an d of
hunting for the h are Was all hi s love for no cost would he S pare
O n e d ay he addre ssed the pilgrim s as follows
There i s a little m atter th at h ath at times perplexed m e greatly
though certes it i s of no great weight ; yet m ay it serve to try the
wits of some th at be c unning in s uch things Nine kennels h ave I
for the use of my do gs and they be put in the form of a square ;
though the one in the middle I do never use it not being of a useful
nat ure Now the riddle is t o find in how m any different ways I
m ay place m y dogs in all or an y of the o utside kennels s o th at the
.
”
.
,
,
.
,
,
.
T HE
40
C A N TE R B U RY P UZZLES
number o f dogs o n e v ery side o f the square m ay be j ust ten
The
sm all di agrams show fo ur ways o f doin g it an d though the fourth
.
,
re ve rs al o f the third it coun ts as different An y
kennels may be le ft e m pt y This p uz z le was e vidently a variation
o f the an cient o n e o f t h e Abbes s and her N u ns
way is
me rel y
a
,
,
.
.
—
The S hfl
18
mzau s P uz z le
’
.
.
thi s person we are told
He knew well all the havens as
they were F rom G o thland to the Cape o f F inisterre And every
cree k in Britt any an d Sp ai n : His b ar que yclep ed was the M ag
dalen
Th e strange p uz z le i n n avi gatio n th at he prop oun ded
was as follows
Here be a chart q uoth the S hipm an o f five isl ands with
the inhabit ants o f whi ch I do trade In e ach ye ar m y good shi p
doth s ail over e very o ne o f the ten courses depicted thereo n b ut
never may she p ass along the same course twice in any y e ar I s
t he re any among the comp any who can t ell me in how m an y dif
feront ways I m ay direct the M agdalen s ten yearly v oy ages
always setting o ut from the s ame isl and P
Of
,
,
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,
.
.
,
,
,
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,
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’
,
T HE
19
C A NTE R B U R Y P UZZLES
The P uz z le of the P ri oress
1
4
.
.
who went by the n ame o f Egl antine is be st
remembered on account o f Ch aucer s rem ark
And Fren ch she
sp ake full fair an d properly After the school of Strat ford att e
Bow Fo r F rench of P aris was to her unknow
But o ur puz z le
h as to do less with her ch aracter an d educ atio n than wi th her
dress
And thereon hung a brooch of gold full sheen On which
was written first a crown ed A
It i s with the brooch th at we are
concerned for when asked to give a pu z z le she showe d t hi s j ewel
to the c omp any an d sa id : A le arned man from Norm andy did
once give me thi s brooch as a ch arm s aying stran ge an d mystic
things anent it how th at it h ath an affinity for the squ are and such
other wise words th at were too s ubtle for me But the good Abbot
of Chertsey did on c e t ell me that the cross may be so cunningly cu t
into four pieces th at they will j oin an d m ake a perfect squ are ;
t ho ugh o n my faith I know not the m anner o f doing it
“
It is recorded th at the pilgrims did fin d n o answer to the riddle
Th e Prioress
,
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’
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,
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,
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”
.
,
42
T HE
C A N TER B U R Y P UZZ L ES
the Clerk o f O xenford thought th at the P rioress ha d been
d ece ived in the m atter thereof ; whereupon the lady was sore vexed
an d
,
though the gentle
did flout and gibe at the poor clerk be
c ause o f his l ac k o f underst andin g over other o f the riddles w hich
did fill him with shame and m ake m erry the compan y
,
”
.
—
The
P uz z le
f the D octor of P hysic
This Doctor learned though he was for In all this world to
him there was none like To spe ak o f phys io and of surgery an d
He knew the c ause of every m al ady yet was he not indi fferent
Gold in physic is a cordi al
to the more m aterial side of life
Th erefore he lov ed gold in speci al
Th e problem th at the D octor
propounded to the assembled pilgrims was this He produced two
spheric al phi als as shown in o ur illustration an d pointed o ut th at
o n e phi al was exa ctly a foot in circumference an d the other two
feet in circumference
I do wish sai d the D octor addressing the compan y
to
have the e xact me asures o f two other phi al s of a like sh ape but
di fferent in siz e that m ay together cont ain j ust as much liquid as
is cont ain ed b y these two
To find ex act dimensio ns in the
20
.
o
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”
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”
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.
T HE C A N TER B URY P U ZZLES
44
would S how the good pilgrims if they willed it one that he h ad
frequently he ard cert ain Clever folk in hi s o wn neighbourhood dis
cuss
Th e lord o f th e m an o r in the p ar t of Sussex whence I
come h ath a pl a t ation of sixt e en fair o ak trees an d they be so
se t o ut th at the y m ake twelve rows with four trees in every ro w
Once o n a ti m e a man o f deep le arning wh o h appened to be travel
ling i n those parts did say th at the S ixteen trees might h ave been
so pl anted th at they would m ake so m any as fifteen straight rows
with four trees in every row thereof Can ye S how me how this
Man y h ave doubted that twere possible t o be done
might be
Th e illustration show
s one of m any ways of forming the twelve
rows How c an we m ake fi fteen
,
,
.
,
fl
,
.
,
,
,
.
”
’
.
.
22
.
—The
F raukli u
’
P uz z le
s
.
A F r an klin was in this comp any White was his b eard as is
the d aisy
We are told by Ch aucer th at he was a great hons
holde r an d an
Without baked me at never was
house Of fish and flesh and th at so plenteous It snowed in
”
.
.
,
,
house o f m e at and drink Of every d aint y th at men co uld bethin k
He was a hospit ab le and gen erous man
His t able dorm ant in
his h all alway Stood rea dy covered all throughout the d ay
At
.
,
.
”
.
CA N TER B U R Y PUZZLES
T HE
45
re pasts o f the Pilgrims he usually presided at o ne o f the t ables
as we fo und him doing on the occ asion when the coo k p ro poun ded
his problem of the two pies
On e d ay at an inn j ust outside Canterbury the compan y c al led
on him to produce the puz z le required of him ; whereupon he pl aced
on the t able S ixteen bottles numbered 1 2 3 up to 1 5 with the
las t one m arked o
Now m y m asters quoth he
it will be
fresh in your memories how th at the good Clerk o f Oxen ford di d
S how us a riddl e touching wh at hath been c alled the m agic s qu are
Of a truth will I se t before ye another th at may see m to be some
wh at o f a like kind albeit there be little in com mon betwixt them
Here be se t out s ixt een bottles in form o f a squ are and I pray yo u
so pl ace them afresh th at they sh all form a m agic sq uare adding
up to thirty in all the ten straight ways But m ark well th at ye
may not remove more th an ten of the bottles from their present
pl aces for therein l ay eth the s ubtlet y of the riddle
This is a
little pu z z le th at may be conveniently tried with sixteen numbere d
counters
the
,
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.
23
—Tke S qui re s
’
.
P uz z le
.
youn g Squire twenty ye ars of age was the so n o f the
He
Knight th at accomp anied him on the historic pilgrim age
Was undo ubt edly wh at in l ater times we should c all a d an dy for
Embroider ed was he as is a me ad All full of fresh flowers white
an d red
Singi ng he was or fluting all the d ay He was as fresh
as i s the month of May
As will be seen in the illustration to
No 2 6 while the H aberdasher was propo unding his problem o f
t h e tri angle this yo ung Squire was st anding in the b ackgroun d
ma king a dr awing of some kind ; for He could songs m ak e and
well in di te Jo ust an d eke d ance an d well portray and write
Th e K night turned to hi m after a while an d s aid
My so n
what i s it over whi ch thou dost t ake so great p ains with al P an d
the Squire an swered
I h ave bethought me how I might po rtray
in one only s troke a picture of our l ate sovereign lord King Edward
‘
th e Third who h ath bee n dead these te n ye ars
Ti s a riddle t o
Th e
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T HE
6
4
CA N TER B URY P UZZ L ES
fin d where the stroke doth b egin and where it doth also e n d
him who first shall S how it u nto me will I give the portraiture
ab le to p rese n t a f acsimile o f the ori g in al drawin g
I
To
.
.
,
by the Man o f Law It m ay be here rem arked that
‘
the p ilgrim age set o ut from Southwar k o n 1 7th Ap ril 1 3 87 and
Edward the Third died in 1 3 77
won
.
,
.
24
.
-
Tke F ri ar s P uz z le
’
.
The F ri ar was a merry fellow with a sweet tongu e and twin
There was
kling e y es
Courteous he was an d lowly o f service
a m an nowhere so virtuous
Yet he was the b est begg ar in all
”
his house an d gave re asons why Therefore i nstead of weeping
an d much pr ayer Me n must give silver to the needy fri ar
He
went by the n ame o f Hube rt One day he produced four mone y
b ags and spo ke as follows
I f the n eedy friar doth receive in ai ms
,
.
.
”
.
,
,
”
.
,
.
five hundred silver pe nnies prithee t ell in
,
ho w
man y differ e nt
T HE C A N TE R B U RY
PU Z ZLES
47
ways they may be placed in the four b ags
Th e good man e x
pl ai ned th at order m ade no di fference (so that the di stribution 50
1 00 1 50 2 00 would be the s ame as 1 0 0 50 2 00 1 5 0 o r 200 50
1 00
and one two or three b ags m ay at an y time be empt y
.
,
,
,
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,
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.
,
.
,
25
,
—
The
P ars on
’
s
P uz z le
.
re ally devo ut an d good man
A be tter
priest I trow there nowhere is
His virt ues an d ch arit y made
him beloved by all his flock to whom he presented his teachin g
wi t h patience an d s impli cit y ; but first he followed it himself
Now Ch aucer is c areful to tell us th at Wide was his p arish an d
The P arson was
a
.
”
.
,
”
.
,
,
T HE C AN TER BU R Y PUZ Z LE S
8
4
houses far asunder But he neglect ed nought for i ain o r thunder
an d it is with hi s p arochi al vi sit ations th at the P arson s pu z z le
a ctually de al t
He produced a pl an o f part of his p arish through
'
,
’
.
,
whi ch a sm all river ran th at j oined the se a some hundreds o f miles
I give a facsimi le o f the pl an
to the south
Here m y worthy Pi lgrims is a strange riddle quoth the
Behold how at the branchi ng o f the river is an isl and
P ar son
Upon this isl and doth st an d my o wn poor p arson age an d y e m ay
Mar k y e also th at
all see the whereabouts o f the vill age church
there be e ight bridges and no more ove r the river in my p arish
On m y way to church it is m y wont to visit sundry of m y flock an d
in the doing thereo f I do p as s over every o n e of the eight bridges
once and no more Can any o f ye find the path after this m anner
from the house to the church without going out o f the parish ?
Nay n ay m y friends I do never cross the river in an y bo at neither
by swimming no r wading nor do I go underground like unto the
m ole nor fly in th e air as doth the eag le ; b ut onl y p ass over b y the
.
.
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‘
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,
C A NT E R B U R Y P UZZLES
T HE
49
bridges
There is a way in which the P arson might h ave made
t h is curious j ourney Can the re ader discover it ? At first it
seems immss ible but the conditions offer a loophole
.
.
.
,
26
Man y
—
The H aberllas her s P uz z le
’
.
.
ttem pts were m ade to induce the H aberdasher who
was o f the p arty to propound a puz z le of some kind but for a
long ti me without success At l ast at one o f the P ilgrim s stop
h e s ai d that he would show them something that
a
,
,
,
’
.
,
would put their brai ns into a twist like unto bell rope
As a
m atter o f fact he was really playing o ff a prac tic al j oke o n the
comp an y for he was quite ignorant o f any answer to the p l z z le
a
-
.
,
,
i
C AN TE R B U R Y P U ZZLES
T HE
0
5
th at he set them He produced a piece of cloth in the sh ape o f a
perfect equil at e r al tri angle as shown in the illustration and s aid
Be there any among ye full wise in the true cuttin g of cloth
I
trow not Every m an to his trade and the scholar m ay le arn
from the varlet an d the wise m an from the fool Show me then
if y e c an in wh at m anner thi s piece of cloth m ay be cut into four
sever al piec es th at m ay be put together to m ake a perfect squ are
Now some o f the more le arned of the comp any fo und a way of
doing it in five pieces but not in fo ur But when the y pressed
the H aberd asher for the correct answer he was forced to admit
a fter m uch be ating abo ut the bush th at he knew no way o f doing
it in any number of piece s
B y S aint F rancis s aith he
any
kn ave c an m ake a riddle methinks but it is for them th at m ay
to rede it aright
F o r this he n arrowl y esc aped a sound be ating
But the c u rio u s point of the puz z le is th at I h ave found th at the
feat may re ally be performed in so few as four pieces an d with
out turni ng over any piece when pl acing them together The
method o f doing this is subtle but I thin k the re ader will find t
problem a most interesting one
.
,
,
.
,
,
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,
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”
.
.
,
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”
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,
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.
'
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,
.
—
27
The
.
Dyer s P uz z le
’
.
the pilgrims was a D yer but Ch aucer tells us nothi
about him
the Tal es being incomplete Time after time
company h ad pressed thi s individual to produce a pu z z le
kind but without effect The poor fellow tried hi
the examples of his friends the Tapiser the We aver
d asher but the necessary
he would All
persevere—and one morning he announced in a st ate
able excitement th at he h ad a poser to set before them
He
o ut a sq u are piece of silk on which were embroidered a nu
fieurs de lys in rows as shown in our illustration
Lordings said the Dy er
he arken anon unto my
—
Since I was awakened at d awn by the crowin g o f coc ks fo r
One
of
,
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,
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,
-
-
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”
,
,
THE C A N T E R B U R Y P UZZ LE S
52
temporary pe ace Unfortun ately trouble broke
very curious dispute in thi s way
.
but
g in o v er
a a
a
.
At one point o f the j ourney the ro ad lay along two sides of a
squ are field an d some of the pilgrims persisted i n spite of trespa ss
in cutting across from corner to corner as the y are seen to be
doing in the ill ustration N ow the F ri ar st artled the company by
st ating th at there was no need for the tresp ass since o n e way
On my faith
was exactly the same dist ance as the other !
then excl aimed the Sompnour thou art a very fool
Nay
if the comp any will b ut listen with p atience I
repli ed the F ri a r
shall presently Show how th at thou art the fool for tho u h ast not
wit enough in thy poor brain to prove th at the di agonal of any
sq u are is l e ss th an two of the sides
If the rea der will refer to the di agrams that we h ave given he
will be able to follow the F ri ar s argumen t I f we suppose the
,
,
,
,
.
,
,
,
”
”
,
,
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,
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”
.
,
’
.
T HE
C A N T ER B U R Y P UZZ L ES
53
side o f the field to be 1 00 yards then the dist ance along the two
sides A to B and B to C is 2 00 yard s He undertook to prove
th at the di agon al di st ance di rect from A to C i s al so 200 yards
Now if we t ake the di agona l p ath shown in F ig 1 it is evident
th at we go the same di st ance for every o ne o f the eight straight
portions of this p ath me asures ex actly 2 5 yards Simil arly in Fig
2
the Zigz ag cont ains ten straight portions e ach 2 0 yards long
th at path is al so the same length 200 yards No m atter how m any
steps we m ake in o ur z igz ag p ath the result is most cert ai nly
‘
,
.
,
,
,
.
.
,
,
,
.
.
,
,
-
.
,
lways the s ame Thus in F ig 3 the steps are very sm all yet the
dist ance must be 200 yards ; as i s al so the case in F ig 4 an d wo uld
yet be if we needed a microscope to detect the steps In this way
the F ri ar argu ed we m ay go on straightening o ut th at Zigz ag path
until we ultim ately re ac h a perfectly straight line an d it therefore
follows th at the di agon al of a squ are is of ex actly the same length
as two of the sides
N o w in the face o f it thi s must b e wro ng ; and it is in f act
absurdly so as we can at once prove by actu al m easuremen t if we
a
.
,
.
,
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.
,
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,
T HE CA N TER BU R Y PUZZLES
54
have any doubt Yet the Sompnour could not fo r the li fe of him
poin t o ut the fall acy an d so upset the F ri ar s re asoning It was
this th at so exasperated him an d consequentl y like m an y o f us
to d ay whe n we get ent angled in an argument he utterl y lost his
tempe r an d resorted t o abuse
In fact if some o f the other pil
grims h ad no t interposed the two would h ave undoubtedl y come
to blows
aw in the
Th e re ader will perh ap s at once see the fl
F ri ar s argument
.
’
,
.
,
,
-
,
.
,
.
’
.
29
—Chaucer s
’
.
P uz z le
.
himself accom panied the pilgrims Being a m athe ma
tici an and a m an o f a thoughtful h abit the Host m ade fun o f him
he tells us s ayi ng
Thou lookest as thou wouldst find a h are
Fo r ever o n the grou n d I see thee st are
Th e poet replied to the
re quest for a t ale b y l aun chin g in to a long spun out and ridiculous
Ch aucer
.
,
,
,
,
,
.
-
-
poem intended to ridi cule the popular roman ces of the day after
twent y two stanz as o f which the comp an y refused to he ar any
more and induced him to st art another tale in prose It is an
in teresti ng fact th at i n the P arson s Prologue Chaucer actu all y
,
,
-
,
.
’
C A N TE R B U R Y P UZZ L ES
T HE
55
introduces a little astronomic al problem In modern E ng lish this
rea ds somewhat as follows
The sun from the south line was descended so low that it was
not to my sight more than twenty nine degrees I calcul ate that
it was fo ur o clock for assuming my height to be six feet my
sh adow was eleven feet a little more or le ss At the same mo
ment the moon s altit ude (she being in mid Libra) was ste adily
increasi ng as we entered at the west end o f the vi llage
A cor
re spondent has t aken the tro uble to work this o ut an d finds th at
the local time was
m
correct
to
min
te
th
t
the
d
a
a
u
a
n
d
a
p
y
o f the ye ar was the 2 2 n d or 2 3 rd of April
modern style This
Speaks well for Chaucer s accuracy for the first line o f the Tales
tells us th at the pilgrim age was in April they are supposed to
h ave set o ut o n 1 7th April 1 3 87 as st ated in NO 2 3
Though Ch aucer m ade this little p uz z le an d recorded it fo r
the interest of his re aders he did not vent ure to propound it to
his fellow pilgrims The puz z le th at he gave them was of a simpler
kind altogether : it m ay be c alled a geographic al o ne
When
in the year 1 3 72 I did go into It aly as the envoy o f o ur sovereign
lo r
d King Edward the Thi rd an d while there did visit F ran cesco
P etrarch that le arned poet did t ake me to the top o f a cert ain
mount ain in his country Of a truth as he did Show me a mug
will hold less liquor at th e top of this mount ain than in the valley
beneath Pryt hee tell me wh at mount ain this m ay be that h as
ithal
A very element ary knowledge of
so strange a propert y w
geograph y will suffi ce for arriving at the correct answer
.
-
.
’
,
,
,
,
.
’
-
”
.
,
,
.
,
’
,
-
.
.
,
,
-
.
.
,
,
,
,
.
,
,
.
”
.
.
Yeoman
f
God save
This person j oined the part y o n the road
quoth he this j olly company ! F ast have I ridden saith he
‘
for your sake Because I would I might you overt ake To ride
Of course he was asked to enter
among this merry comp any
t ain the pilgrims with a puz z le and the one he propounded was
the following He showed them the di amond shaped arrangement
3o
-
.
The P uz z le
the C anon
o
’
s
.
’
.
,
’
,
,
,
,
’
.
,
,
-
.
,
T HE
56
C A N T E R B U R Y P UZZLES
letters presented in the accomp anyin g ill ustration and said
I do call it the rat c atcher s riddle In how m any di fferent
ways can st
re ad the words Was it a rat I saw ?
You
of
,
,
’
-
.
,
may
g o i n any direction b ackwards and forwards
or
down wards only the successive lette rs in any re adi ng must alway s
adj oin o n e an oth e r
,
,
.
31
.
—The
M anciple s P uz z le
’
.
The Manciple was an offi cer who h ad the c are o f b uying victu als
—
for an Inn o f Court like the Temple Th e p articul ar indi vidu al
who accomp anied the p arty was a wily m an who had more th an
t hi rty m asters an d m ade fools of them all Yet he was a m an
whom purch asers might t ake as an e x am ple How to be wi se in
buying of their victu al
It h appened th at at a cert ain st age o f the journey the Miller an d
Th e Miller produced five
the We aver sat down to a light rep ast
loav es an d the We aver three Th e Manciple coming upon the
scene asked permission to e at with them to which the y ag reed
Wh en the Manciple h ad fed he l aid down eight pieces of mone y
an d said with a sly smile
Settle betwixt yourselves how the
Tis a riddle for thy wits
money shall be fairly di vided
.
.
,
”
.
.
.
”
.
,
,
’
.
.
T HE C A N TE R B U R Y P UZZ LE S
57
A discussion followed an d many of the pilgrims j oined in it
Th e Reve an d the Sompno ur held th at the Miller sh o uld receive
five pieces an d the Weaver three the simple P lo ughm an was
ridic uled for sugg esting th at the Mi ller should receive se ven an d
the Weaver only one while the Carpe nter the Monk an d the Cook
,
.
,
,
,
,
sted th at the mon ey should be divided equ ally between the two
Various other Opinions were urged with con siderable vigo u r
it was fin ally decided th at the Manciple as an expert in such
should himself settle the point His deci sion was quite
e rs
Wh at was it P Of c ourse all three are supposed to have
ual sh ares of the bre ad
,
,
.
,
,
.
EVE RYBODY th at h as he ard of Solvam hall Castle and o f the qu aint
c ustoms an d ceremonies th at obt ained there in the olde n times is
famili ar with the fact th at Sir H ugh de F o rtibus was a lover o f all
kinds o f puz z les an d enigm as Sir R obert de R id dle sd ale hi mself
declared o n one occ asion
By the bones of S aint Jingo this Sir
Hugh h ath a sh arp wit Certes I wot not the riddle th at he may
not rede withal
It is therefore a source o f p art icul ar s atisfaction
that the recent discovery of s ome ancient rolls an d
rel ating m ainly to the family of D e
before m y re aders a few o f the posers t
the good old d ays The selec tion h as been m ade to suit all t astes
and while the m aj ority will be found s u fficientl y e as y to interest
those who like a puz z le th at i s a puz z le but well within the scope .
o f all two th at I h ave incl uded may perh aps be found worthy o f
engaging the attention o f the more advanced student o f these
things
—
d
B
l
a
e
o
B
a
n
a
l
G
2
T
h
e
m
3
f
y
B an dy b all c ambuc o r goff (the g ame so well known to day by
the nam e of golf ) is o f great antiquit y and was a sp eci al favourite
,
,
.
,
,
.
,
”
.
,
,
.
,
,
,
.
-
.
.
-
-
,
,
,
,
68
T HE
60
C A N T E R B U RY P UZZ L ES
dvent ure as a yout h in rescuing from c aptivit ya noble
wh o was l ang ui sh ing in the d ungeon of the c astle belon
f ather s gre ate st enem y Th e story was a thrillin g
he rel ated the fin al esc ape
gre at D e ath s he ad D ungeon with the fair b ut unc o nsc io u
in hi s arms all exc l aimed
Twas m arvello us v al i an t l
H ugh said I would never have turned from m y purpose not
to s ave m y body from the berni c les
a
’
.
’
-
’
,
,
,
,
”
.
Sir H ugh then prod uced a pl an of the thirt y five cells in
dungeon an d asked hi s com p anions to di scover the p artic ul ar
th at the demoiselle occupied He s aid that if yo u st arted at
of the out side cells an d p as sed thro ugh every doorway once
once only you were bound to end at the cell th at was
Can yo u find the cell ?
Unless yo u st art at the c orrect
c ell it i s impos s ible to p as s thro ugh al l the doorway s once an d 0
only Try tracing o u t the route with your pencil
-
.
,
,
.
.
—
h
e
T
5
3
.
Archery Butt
.
butt or t arget used in archery at So lvamh all was not m arked
in concentric ri ngs as at the present day b ut was prep ared in
Th e
o ut
,
P UZZ L I N G TI M ES AT SO LV AM HALL C ASTLE
61
des igns In the ill ustration is shown a numbered t arget
ire arc d by Sir H ugh himself
It
is
someth
ng
of
curiosity
i
a
p
bec aus e it will be fo und th at he h as s o cleverly arr anged the num
bers th at every one of the twelve lines of three adds up to exactly
we nty two
On e d ay when the archers were a little tired of their sport
de F o rtib us sa id Wh at ho merry arc hers
Of a truth
a fool s bolt is soon shot but by my f aith I kn ow
an c i ful
.
.
,
-
.
,
,
,
,
’
,
,
,
mong yo u who sh all do that whi c h I will now put
Let these n umbers that are upon the b utt be se t down
so th at the twelve lines thereof sh all m ak e twenty and
of twenty an d two
e the n umbers one to nineteen so that all the
add up to twent y three will be found a fascin a
the lines are of course on the S ides an d the
an y
m an
a
.
-
,
,
,
T HE CA N TE R BU R Y PUZZLES
62
—
Thc
36
Wi ndow
On o ne occ asion Sir Hugh gre atly perplexed his chie f builder
He took t hi s worthy man to the walls o f the donj on keep an d
pointed to a window there
s ai d he
yon window is square an d me asures
Methinks
on the i nside one foot every way an d is divided b y the n arrow
b ars into fo ur lights me as uring h alf a foot on every side
Of a truth th at is so Sir H ugh
Then I desire that another window be m ade hi gher
D onion K eep
.
.
.
.
.
”
,
,
,
,
,
,
”
.
,
”
.
,
fo ur sides sh all also be e ach o ne foot but it shall be divided by b ars 1
into eigh t lights whose sides sh all be all equ al
Truly Sir Hugh
s aid the bewildered chief b uilder I know
not ho w it may be done
By m y h alid ame
excl aim ed De Fo rtibus in pretended rage
let it be done forthwith
I trow thou art but a sorry cr aftsm an
if thou c anst not forsooth s e t such a window in a kee p wall
It will be noticed that Sir Hug h i gnores the thic kn ess o f the bars
,
”
,
.
”
,
,
,
”
.
,
.
,
,
.
.
SO LV AM HALL
PUZZLI N G T IM ES AT
37
.
The Crescent
and
the Cross
C AST L E
63
.
When Sir Hugh s kinsm an Sir John de Collingh am c ame b ac k
from the Holy Land he brought with him a flag be aring the S ign
of a crescent as shown in the illustration It was noticed th at
De F o rti b us spent much time in ex amining this crescent an d
comp aring it with the cross borne by the Crus aders on their o wn
b anners One d ay in the presence of a goodly comp any he m ade
the following striking announcement
I h ave thought m uch of l ate friends an d m asters o f the
conversion of the crescent to the cross an d this has led me to the
’
,
,
,
.
,
.
,
,
,
,
,
fin di ng of m atters at which I m arvel gre atly for that which I shall
no w m ak e known is m y stic al an d deep
Trul y it was shown to me
in a dream that this crescent of the enem y m ay be exactly converted
into the cross o f our own b anner Herein is a sign that bodes goo d
for o ur wars in the Holy Land
Sir Hugh de Fo rtib us then expl ained that the crescent in o ne
b anner might be c ut into pieces th at would exactly form the perfect
cross in the o th eré fit is cert ainly rather curious ; an d I Show
how the con version from crescent to cross m ay be made in ten
,
.
.
”
.
T HE C AN T E R B U R Y P UZZLES
64
pieces u si ng every p art of the c rescent The flag was
both sides so pieces m ay be t urned over where required
ik e on
al
.
,
.
,
—
u
T
A
m
e
t
h
e
l
8
3
.
.
A strange m an was one d ay found loitering in the courtyard of
the castle an d the ret ainers noticing th at hi s speech h ad a foreign
So the fellow was brought
a ccent s uspe c ted him of being a spy
before Sir H ugh who could m ake nothing of him He o rd e re d l
the varlet to be removed an d ex amined in order to di scover whether
an y secret lette rs were conce aled abo u t him
All they found was :
a piece o f p archment securely su spended from the neck
be ari ng
thi s mysterious inscription
,
,
.
,
.
,
,
.
,
To d ay
we know th at Abrac adabra was the s upreme deity o f
the Assyri ans an d this c uri ou s arr angement of the letters o f the
word was commonly worn in Eu rope as an am ulet o r ch arm agai nst
dise ases But Sir H ugh h ad never he ard of it and regarding the
doc ument rather seriously he sent for a le arned priest
I pray yo u Sir Clerk said he S how me the true intent
thi s strange writing
Sir H ugh replied the holy m an after he had spoken in
forei gn tongu e with the str anger
it is b ut an am ulet th at
poor wight doth wear upon hi s breast to ward o ff the ague
too thache an d such other afflictions of the body
Then give the v arlet food an d rairne n t an d se t him o n
way sai d Sir H ugh
Meanwhile Sir Clerk c anst
-
,
.
,
,
.
,
,
,
,
”
.
”
,
,
,
,
”
,
.
”
,
.
,
,
P UZZLI N G TI M ES AT SO LV AM HALL C AS T L E
65
how many ways this word Abracadabra m ay be re ad on the
amulet always st arting from the A at the top thereof
P l ace your pencil on the A at the top an d co unt in h o w m any
different ways you c an tr ace o ut the word downwards always
passing from a letter to an adjoining one
,
,
.
—
e
T
h
39
.
S n ai l
'
on
the F lagstafi
.
would often be interesting if we could trace b ack to their
m any of the best known puz z les Some of them would be
to h ave been first propo unded in very ancient times and
c an be very little do ubt th at while a cert ain n umber m ay
improved with age others will have deteriorated and even
.
,
,
their origin al point an d bearin g It is curious to find in the
records o ur famili ar friend the climbing sn ail puz z le
be seen that in its modern form it h as lost its ori gin al
.
,
occasion of some great rej oicin g s
at
the
Castle ,
Sir
i ugh
g
T HE
66
C A NT E R B U R Y P UZZ L ES
superintending the flying of fl ags an d b anners when somebody
pointed o ut th at a wandering sn ail was Climbing up the fl agst aff
On e wise old fellow said
They do say Sir K night albeit I hold such stories as mere
fables that the sn ail doth Climb upwards three feet in the d aytime
b ut slippeth back two feet b y night
was
,
.
,
,
,
,
”
.
Then ,
replied Sir Hugh tell us how m any day s it will t ake
this snail to get from the bottom to the top o f the pole
By bread and water I m uch m arv el if the same can be done
unl ess we t ake down an d me asure the st aff
Credit me
replied the kn ight there is no n eed to meas ure
the st aff
Can the reader give the an swer to thi s version o f a pu z z le that
we all kn ow so well
,
.
,
.
,
”
.
,
a dying
A ND RE W quoth the Lord Abbot as he
methinks I co uld now rede thee the riddle of riddles—an I had
the time—a n d
The good fri ar put his e ar close to the holy
Abbot s lips but al as they were silenced for ever Thu s p assed
away the life of the jovi a l an d gre atly beloved Abbot o f the o ld
mon astery of Riddle we ll
Th e monk s o f Ri d dl e we ll Abbey were noted in their d ay for
the quaint enigm as an d p uz z les th at they were in the h abit o f
propoundi ng Th e Abbe y was b uilt in the fourteenth century
near a sacred spring known as the Re d hill Well This became
in the vern ac ul ar R e d dle well an d Ri d dle we ll an d under the Lord
Abbot David the monks evidently tried to j u stify the l atter form
by the riddles they propo unded so well The solving of puz z les
1
became the favourite re c re ation no m atter whether they h appened
to be o f a met aphysic al philosophic al m athem atic al or mech anical
kind It grew into an absorbing p assion with them an d as I h ave
shown above in the c ase of the Abbot this passion was
even in death
It would seem th at the words pu z z le
problem
etc did not occ ur in their voc ab ul ary They were accustomed
c all every poser a riddle no m atter whether it took the form
Where was Moses when the light went o ut
or the Squ aring
the Circle On o ne of the walls in the refectory we
FR I AR
lay
,
,
-
,
’
.
,
.
,
.
-
.
,
.
,
,
,
,
.
,
,
.
”
,
.
,
.
08
,
T HE
M E RR Y M ON KS O F RI D D LEW ELL
69
the words of S amson
I will now put fo rth a riddle to you to
remind the brethren of wh at was expected of them an d the rule
was that e ach monk in t u rn should propose some riddle weekly to the
comm unity the others being always free to c ap it with another if
disposed to do so Abbot D avid was undoubtedly the puz z le
geni u s of the mon astery an d everybody n at urally bowed to his
decision Only a few of the Abbey riddles h ave been preserved
I sh all
an d I propose to sel e ct those th at seem most interesti ng
try to make the conditions o f the p uz z les perfectly cle ar so that
the mod ern re ader m ay fully underst and them and be amused
in trying to find some of the sol utions
,
,
,
,
.
,
,
,
.
,
.
,
,
.
R iddle
f
o
the F i sh
-
pond
.
At the bottom of the Abbe y me ds
a sm all fish po n d W here
the mon ks used to spend m any a contempl ative ho ur with rod an d
a
was
-
when they h ad h ad very bad luck an d only Caught
fish e s amongst them Brother Jonathan suddenly declared
On e d ay,
,
T HE
9
7
C A N TE R B URY PUZZLES
there was n o sport that d ay he wo uld put forth a ri ddle
He thereupon took twelve fish b asket s
fo r their entert ai nment
an d pla ced them at equ al di st anc e s round the pond as sho wn in
o ur ill ustr ation with o n e fish in e ach b asket
Now gentle an glers s aid he
rede me thi s riddle o f the
St art at any basket yo u like an d always going in
Twelve F ishes
o n e direction round the pond t ake up one fish p ass i t o ve r two
other fis hes and pl ace it in the next b asket Go on again t ake up
h aving p assed th at also over two fishes
anothe r sin gle fish an d
pl ace it in a b as ket an d so continue y our j ourney Six fishes only
are to be removed an d whe n th ese h ave been pl aced there should
be two fishes in e ach of s ix b askets an d six b askets empty Which
uch a m anner th at yo u sh all go
wights
will
do
this
in
o f you merr
s
y
round the pond as few times as possible
I will expl ain to the re ader th at it does not m atter whether the
two fishes th at are p assed over are in o ne o r two b as k ets nor ho w
m an y empty b askets you p as s And as B rother Jon ath an said
u
a
a
o
m
u
s
t
lw
ys go in o ne direction round the pond (without any
y
doubling b ac k) and end at the S pot fro m which y ou set o ut
th at
as
.
,
.
,
”
,
,
,
,
,
.
,
,
f
.
,
,
,
,
.
,
,
.
,
,
.
,
,
.
—
2
T
h
e
4
f
One d ay when the monks were se ated at their repast th e Abbot
announced that a messenger h ad th at morning brought news th a t
a number o f pil grims were o n the ro ad an d would require their
hospit ality
You will put them he s aid in the square dormitory that
h as two floors with eight rooms o n e ac h floor
There m ust be
eleven persons sleeping on e ach side of the building and twice as
m any o n the upper floor as on the lower floor Of course every
room must be occupied an d y ou kn ow m y rule th at not more
than three pe rsons may occupy the s ame room
I give a plan of the two floors from which it will be
the s ixt een rooms are approached by a well st airc ase in t
.
Ri ddle
o
the P ilgrims
.
,
,
.
,
,
.
,
.
,
.
,
M ER R Y M O N KS O F RI D D LEW ELL
T HE
7:
ccommod ation the pilgrims arrived when it was foun d th at
they were three more in number th an was at first st ated This
necessit at e d a reco nsid eration of the question but the wily monks
the
a
,
,
.
,
P LAN
E igh t R m
oo
s on
U
pp Fl oo
er
OF
D O R M IT O R Y
.
E igh t R m
r.
oo
s on
Lo
w e Fl
r
oo r.
succeeded in getting over the new diffi cult y without bre aking the
Abbot s rules Th e c urious point of this puz z le is to discover the
t ot al num be r o f pil grims
’
.
.
—
T
h
e
43
Ri ddle
the Ti led H earth
f
It seems th at it was F ri ar Andrew wh o first m an aged to rede
the riddle of the Tile d He arth
Yet it was a simple enough little
puz z le The squ are he arth where they burnt their Yule logs an d
round which they h ad such merry c aro usings was floored with
sixteen large orn ament al tiles When thes e bec ame cracked an d
burnt with the he at of the gre at fire it was decided to put down
new tiles W hi c h h ad to be select ed from four di fferent p atterns
u
a
l
s
a
b
the
ross
the
leur
de
the
Lion
the
St
r
pl
in
tile
F
n
d
t
s
C
a
)
(
y
were al so avail able Th e Abbot proposed th at they s hould be
laid as shown in o ur sketch without any pl ain tiles at all ; b ut
Brother R ichard broke in
I trow my Lord Abbot that a riddl e is req uired of me thi s
Let thes e
day Listen then to that whi ch I sh all put forth
.
o
.
.
.
,
,
.
,
,
-
-
,
,
,
.
,
,
,
,
.
,
,
.
C AN T E R B U R Y P UZZ L ES
T HE
2
7
sixt een ti l e s be so pl aced that no tile sh al l be in line with another of
the same design —(he me ant of course not in line hori z ont ally
v e rtic al ly o r di agon ally)
an d in such m anner th at as few plai n
,
,
,
,
tiles as possible be required
When the monks h anded in their
pl ans it was found th at only F ri ar Andrew h ad hit upon the correc t
even F ri ar Rich ard himself being wrong All had used
answer
too m an y pl ain tiles
.
.
,
.
—
T
h
e
44
i
ne
W
f
O ne evening when se ated at t able Brother Benj amin was c all e d
upon by the Abbot to give the riddle th at was th at d ay dem anded
.
R i ddle
,
o
the S ack
.
,
s aid he I am no good at the making of riddles
as thou kn owest full well
but I h ave been te asing my poor brain
over a m atter th at I trust some among yo u will expound to me
fo r I c annot rede it m y self
It is this Mark me t ake a glass o f
sack from thi s bottle that cont ains a pint of wine and pour it int o
that j ug which cont ains a pint o f water
Now I fill the gl ass with
th e m ixture from the j ug an d pour it b ack into the bottle holdi ng
F orsooth
,
,
,
,
.
.
.
,
T H E M E R RY M O N KS O F
R I D D LEW E LL
.
73
the sack P r ay tell me h ave I t aken m ore wine from the bottle
O r h ave I t aken m ore water fro mt he
than water from the j ug
jug th an Wine from the bot tle
I gather th at the monks got ne arer to a gre at qu arrel over this
little poser th an h ad ever h appened before One brother so far
forgot himself as to tell his neighbour th at more wine h ad got into
his pate than wit c ame o ut of it Whi le another noisily insisted th at
it all depended o n the sh ape of the gl ass and the age o f the wine
But the Lord Abbot intervene d showed them what a simple
quest ion it really was and restored good feeling all rou nd
,
.
.
”
,
.
,
.
,
—
T
h
e
5
4
Ri ddle
f
Then Abbot D avid looked gr ave an d said th at t his incident
to his mind the p ainful fact th at J ohn the Cellarer had
.
the C ellarer;
o
,
been c aught robbing the c as k o f best Malvoisie that was
for speci al occ asions He ordered him t o be brought in
Now varlet sai d the Abbot as the ruddy faced
-
,
rved
.
.
,
rese
,
Cellarer
CA N TE R B U R Y P U ZZLES
T HE
74
m e be fore him thou knowest th at thou wast t aken this morn
What
ing in the ac t o f steal ing good wine th at was forbidden thee
has t thou to say fo r thy self
he cried falli ng on
P rith ee m y Lo rd Abbot forgive me !
Of a truth the Evil One did come an d tempt me
his knee s
an d the cas k was so h andy an d the wine was so good withal an d
—and I had drunk o f it Ofttimes without be ing found out and
Rasc al ! that but m ak eth thy fault the worse ! How m uch
wine h ast thou t ak en
Al ac k a day l There were a hundred pint s in t h e c ask at the
s t art and I h ave t aken me a pint every d ay this month o f Jun e
—
o
it be ing tod ay the t h irtieth there f an d if my Lord Abbot c an
t e ll me t o a nicet y h o w much good wine I h ave t ak en in all let
him punish me as he will
Why kn ave th at is thirt y pints
Nay nay fo r each time I drew a pint o ut o f the c as k I put
in a pin t o f water in its stead I
It is a c urious fact th at this is the only riddle in the o ld rec ord
t hat is n o t accomp anied by its solution
Is it possible th at it prove d
to o h ard a nut fo r the mon ks
oh
n
There is merel y the n ote
J
suffere d no punishment for hi s sad f ault
ca
,
.
,
,
,
,
,
.
,
,
,
-
-
,
,
”
.
.
,
,
,
,
.
,
”
.
nother o cc asion a cert ai n knight Sir R alph de Bohun was
a gu es t o f the monks at R i ddle we ll Abbe y
Towards the close o f
a sum pt uous re past he spoke as follows
My Lord Abbot knowi ng full W ell th at ridd les are greatl y to
thy liking I will by y our le ave put forth one th at was told unto
me in foreign lands
A body o f Crus aders went forth to fight the
good cause and s uch was t heir number that the y were able to
form them selves into a sq uare But o n the way a stranger too k
up arms an d j oin ed them an d they were then able to form ex actly
thirtee n sma ller squ ares P ray tell me merry mo nks ho w m any
men we nt forth to battle P
On
a
,
,
.
,
,
,
,
.
,
.
.
,
.
,
,
THE C A NTE R B U R Y PU Z Z LES
6
7
Methinks
killed the lot sai d Brother Benj amin
Out upon thee brother 1 I said c ats
Well then persisted Benj amin
pe rch ance
c ats
each killed o n e mo use
No
replied F ather P eter after the monks j ovi al l aughter
“
‘
—
a
d
ende
d
I
s
a
id
mice
a
n
d
a
ll
I
need
d
is
thi
s
th at e ach
had
;
ca t killed more mice th an there were c ats
They told me it was
merely a question of the di vision of numbers but I know n ot the
answer to the ri ddle
The correct answer is recorde d b ut it is not shown how the y
arrived at it
o n e cat
.
,
’
.
,
,
,
,
”
.
’
,
,
,
.
,
.
,
.
—
8
The
4
R i ng
f
One Chri stmas the Abbot o ffered a pri z e o f a l rg e b l k j c k
a
ac
a
mo un ted in silver to be engraved with the n ame of the mon k who
sh ould put forth the best n e w ridd e
l
This tourn amen t of wit was
won by Brother
Benedict who curiously enough never before or
o
.
the F rogs
’
.
,
.
,
,
,
M O N KS O F RI D DLEW ELL
T HE M E R R Y
77
fter gave o ut anything th at did no t excite the ridicule o f his
brethren It was c alle d th e Frogs R ing
A ring was m ade with ch alk on the floo r of the h all an d divided
into thirteen comp artments in which twelve di scs of wood (c alled
frogs
were placed in the order shown in o ur ill ustration one
pl ace being left vacant Th e n umbers 1 to 6 were painted white
Th e p uz z le was to get all the
an d the n umbers 7 to 1 2 bl ack
whi te n umbers where the bl ack ones were an d vice versa The
white frogs move round in one direction an d the bl ack ones the
Opposite way They m ay move in any order o ne step at a time or
j umping over one of the Opposite colo ur to the pl ace beyond j ust as
Th e only other condition is that when
we play draughts to day
all the frogs h ave ch anged sides the 1 mu st be where the 1 2 now is
The p uz z le was to
an d the 1 2 in the pl ace now occupied by 1
perform the feat in as few moves as possible Ho w m an y moves
are ne c essary
I will concl ude in the words of the old writer : These be some o f
the riddles whi ch the monks of Ri d dle we ll did set forth an d expound
e ach to the others in the merry d ays of the good Abbot David
a
’
'
.
.
,
,
,
.
.
,
.
,
.
,
,
~
.
,
.
.
"
.
TH E STR ANG E E SCAP E O F TH E
KI NG S
’
R
S
E
T
E
J
.
A P U ZZLI NG AD VE N TURE
.
time I was greatly in favour with the kin g and his
Majesty never seemed to we ary of the companionship of the court
fool I had a gift for making ri ddles an d qu aint p uz z les which
Oft times caused great sport for albeit the king never found the right
yet would he make
answer o f o n e o f these things in all his life
merry at the bewilderment o f those about him
But let every cobbler stick unto his l ast ; for when I di d set o ut
to lea rn the art o f performing str ange tricks in the m agic wherein
the hand doth ever deceive the eye the king was affrighted an d
did accuse me o f being a wi z ard even comm an d in g th at I should
be put to de ath Luckily my wit di d save my life I begged th at
I mi ght be slain by the royal h and an d not b y that o f the e xe cu
AT
o ne
,
.
,
.
,
,
,
,
.
.
the saints said his Majesty
wh at di fference can it
make unto thee ? But since it is th y wish thou sh alt have thy
c ho ice whether I kill thee o r the e x ec utioner
Your Maj esty I answered
I accept the choice that thou
hast so gr aciously o ffered to me I prefer that your Maj est y should
kill the executioner
Yet is the life of a royal je ster beset with gre at dangers and the
ki ng having once gotten it into hi s royal he ad th at I was a wiz ard
it was no t long before I again fell into trouble from which m y wi t
did no t a se cond time in a like way save me I was ca st into the
By
,
,
,
.
,
,
.
,
,
,
.
18
S T R A N G E ES C A PE O F T HE KI N G S JESTE R
’
79
dungeon to await my death How by the help of my gift in
I did escape from captivity I will
answering riddles an d p u z z les
now set forth ; an d in ca se it doth perplex an y to know how some
of the strange fe ats were performed I will hereaft er make the
m anner thereof pl ain to all
.
,
,
,
.
—
l
49
M ysteri ous Rope
.
My dungeon did not lie bene ath the mo at but was in
,
mo st hi gh p arts of the castle So stout was the door
locked an d secured withal th at escape th at
way was no t to be found
By h ard work I
did after m any d ays remove one o f the b ars
from the n arrow window an d was able to
crush my body thro ugh the Opening ; but the
dist ance to the courtyard below was so ex
ce e di n g great that it was cert ain de ath to drop
thereto Yet by gre at good fort une did I find
in the corner o f the cell a rope th at h ad been
there left an d lay hid in the gre at d arkn ess
But this rope h ad not length enough an d to
drop in safety from the end was nowise po s
sible Then did I remember how the wise
man from Ireland di d lengthen the bl anket
that was too short for him by cutting a yard
o ff the bottom of the same an d j oining it on
to the top 5 0 I m ade h aste to divide the
rope in h alf an d to tie the two p arts thereo f
together ag ai n It was th e n full long and did
reach the ground an d I went down in safety
Ho w could this h ave been
.
,
one of
an d so
the
well
,
.
,
,
,
.
.
,
.
.
/
.
,
The
a
,
.
only way out of the yard that I no w was in was to d escend
few st airs t hat led up mto the centre (A) o f an un derground
U
ZZ
LES
P
R
R
A
N
TE
B
U
Y
T HE C
80
a
th
o
gh
wi
n
di
ng
which
I
must
p
ss
before
I
could
f
o
e
t
h
r u
maz e
a
e
u
t
h
t
B
u
ke
m
y
le
ve
by
door
B
I
knew
f
ll
well
th
t
in
th e
a
( )
ta
grea t darkness o f this dreadful pl ace I might well wander fo r hours
w
a
s
t
u
o
return
pl
ce
f
rom
which
I
set
How
I
then
a
e
t
o
t
h
e
t
and y
,
.
.
reach the door with certai nty P With a plan of the m az e it is
bu t a simple m atter to tr ace out the route but ho w was the way
to be foun d in the pl ac e itself in utter d arkness ?
to
,
51
.
—The
S ecret Lock
.
When I did at l ast reach the door it was fast closed and o n
sliding a p anel se t before a gr ating the light th at ca me in thereb y
showed unto me th at m y p ass age was b arred by the king s secret
lock Before the handle of the door might be turned it was need
ful to pl ace the hands o f three several di al s in their proper places
If yo u but knew the proper letter for e ach di al the secret was of a
truth to your h and ; b ut as ten letters were upon the face of every
di al yo u might try nine hundred an d ninety nine times an d onl y
succee d o n the thou sandth attempt with al
If I was indeed to
e scape I must waste not a moment
Now once had I heard the learned mon k wh o did invent the
lock say that he feared that the king s serv ants h aving such b ad
,
’
.
,
.
,
-
,
.
.
,
'
,
ST R A N G E ES C A PE O F T HE KI N G S J ESTE R
’
81
memories would m ayh ap forget the right letters ; so perch ance
thought I he h ad on thi s account devised some way to ai d their
memories And wh at more n atur al than to m ake the letters
,
,
,
.
form some word
I soon found a word that was E nglish m ade o f
—
three letters o ne letter being o n each o f the three di als After
th at I h ad pointed the han ds properly to the letters the doo r o pened
an d I p assed o ut
Wh at was the secret word
,
.
.
52
.
—Crossing
the
M oat
.
I was now face to face with the c astle moat which was indee d
very wide an d very deep Alas I could not swim an d my c hance
o f esc ape seemed of a truth hopeless as doub tless it would have
been h ad I not espied a boat tied to the wall b y a rope But aft er
I had got into it I did fin d th at the oars had be en t aken away and
,
.
,
,
,
,
,
,
.
,
(A077)
6
quite
there being no stre am o r current
then did I yet t ake the bo at across the mo at
to
,
53
.
The Royal
Gardens
.
It was no w daylight and still had I to pas s through the ro yal
n
u
a
e
e
e
s
a
d
rd
n
o
t
s
ide
o
c
stle
w
l
s
hese
g
rdens
once
b
f
t
h
a
a
l
a
h
e
T
g
laid o ut by an o ld kin g s gardener who h ad becom e bere ft o f his
se nse s
but was allowed to amuse himself therei n They were
sq uare and di vided into 1 6 p arts by high w al ls as shown in th e
plan there of so that th e re we re ope nin gs from o ne garden to an
,
.
’
,
,
.
,
,
,
T HE C A NTE RBU R Y PU ZZ LES
84
fo und eight narrow planks o f wood lyi ng togetherm a he ap
the se alone and the pl an ks were each no more th an 9 feet
I did at las t m an age to m ake a bridge across the di tch How
this done
Being now free I did h asten to the house of a friend who
.
,
.
me with a horse and a disguise with which I soon succ
in placing myself o ut o f all fe ar o f c apture
Through the goodly offices of divers persons at the king s
I did at lengt h obt ain the royal p ardon though indeed I was never
rest ored t o that full favour th at was once my j oy an d pride
Oft ti mes h ave I been asked b y m any th at do know me t
set forth to them the str ange m anner of my esc ape which m
“
t han o ne hath deemed to be o f a truth wonderful albeit the feat
was nothing asto nis hing with al if we do b ut remember that
my youth upwards I had tr ained my wit to the m aki ng an d an
ing o f cunni ng enigm as
And I do hold that the study o f
cr aft y matters is good not alone for the pleasure th at i s
t he re by b ut because a m an ma y never be sure th at in some
and untoward di ffi c ulty t hat ma
beset
him
in
p
ss
a
y
life o f ours su
and m ay hap help him o ut o f many diffic ulties
I am no w
vid e d
,
.
’
,
,
,
.
,
,
.
,
,
,
,
.
ST R A N G E ES C A PE O F T HE K IN G S JESTE R
’
85
puz z les an d conceits ; b ut of a truth n ever h ave I found
gre ater ple asure in m aking o ut the answers to an y of these things
than I h ad in m astering them th at did en able me as the kin g s
jester in di sgrace to gain my freedo m from the ca stle dungeo n and
so save my life
fo r qu aint
,
,
’
,
,
.
TH E SQ U I RE S C H R I ST M AS P U ZZ L E PAR T Y
’
A F INE specimen o f the o ld English country gentlem an was
Sq uire Davidge of Stoke Courcy H all in Somerset When the
las t century was yet in its youth there were few men in the west
co untry more widely known an d more gener ally respected an d
beloved th an he A born sportsm an his fame extended to Exmoor
itself where hi s dari ng an d splendid riding in pursuit o f the red
deer had excited the adm iration and envy o f innumerable you nge r
huntsmen But it was in his o wn p arish and p articul arly in his
o wn home th at his geni al hospit alit y generosit y an d r are j ovi al
—
a
humour m de him the idol o f his friends and eve n o f his rel ations
which sometimes me ans a good deal
At Christmas it was always an open house at Sto k e Courcy
H all fo r if the re was o ne thing more th an another upon which
Sq uire Davidge h ad very prono unced views it was on the question
o f kee ping up in a ro yal fashion the gre at festiv al o f Yule tide
H ark ye m y lads he would say to his sons : o ur country wi ll
be gin to fall on evil d ays if ever we grow indi fferent to the cl aims of
thos e Christm as festivities th at h ave helped to win us the proud
nam e o f Merrie Engl and
Therefore when I say th at Christm as
at S toke Co urcy was kept up in the good old h appy
rollicking
fes tive style that o ur gr andfathers and gre at gr andfathers so de arly
loved it wi ll be unneces s ary for me to attempt a description We
have a faithful pict ure o f these merry scenes in the Bracebri dge
Hall o f Washington Irv ing
I must confine m yself in this sketch
to o ne spe cial feature in th e Squire s round o f o llificatio n during
j
t he seaso n of peace and good will
.
,
,
,
.
,
,
.
,
,
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,
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,
,
-
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,
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”
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,
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,
-
,
.
.
’
.
86
S Q U I RE S C H RIST M AS PUZZL E PA RTY
’
T HE
87
He too k a curious and intelligent interest i n puz z les o f e very
kind an d there was always o ne night devoted to what was known
Squire D avi dge s P uz z le P arty
Every guest was expected
as
t o come arm ed with some riddle or puz z le fo r the be wilderment an d
pos sible delect ation o f the company The o ld gentlem an always
presented a new watch to the gues t who was mos t successful in his
It is a pit y that all the puz z les were n ot preserved ; but I
answers
propose to present t o my re aders a few selected from a number th at
h ave p assed down to a survivi ng m ember o f the famil y who has
kin dly allowed m e to use them on this occ asion There are some
very easy ones a few t hat are m oderately difficult and o ne hard
brain racker so all should be able to find something to their t aste
The little record is written in the ne at angul ar h and o f a y ou ng
l ady o f that day and the puz z les the conditions o f which I think it
best to give mai nly in my o wn words fo r the sake of great e r clearn ess
ap pe ar to have b ee n all propounded o n o ne oc casion
,
”
’
.
.
.
,
.
,
,
-
,
.
,
,
,
.
young lady—o f whom o ur fair histori an re cords with
delight ful inco nsequence
This Miss Charit y Loc kyer has since
—
b ee n married to a c urat e from Taunton Vale
placed three empt y
On e
teacups o n a t able an d challenged anybody to put ten lumps o f
sugar in the m so that there would be an odd number o f lumps in
every cup
One young m an who has been to Oxford Un iversit y
and is studying the law decl ared with some heat that beyond a
doubt there was n o possible way of doing it and he o ffered to give
proof o f the fact to the compan y
It m ust have been interesting
to se e his face when he was shown Miss Ch arity s correct answer
,
.
,
,
,
,
,
,
.
.
’
.
T H E C ANTE R B U RY PUZZLES
88
—
l
even P enni es
E
h
e
T
6
5
.
.
A gue st asked some one to favour hi m with eleven pennies and
he passed the coins to the company as depicted in o ur illustration
u
writer
y
s
He
then
req
ested
us
to
remove
fi
ve
coins
from
sa
Th e
,
.
,
four coins and le ave nine We could not but think
there must needs be ten pennies left We were a good de al am used
at the answer h e reof
—
The Chri stmas Geese
57
—
r
Squire Hemb ow from Weston Zoylan d wherever that may
—
be proposed the following little arithmetic al pu z z le from which
i t is probable that se veral somewh at simil ar modern ones h ave been
derived : Farmer R ouse sent his m an to m arket with a flock of
s
ee
g e tellin g him th at he mi ght sell all or any o f them as he con
sid ered bes t for he was s ure the m an knew how to m ake a good
bargain Thi s is the report th at Jabe z m ade though I h ave t aken
it out o f the old Somerset di alect which might p uz z le some re aders
t he eleven
,
ad d
.
.
”
.
t
.
.
,
,
,
,
,
.
,
,
S Q U I RE S C H RIST M AS PUZZL E PA RTY
T HE
’
89
in a way not desired
Well first o f all I sold Mr Jasper Tyler
h alf of the flock and h al f a goose over then I sold Farmer Avent
then I sold
a thi rd o f wh at rem ained an d a third o f a goose over
Widow F oster a quarter of wh at rem ained an d three quarters of
an d as I was co ming home whom S hould I meet
a goose over ;
b ut Ned Collier : so we h ad a mug o f cider together at the B arley
Mo w where I sold him exactly a fifth of wh at I h ad left an d g ave
him a fifth o f a goose over for the missus These nin eteen th at
I h ave brought b ack I co ul dn t get rid of at any price
Now how
m any geese di d F armer R o use send to market P My hum ane
readers may be relieved to know that no goose was divi ded o r put
to any i nconve nience wh atever by the sales
.
.
,
’
.
-
,
,
,
.
”
’
.
,
.
58
.
The Chalked
We l aughed greatly at a pretty j est o n the p art o f Maj or
Trench ard a merry friend of the Squire s
With a piece o f chal k
’
,
.
T HE C A N TE RB U R Y PUZZLES
0
9
marke d a different n umber o n the b acks o f eight lads wh o were
Then it see ms he divided them in two groups as
at th e part y
sh own in t h e illus tration 1 2 3 4 bein g on o n e side an d 5 7 8
s een th at the numbers o f the left h an d
t
o
her
It
will
be
n
e
o
t
h
9
‘
u
0
1
o
p
t
o
while
the
numbers
in
the
other
group
up
u
a
d
d
r
a
d
d
to
p
g
Th e Major s p uz z le was to re arr ange the eight bo y s in two new
29
t
u
a
s
roup
so
th
a
the
fo
r
numbers
in
e
ch
group
should
up
like
a
d
d
a
g
The Squire s niece asked if the 5 should not be a 6 ; but the Maj or
e xpla ined th at the numbers were quite correct if properly reg arded
he
’
”
.
,
,
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,
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,
,
,
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,
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.
,
'
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,
.
'
.
T HE C A N T ER B U R Y PUZZL ES
2
9
boys an d ten m aiden s an d little girls No w everybody was
foun d to have ki ssed everybody else with the following exceptions
kissed a m ale No m arri ed
and additions : No m ale of co urse
All the
man kisse d a m arried wom an except his own wife
bachelors and boys kissed all the m aidens an d girls twice The
widower did not kiss anybody an d the Widows did not kiss each
other The puz z le was to ascert ain j ust how m an y kisses had bee n
an d
.
,
,
,
,
.
,
,
.
'
.
,
.
thus given under the mistletoe bo ugh assumin g as it is ch t ble
ari a
to d o
a
th t every ki ss was return ed—the double act bei ng coun ted
as one ki ss
,
,
,
.
61
.
—The
S ilver C ubes
.
The
h
se
t o
last extract th at I will gi ve is o ne that will I thi nk inte e t
r s
ea e s who ma
r d r
y fin d some o f the abo ve p uz z les too easy
,
,
.
THE S Q UI RE S C H RIST M AS PU ZZ LE
’
PA RTY
93
It is a h ard nut an d should only be attempted by those who fl atter
themselves that they posse ss strong in tellec t ual teeth
Master Herbert Spe aring the son o f a Widow l ady in o ur
p arish propo sed a p uz z le in arithmetic that loo ks si mple but
nobo dy present was able to solve it Of a truth I did not vent u re
to attempt it myself a fter the young l awyer from Oxford wh o
they say is very learne d in the m athem ati c s an d a gre at schol ar
f ailed to show us the an swer He di d assure us th at he believed
it co uld not be done b ut I h ave since been tol d th at it is possible
though o f a cert ainty I m ay not vou ch for it Master Herbert
brought with him two c ubes of solid silver th at belonged to his
,
.
,
,
,
,
.
,
,
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,
,
,
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,
mother He showed t hat as they me as ured two inches every way
each cont ained eight c ubic inches of silver an d therefore the two
That which he wanted
cont ained together sixteen c ubic inches
to know was
Co uld anybo dy give him ex act dimensions for two
ld together cont ain j ust seventeen cubic inche s o f
cubes th at sho u
Of course the c ube s m ay be of di fferent si z es
silver ?
Th e idea of a Christmas Pu z z le P arty as devised by the o ld
Squire seems to have been excellent an d it might well be revived
at the present d ay by people wh o are fond of puz z les an d who h a ve
grown tired of Book Teas an d Simil ar recent introd uctions for the
P ri z es could be awarded to the
amusement o f evening p arties
best solvers o f the pu z z les propounded by the guests
.
,
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,
,
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.
WHE N it re ce ntly became known th at the bewilderi ng mystery o f
the Pri nce an d the Lost Ba lloon was really solved b y the members
o f the Puz z le Cl ub the gener al pub lic was quite un aware th at an y
Th e fact is that the members always deprec ated
such cl ub existed
publicity but since they have been dragged into the lig ht in con
n ec tio n with this celebrated c ase so m any absurd an d u ntrue sto ries
have become c urrent respecting their doings th at I have been per
mitted to p ublish a correct acco unt o f some of their more interest
ing achievements
It was however decided that the re al n ames o f
the members should not be gi ven
‘
The cl ub was starte d a few ye ars ago to bring together those
interest ed in the solution o f pu z z les of all kinds an d it cont ain s
so me o f the p rofo undest m athem atici ans an d some o f the most
subtle thinke rs resident in London
These h ave done some excel
lent work o f a high an d dry kind But the m ain body soon took
to investig ating the problems o f re al life th at are perpetually
cropping up
It is only ri ght to say that they t ake no interest in crimes as
such b ut onl y investig ate a c ase when it possesses fe at ures of a
distinctl y puz z ling char acter They seek perplexity fo r its o wn
sake—
s omethi ng to unr avel
As often as not the circ umst ances
are o f no impo rt an ce to anybody but the y j u st form a little pu z z le
in real life and that is sufficient
,
.
,
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,
,
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,
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,
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62
.
—The
Ambiguo us P hotograph
.
A g ood e xample o f the lighter kind of problem th at occ asion ally
co mes be fore them is th at which is kn own amongst them b y the
94
A DV E N TU RE S O F T HE PU ZZL E C LU B
95
n ame o f The Ambiguous P hotogr aph
Though it is perplexing
to the inexperienced it is reg arded in the club as quite a trivi al
thi ng Yet it serv es to show the close observ ation o f these sh arp
witted fellows The origin al photograph hangs o n the club wall
an d h as b affled eve ry g uest who h as ex amined it
Yet any child
should be able to solve the mystery I will give the reader an
Opportunity of tryi ng his wits at it
Some of the members were one evening se ated togeth er in their
clubhouse in the Adelphi Those present were : Henry Melville
a b arrister not overburdened with briefs
who was disc ussin g
a problem with E rnest Ru ssell
a be arded man o f middle age
who held some easy post in Somerset House an d was a Senior
Wrangler an d one of the most subtle thinkers of the club ; F red
Wilson a j ourn alist o f very buoyant spirits wh o had more re al
cap acity th an one would at first suspect ; John Macdon ald a
Scotsm an whose record was th at he h ad never solved a p uz z le
himself since the club was formed though frequen tl y he had put
others o n the tr ack of a deep solution Tim Churton a b ank clerk
full o f cranky unorthodox ideas as to perpe tual motion ; also
H arold Tomkin s a prosperous account ant remarkably famili ar
with the e l e gant bran ch o f m at h ematics—the the o ry of n umbe rs
S uddenly Herbert B aynes entered the room and everybody
saw at o n ce from his f ace th at he had something inte re sti ng to
comm unicate B ayn es was a man of private mean s with n o
occup ation
Here s a qu ai nt little poser for you all said B ayn es
I
have received it to d ay from D ovey
Dove y was proprietor of o ne o f the m any private detective
agencies th at fo und it to their advant age to keep in touch with the
Cl ub
Is it another of those e as y cryptograms ? asked Wilson
If so I would suggest sending it upst airs to the billi ard m arker
D on t be sarc astic Wilson
R emember we
said Melville
are indebted to Dovey for the gre at Railway Signal P roblem th at
gave us all a week s amusement in the solving
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’
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,
T HE
6
9
If
ou
y
C A N TE RBU R Y PU Z ZLES
fe lows want
l
hear
to
resumed Bayn es
,
‘
‘
,
j ust try to
P
a
a
L
dy
her
h
u
sb
a
nd
h
ve
been
in
ris
for
Marksfo rd an d
a
ago ?
Well th e poor cre at ure soon got under the
two o r three mon ths
influen ce o f the green eyed monster an d formed the Opinion th at
Lo rd Marksfo rd was fli rting with other l adies o f his acqu aint ance
No w she has actuall y put one of D o ve y s spies on to th at
exce lle nt husban d o f hers and the myrrnid o n h as been sh ad owi ng
him abo ut fo r a fortnight with a pocket c amer a A few d ays ago
He h ad sn apshott e d
he cam e to Lady Marks fo rd in gre at glee
his lords hip while act ually walking in the public streets with a
lady who was not his wi fe
What is the use of this at all P as ked the j ealous wom an
Well it is evidence your ladyshi p that your husb and was
walking with the lady I know where she is st aying and in a few
days sh all have found out all about her
But you stupid man cried her ladyshi p in to n es o f great
co nt empt ho w can any o n e S we ar th at this is his lordship when
the great e r p art o f hi m includi ng his head an d s houlders is hi dden
—
—
r
m
?
s
a
n
fo
ight
And
d
s he scrutini z ed the photo c arefully
why I guess it is impossible from thi s photograph t o say whether
the ge ntl e man is walking with the lad y o r going i n the Oppos ite
direction 1
Th ereupon she dismiss ed the detect i v e in high dudge on
Dovey has himself j ust returned from P aris an d g ot this account
o f the incident from her Iadyshi p
He wants to j ustify hi s man
if possible by S howin g that the photo does disclose which way
t e man is going
Here it is See what y ou fellows can m ake
0 It
Our ill ustration is a faith f ul dr awing m ade from the ori ginal
It will be seen th at a slight but sudde n summer
Pho tograph
sho wer Is the real c ause o f the diffi cult y
.
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A D V ENTU RES O F T HE PU ZZ LE CLU B
Her l adyship is wrong
m ade a close scrutiny
the picture
.
97
said B ayn es after every body had
I find there is import an t evidence in
,
,
.
Of
cO
urse ,
Melville
,
we
can
tell nothi ng from the
S
P
R
R
A
NTE
BU
Y
U
ZZLE
C
H
E
T
8
9
r
m
w
a
hi
s
a
r
s
a
m
h
i
his
overco
t
over
but
which
a
y
has
im mss ible to se e
C
a
P
bout
the
bend
of
the
le
g
s
sked
hurton
Ho w a
Bend ! why there isn t any bend put in Wilson as he
F rom the picture you might
glan ce d over the other s shoulder
h
n
T e he
o
s
it
i
s
e
g
,
”
.
”
’
,
,
,
’
.
Im
that pe rha ps
began Macdon ald
his eye gl asses
D on t think Mac
advised Wilson
It might
Be si des it is no use you thinking th at if the dog
pas s o n things would be e asy He won t
The man s gener al pose seems to me to imply mo v eme nt
th e left
Tomkins thought
On the contrary
it appears to me
Melville decl ared
clea rly to sug es t movement to the right
g
No w look here yo u m en
whose o
said Russ ell
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"
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”
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”
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”
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,
,
,
THE C A NTE R B U R Y PUZZ LES
roo
—
z lement at Tod d s B
z
ah
ith
which
it
co
nected
embe
n
s
a
w
w
a
a
n
d
M
t
f
w
o
o
o
nhill
y
e
rs
L
a
mson
rsh
the
a
o
a
w
f
a
e
C r
g
clerks suddenly disappe ared ; an d it was found that
There
absc onded with a very l arge sum o f mone y
hunt fo r t hem by the police who were so prompt in
that it was impossible for the thieves to get o ut of the
They were traced as far as Truro an d were known to be
in Cornwall
appened th at He n ry Melville and
ust
th
s
time
it
h
i
a
t
J
Wil son were away together o n a wal king tour round the Co
Like most people they were interested in the c as e ;
c oas t
o ne morning while at bre akfas t
absconding men h ad been tracke
’
,
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,
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,
,
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,
.
,
m aking an esc ape very improb able
c onst able c ame into the inn to m ak e
civilities with the two members o f the P u z z le Cl ub
e nces to some o f the le ading London detectives an d t
o f a co nfidenti al letter Melville h appened to h av e in his
c
e
t
o
k
l
p
fro m o ne o f them soon est ablished complete confidence and the
ins pect or opened o ut
He said that he had j ust been to examine a very import ant
a q uarter o f a mile from there
an d expressed the Opinion
Mes srs Lamson and Mars h would never ag ain be found alive
the suggestion o f Melville the four men walke d al ong the
t ogether
Th e re is o ur stile in the di st ance s aid the inspector
const able found beside it the poc k et book th at I h ave shown
cont ai ning the n ame o f Marsh and some memoranda in his h
writing It had evidently been dropped by accident
.
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A D VE NTU RES O F T HE PU ZZ LE C LUB
Ioi
‘
the two men were here very clearl y i m
soft soil and they all too k c are no t t o
They followed the prints closely an d
the edg e of a cliff forming a sheer
at the foot of which the se a some
,
,
,
gentlemen you see sa id the inspector that the foot
lead straight to the edg e of the cli ff where there is a g ood
,
,
,
,
of
tramplin g abo ut and there end Th e soil
disturbed for yards around except by the footprin t s that you
The conclusion is obvious
That knowing the y were un able to esc ape capture th ey de
no t t o be t ak en alive an d threw themselves over th e cli ff P
.
,
,
”
.
,
,
,
Loo k to the rig ht
be
sati sfied that
an d
the
the le ft
,
and
o
u
y
will fin d
no
most experienced mo unt ai neer
PU ZZLES
THE C A NTE RBU R Y
102
h t ever li ve d could not m ake a descent or even an ywh
over the edge of the cli ff There is no l e dge or foothold
fifty fee t
Utterly impossible said Melville after an inspection
do you propose to do P
“I am goi ng straight b ack to communic ate the
We sh all withdraw the cordon an d
headquarters
for the dead bodies
said Melville
Then you will m ake a fat al mist ake
men are alive an d in hiding in the di strict
Just examine
prints again Whose is the l arge foot P
Th at is Lamson s an d the sm all print is Marsh s
was a t all m an j ust over six feet an d Marsh was a little
I thought as much said Melville
And yet you
that Lamson t akes a shorter stride than Marsh Notice
pe culi ari ty that Marsh walks he avily on his heels while
treads more o n hi s toes Nothing rem arkable in that P
no t ; b ut has it 0
Becau se yo u will find that he sometimes
steps th ough you wi ll neve r find Marsh tre ading in the
the other
Do yo u suppose that the men wal ked b ac kw ar d s
o wn footprints P
asked the inspector
No
th at is impossible No two men could walk b
some two hundred yards in th at wa
with
such
e
x
t
ac
itu
y
will no t find a single pl ace where the y h ave missed the
e ve n an eighth o f an inch
ite
Nor
do
u
i
r
n
s
s
i
l
o
b
e
Q
p
that two me n hunt e d as they were could h ave provi
wi th flying machines b alloons or even p arachutes They di d
drop over the cliff
Melville then explain ed ho w the men h ad got away
acc oun t p roved to be quite correct for it w
ill be remembered
t e y we re ca ught hiding under some straw in a b arn withi n
h
mi les o f the spot
Ho w di d the y
t a
,
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,
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’
’
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”
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"
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,
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-
,
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”
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,
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.
d id P
,
UZZ
LES
P
R
R
ANTE
B
U
Y
THE C
1 04
h
umber
which
c
se
the
thing
is
solved
But
eve
n
i
f
a
i
n
n
o ne suc
there are se veral cases the owner o f the act u al car may e asily be
found
o d y asked
?
a
will
you
m
n
a
ge
th
t
someb
a
Ho w
Surely replied R ussell the method is quite obvious B y
.
,
,
.
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'
”
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,
,
the proc ess o f elimin ation Every own er except the o ne in
will be able to prove an alibi Yet merely g uessing o ffh and I
t hink it quite probable th at there is only o ne n umber th at fits the
case We shall se e
Russell was right for th at very night he sent the number b y
post with the result th at the run away c ar was at on ce traced
and its owner who was himse lf driving h ad to
o f the
the
cost
a
p y
damages resulting from his carele ssness Wh at was the number o f
.
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”
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,
,
,
.
t he car ?
PUZZ LE C LU B
A DV E NTU RES O F THE
—
The
65
.
1 05
"
M ystery of Ravensden e P ark
.
mystery of Rave n sd e n e P ark which I will n ow present
was a tragic a ffair as it involved the ass assin ation of Mr Cyril
Hastihgs at his country ho u se a short dist ance from London
On F eb ru ary 1 7th at 1 1 p m there was a he avy f all o f snow
an d though it l asted o n ly h alf an ho ur the gro und was covered to
Mr H astings h ad been spending the
a depth o f several inches
evening at the house of a neighbour an d left at midnight to walk
home t aking the short route th at lay through R ave nsde ne Park
Th e
,
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.
,
.
,
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,
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,
,
that is from D to A in the sketch pl an But in the early mornin g
h e was fo und de ad at the point in dicat ed by the st ar in o ur di agram
st abbed to the he art All the seven g ates were promptly closed
an d the footprints in the snow exa mined
These were fort un ately
very di stinct an d the police obt ained the followin g fac ts
Th e footprints of Mr H astings were very c lear straight from
D to the spot where he was fo und
There were the footprin t s of
—
R
a
n
n
r
ve sd e e b utle
the
who retired to bed five min utes before
—
midnight from E to E E There were the footprints o f the game
kee per from A to his lodge at AA Other footprints showed that
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.
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.
.
T HE C A N TE RBU R Y PUZZLES
1 06
in dividual had come in at gate B an d left at gate B B while
an o th er ha d entered by gate C and left at g ate CC
Only these five persons h ad entered the p ark sin ce the fall o f
No w it was a very foggy night an d some of these p edes
sno w
tri ans had conseq uently t aken circ uito u s routes but it was par
ti cularly noticed that no track ever crossed another tr ac k
Of this
th e police were absol utely cert ain b ut they stupidly omitted to
make a sketch o f the various routes before the snow h ad melted
an d utterly e fiace d them
The m ystery was brought before the members o f the P uz z le
Club who at once set themselves the t ask of solvin g it
Was it
o ne
,
.
.
,
,
,
.
,
.
,
.
poss ible to di scover who committed the crime P Was it the butler P
Or the gamekeeper ? Or the man who came in at B an d went
o ut at BB P Or the man wh o went in
at C an d left at CC P They
r
d
—
a
s
a
p ovi ed themselves with di gr m sketch pl ans like the o ne we
a
e
r
h v eprod uced which simplified the real form o f R ave n sd e ne
Park without dest ro ying the neces sary conditions of the problem
Our fri e nds then proceeded to trace o ut the route o f e ach person
acc
a
In ord nce with the po sitive st atements of the police th at we h ave
gi ven
It was so on eviden t th at as no path ever crossed another
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,
C A N TE RB U R Y PU ZZ LES
THE
1 08
o
o
f
e
t
w
a
ar
r
st
ct
S
qu
re
I
doubt
whether
the
e
ex
ctl
y
d
n
a
a
ar
e
di ri
;
o
f
z
me
si
e
If
only
I
knew
the
si
e
the
field
I
could
soon
z
th e sa
disco ve r it and by t aking these S imple me asurements quic kly
se cu re th e t reasure
‘
a
would
not
k
n
ow
which
cor
n
er
to
st
rt from n or
But yo u
which dire c tion to go to the next corner
chap that onl y me an s
S pots at the mos t to
.
,
,
,
’
.
,
’
.
,
ove r ; and as the p aper s ays th at the tre asure is three f eet
dee p yo u bet that wouldn t t ake me long
continued D awkins I h ap pen to be a bit
Now gentlemen
of a math e matici an
an d he aring the convers ation I saw at once
th at fo r a spot to be e x act l y two three an d fo u r furlongs from
su cce
s si ve co rners o f a squ are the squ are must b e o f a p articular
‘
area
Yo u can t get such measurements to mee t at o ne point in
any sq uare
ne
o
o
f
u
c
l
o
ho
ose
e
y
o
n
l
y
h
pp
e
n
i
n
fi
e
d
a
T
h
c
a
n
a
y
dig
’
’
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’
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,
O F T HE PUZZ LE C LU B
A D V E NTU R ES
1 09
siz e an d th at is j ust wh at these men never su spected I will
leave yo u the puz z le of working o ut j ust what that a re a is
Well when I found the si z e of the field I was not long in
di scovering the field itself for the m an h ad let o ut the district in
the conversation And I did not n e ed to m ake the eight digs for
The
as luck would h ave it ; the third spot I tried was the right o n e
treasure was a subst anti al sum for it h as brought me home an d
en abled me to start in a business that alre ady shows signs o f being
I often smile when I think o f th at
a p artic ul arl y lucrative o n e
poor fellow goin g about for the rest of his life saying : If only I
knew the si z e o f the field I while he h as pl aced the tre asure s afe
in my o wn possession I tried to find the m an to m ake him some
compen sation anonymously but without success P erh aps he stood
In little need o f the mone y while it h as saved me from ruin
Co uld the re ader h ave discovered the requ ired a rea of the field
from those det ails overhe ard in the win e sh 0 p P It is an elegant
litt le puz z le an d furnishes another ex ample of the practic al utilit y
o n unexpected occ asions o f a kn owledge o f the art o f p roble m
solving
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TH E P R O FE SSO R S P U ZZ L E S
’
We ll make
WHY here is the Professor ! exclai me d Grigsby
him sh ow us so me new pu z z les
It was Christmas Eve an d the club was nearl y deserted
Onl y Grigsby H awkh urst and mys elf o f all the members
se e med to be det ai ned in town over the season o f mirth an d mince
pies The man however wh o h ad j ust entered was a welcome
as we h ad
Th e Professor o f Pu z z les
ad dition to o ur num ber
nickname d him was very popular at the club an d when as o n the
nt
o
s ion thin gs got a little slow his arri val was a p ositive
e
s
cca
r
e
p
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”
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”
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,
He was a man o f middle
cheery
kind he arted but
inclined to be cyn ical He h ad all his life d abbled in pu z z les
problems and eni gm as o f every kind an d wh at the P rofessor
di dn t know abo ut these m atters was admittedly not worth know
in g
His p uz z les always h ad a ch arm o f their o wn an d this was
mainl y because he was so h appy in dishing them up in p al at able
an d
age ,
-
,
,
.
,
,
’
.
,
Yo u
the man o f all others th at we were hoping would
drop in said H awkh urst
H ave you got anything new P
I have always something new was the reply uttered with
‘
fe igned co nce it—for the Professor was re ally a modest m an
Im
sim ply gl utted with ideas
Where do yo u get all yo ur notions P I asked
Everywhere anywhere du ring all my waki ng moments I n
de ed t o o r three o f m y best pu z z les h ave come to me i n m y
are
"
,
.
,
,
”
.
.
,
w
,
,
.
THE
1 12
C A NTE RBU R Y
PU Z ZLES
co ins in the se ven empty di visions so that e ach o f the three
s
s
t
l
a
d
d
a
a
l
o
u
n
th
ro
s
two
di
a
gon
s
S
h
ll
up
fif
een
hi
ling
w and
ree
c l m s
o
t
a
n
d
w
t
a
a
u
ours
division
be
witho
t
le
st
one
coin
no
a
m
e no
Of c
y
di visi o ns may cont ain the s ame val ue
s
a
P
the
coi
s
ffect
the
question
s
k
ed
Grig
by
a
n
But ho w can
a
a
h
t
you
will
find
out
when
y
ou
ppro
ch the solution
T a
I shall do it with numbers first s aid H awkhurst an d the n
subs titut e coi ns
a
ll
!
a
a
iv
mi
n
utes
l
ter
however
he
excl
imed
H
ng
it
I
a
F e
can t help getting the 2 in a corner May the dorin be move d fro m
its prese nt position P
Cert ainly not
Then I give it up
But Grigsby and I decided that we would wor k at it another
t ime so the P rofesso r showed H awkhurst the solution privately
and th en went o n with his ch at
,
.
,
,
,
,
”
.
.
”
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,
”
,
,
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,
,
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’
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.
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,
,
.
—
The P ostage S tamp s P uz z les
68
.
.
instead o f c oins we ll substitute postage-s tam ps Take
ten c urre n t English st amps nine of them being all of d iff erent
values an d the tenth a duplic ate Stic k two of the m in o ne divi
s ion and o ne in each of the others
so th at the squ are sh all t hi s
time add up ninepenc e in the eight directions as before
Here yo u are l cried Grigsby after he h ad been scri bbling
fo r a few minut es on the b ac k o f an envelope
The Professo r smiled indulgently
Are yo u sure th at there is a c urrent English post age st amp o f
the v al ue o f threepence h alfpenny P
For the life of me I don t know
I s n t there P
That s j ust like the P rofes sor
put in H awkhurst
There
ne ve r was such a tric ky m an Yo u never know when you h ave
ust
when
you
m
ke
sure
y
ou
go t to the bottom o f his puz z les
a
J
have fo und a solution he trips y ou U over some little point o u
p
y
never tho ught o f
No w,
’
.
,
.
,
,
”
.
,
.
.
-
-
’
’
,
.
’
”
,
.
.
,
"
.
.
T HE PR O FE SS O R S PU ZZ LES
’
When yo u h ave done th at said the P rofessor
here is a
much better o ne for you Stick English postage st amps so that
every three di visions in a line s hall add up alike usi ng as m an y
st amps as you choose so long as they are all o f di fferent values
It is a h ard nut
,
,
.
,
.
,
.
—
The
69
.
F rogs
and
Tumblers
.
What do yo u thi nk of these P
Th e P rofessor brought fro m his c apa cious poc ke ts
frogs snails liz ards and other cre atures o f J
,
(
,
)
,
a
n u mbe r
of
T HE C A N T ER B U R Y PU ZZLES
1 14
—very grotesque in form
brilli ant in colour While we we re
loo king at them he as ked the waiter to pl ace S ixty four tumblers
When thes e h ad been brought an d arranged in
o n the club t able
the fo rm o f a squ are as shown in the illustration he pl aced eight
o f th e little green frogs on the gl asses as shown
z
i
a
l
No w he said
see
these
tum
b
lers
f
orm
e
ght
hori
ont
o
u
y
and eight v e rtical lines and if you loo k at them di agon ally (both
ways) there are t went y six other lines If yo u run your ey e along
all the
s e forty two lines
u
wil
l
fin
d
t
w
f
r
ogs
a
n
y
w
here
in
o
n
o
o
ar
e
y
a line
The pu z z le is thi s
Three o f the fro gs are sup posed to im p
from their pres ent position to three vac ant gl asses so th at in their
ne w rel ative positions still no two frogs sh all be i n a lin e
What
are th e j umps m ade ?
I suppose
began H awkhurst
I know what yo u are going to ask antici pated the P ro fesso r
No ; th e fr ogs do not exch an ge pos itions but each o f the three
j umps to a glass th at was no t previ ously occupied
But surely there m ust be scores o f solutions P I said
I sh all be very glad if yo u c an fin d them repli e d the Pro
fesso r with a dry smile
I only kn ow o f o ne—o r rather two
countin
g a reversal which occurs in con se que nce o f the positio n
bei ng symmetric al
an d
.
-
.
,
,
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”
,
,
,
-
.
-
,
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.
,
.
.
.
,
,
”
.
.
,
.
.
,
”
.
—Romeo
and
uli et
J
For some time we tried to m ake these little rept iles per form the
fea t allotted to them and fai led Th e P rofessor however would
no t give away his solution but s id he would inste d i tr
a
a
n od uc e
o us a litt le thing th at is chil di shl y simple when
h
ve
onc
s
n
o
u
a
e
ee
y
t
It but cannot be m astered by everybody at the very first attempt
Wai ter l he c alled again
J ust t ake away these gl asses,
please and bring the chessbo ards
I ho pe to goodn es s e xcl aimed Grigsby yo u are no t going
to sho w us some o f those awf ul chess problem
White
s o f y ours
to mate Black in
2
The
4 7 moves without mo vi ng his piece s
o
7
.
,
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.
,
,
,
,
.
.
,
.
”
,
,
.
’
.
THE C A NT ERB U RY PU ZZ LES
1 16
a
e
m
a
e
d
a
n
visit
d
ever
y
squ
once
onl
y
onc
but
you
h
ve
d
r
a
e
;
e
and
him turn ninet een t imes an d that is not doing the tric k in the fewest
turns possible
Hawkhurst curiously enough hit on the so lution at once and the
z
o
f
z
u
rofes
or
rem
rked
th
t
th
j
st
one
those
pu
les th at a
as
w
i
s
a
a
s
P
pe rs on might solve at a gl ance o r not m aster in six months
,
,
”
.
,
,
,
.
.
1
7
— Romeo s S econd J ourney
’
.
.
It was a Sheer stroke o f luck o n your p art H awkhurst he
“
Here is a much e asier p uz z le bec ause it is c ap able o f
added
more system atic an alysis ; yet it m ay j ust h appen th at you will not
P ut R omeo on a white squ are an d m ak e him
d o it in an hour
crawl into every other white squ are once with the fewest possible
turnings This time a white squ are may be visited twice but the
snail must never pass a second time through the s ame corner o f a
square no r ever enter the bl ac k squ ares
May he leave the board for refreshments P as ked Grigsb y
No he is no t allowed out until he h as per form ed his feat
,
,
,
.
.
.
,
”
.
.
”
.
2
7
.
The F rogs who would
a
-
wooi n
o
g g
.
While we were vai nly attempting to solve this puz z le the
Profe ssor arranged o n the t able ten o f the frogs i n two rows as they
will be fo und in the illustration
,
,
.
m m
fi
e
T HE PR O FESS O R S PUZZL ES
’
1 17
wooing go
F o ur of them are s upposed to go a wooin g and
after the fo ur h ave e ach m ade a j ump u pon the t able the y are in
s uch a position that they form five straight rows with four frogs i n
every row
Wh at s th at P asked H awkhurst
I think I c an do th at
A few min utes l ater he exc l ai med How s this P
They form o nly fo ur rows inste ad of five an d you h ave moved
six o f them expl ained the Professor
H awkhurst said Grigsby se verely you are a du ffer I see
the solution at a glance Here you are
These two j ump on their
comr ades b acks
No no admonished the P rofessor
th at is n ot allowed
I di stinctly said th at the j umps were to be m ade upon the t able
Sometimes it passes the wit of m an so to word the conditions o f a
problem th at the quibbler will not persuade himself th at he has
found a flaw through whi ch the solution m ay be m astered by a
child of five
After we h ad been vai nl y pu z z ling with these b atr achi an lOvers
for some time the Professor reve al ed his secret
The P rofessor g athered up his Jap anese rept iles an d wished us
good night with the u sual se ason able compliments We three who
remained h ad o ne more pipe together and then also left for our
respective homes E ach believes th at the other two racked lthe ir
brains over Christm as in the determined attempt to master the
P rofessor s puz z les ; b ut when we next met at the c l ub we were all
unani mous in decl aring th at those puz z les which we h ad failed to
solve we re ally h ad not had time to look at while those we h ad
mastered aft er an enormous amo unt o f labour we had see n at the
first glan ce di rectl y we got ho me
’
a
-
-
,
.
,
”
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"
’
.
.
’
,
,
”
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,
”
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,
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”
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”
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”
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”
.
M I SCE LL AN E O U S P U ZZ LE S
—
The Game
a
l
e
s
K
f
y
73
NE ARLY all of o ur most popul ar g ames are of very an cient ori gin
t ho ugh in many cases they h ave been consider abl y developed an d
—
—
s
F
u
i
l
was a
l
e
improved Kayles d erived from the rench word q
great favourite in the fourteenth century an d was undoubtedl y the
parent o f o ur modern game of ninepins K ayle pins were not co n
fined in those d ays to an y p articul ar number an d the y were gen
e rally made o f a conic al sh ape an d set up in a straight row
At first they were knocked down by a club th at was thrown at
them from a d ist ance which at once suggests the o ri gin o f the
past ime o f shyin g for coco an uts th at is to d ay so popular on
Bank Holidays on H ampstea d Heath an d elsewhere Then the
players introd uced b alls as an improvement on the club
In the illustration we get a pict ure o f some o f o ur fourteenth
cen tury ancestors pl aying at kayle pins in this m ann er
No w I will introd uce to my re aders a new game o f p arlour
kayle pins that can be played across the t able without anyprep ara
tion whatever
Yo u simply pl ace in a straight row t hirteen domi
noes chess pawns dr aughtsmen counters coins o r be ans
an yt hing will d o —
all clo se to e t h e r an d then remove the second
E g
on e as shown in the pict ure
I t is assumed th at the an cient pl ayers h ad become so expe rt
that they co uld always knoc k down an y single k ayle pin or an y
two kayle pins that stood close together
The y therefore altered
the game and it was agreed th at the pl ay er who knocked down the
last pin was the winner
.
o
.
,
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,
-
.
,
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,
-
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-
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,
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,
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,
,
,
,
,
,
.
-
,
-
.
,
.
THE C AN T E RBU R Y
1 20
P UZ ZLES
the o ne to suppresse either the insolence or leviti c of the other
t
a
a
C
c
F
:
h
we
n
t
to
g
ether
to
visit
the
rench
kin
g
l
y
ing
onst
n
e
T ese
where e ntertainin g the time with varie ti e o f disports Henry played
.
,
,
Hereat Lo uis beganne to gro we warme in words an d was
therein little res pected by Hen ry
Th e gre at imp atience of the one?
an d the sm al l forbe arance o f the other did strike
i n the end su ch a
e
h at between them th at Loui s threw the chessmen at Henry 5 face
,
.
’
.
M IS C ELLANE O US PUZZ LES
121
Henry again stroke Louis with the chessbo ard drew blood
with the blowe and had presently sl ain him u pon the pl ace had he
not been st ayed by his brother R obert
Hereupon they presently went to horse an d their Spurre s
cl ai med so good haste as they recovered P ontoise albe it they were
sharply pursued by the F rench
Now tradi tion—o u this point not trustworthy—says th at the
c hessbo ard broke into the thirteen fr agments shown in o ur ill ustra
tion It will be seen th at there are twelve pieces all different in
sh ape e ach cont aining five squ ares an d one little piece o f four
squares only
We thus h ave all the sixt y fo ur squ ares of the chess bo ard and
the puz z le is simply to cut them o ut an d fit them together so as
to m ake a perfect bo ard properly chequered The pieces m ay be
e asily cut o ut of a sheet of squ ared p aper ; an d if mounted on
cardbo ard the y will form a source of perpet u al amusement in the
home
If yo u succeed in constru cting the chessbo ard b ut do not record
the arr angement you will find it j ust as pu z z lin g the next time you
feel di sposed to att ack it
P rince Henry himself with all his skill an d le arning would h ave
found it an amusing pastime
,
,
.
,
,
”
.
,
~
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,
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,
.
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-
,
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,
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,
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,
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,
,
.
75
The Spi der
.
and
the F ly
.
Inside a re ct an gul ar room me asuring 3 0 feet in length and
feet in width and height a spider is at a point on the middle of
,
12
,
the end walls
the op posite wall
o ne o f
on
,
I
,
I
foot from the ce iling as at A ; and a fly is
foot from the floo r in the centre as shown
,
,
C AN TE R B U R Y PUZ Z L ES
THE
1 22
B Wh at is the shortest dist ance th at the S pider must crawl in
orde r to reach th e fly which rem ains st ation ary ? Of course the
spider ne ver d r0ps o r uses its we b but crawls fairl y
at
.
,
.
,
—
T
h
e
6
7
.
P erplexed Cellarman
.
Here is a li ttle p uz z le culled from the traditions o f an o ld mon
Abbot F rancis it seems was a
ast ery in th e we st o f Engl and
an d his methods o f eq uit y e x tended to tho se
ve ry worthy man
li ttle acts of charit y fo r which he was noted for miles roun d
.
,
,
.
The Abbot moreo ver h ad
fine t aste in wines On o ne occa
si on he sent fo r the cell arm an and compl i ed th t
an
a a p articular
bot tling was not to hi s pal ate
Pray tell me B rother ohn how much o f this win e thou didst
J
b ottle withal
,
,
a
.
,
.
,
”
.
,
T H E C A NTE RBU R Y P UZZ LES
r2 4
plac ed This would be e asy enough if it were not for the four
t
a
c
u
ro ses as we should me rely h ve to : from A to B an d insert the
piece at the bo ttom o f the flag But we are not allowed to cut
t hro ugh an yo f the rose s an d therein lies the diffi c ult y o f the pu z z le
turnin gs
Of course we make no allowan ce for
.
,
,
.
,
.
”
.
8
7
—Catehz ng
°
.
the Hogs
.
In the illustration Hen drick an d Katrii n are see n en gaged in the
exhil aratin g sport o f attempting the c apture o f a c ouple o f hogs
Why did they fail
.
t
r
a
e
S ng
h ttle
it may
seem a complete an swer is afforded in the
puz z le gam e th at I will now expl ain
35
.
.
M IS C ELLAN EO US PU ZZLES
1 25
Cop y
the simple diagram o n a con veniently large sheet of card
bo ard or p aper an d use four m arked counters to represent the
D utchm an his wife an d the two hogs
At the beginning of the game these must be pl aced o n the
On e pl ayer represents Hendrick
s quares on which they are shown
Th e first pl ayer moves the
an d the other the hogs
an d K atriin
D utchm an an d his wife o n e squ are e ach in an y direction (b ut not
di agon all y) an d then the second pl ayer moves both pigs one square
e ach (no t di agon ally) an d so o n in turns until Hendrick c atches
o n e hog an d K atrii n the other
This yo u will find would be abs urdly e asy if the hogs moved
first but this is j ust wh at Dutch pigs will not do
,
.
,
,
.
.
,
,
,
,
.
.
,
—
T
h
e
79
.
Thi rty one
-
Game
.
is a game th at u sed to be (an d m ay be to this d ay for
aught I know) a f avo urite me ans of swindling emplo y ed b y c ard
sharpers at raceco urses an d in r ailway c arri ages
As on its o wn merits however the game is p artic ul arly interest
in g I will m ake no apology for prese nting it to my re aders
Th e c ardsh arper l ays down the twenty fo ur c ards shown in the
illustration an d invites the innocent wayf arer to try his luck or
skill by seeing which o f them can first sc ore thi rt y o ne or drive
his opponent beyond in the following m anner
two
On e pl ayer turns down a c ard s ay a 2 an d counts
the second pl ayer t urn s down a c ard say a 5 an d adding this to
the score counts seven
the first pl ayer t urns down another
an d counts
an d so the pl ay proceeds
eight
say a I
ca rd
thirt y o ne
an d so
al tern atel y u n til o n e o f them scores the
This
,
.
,
,
,
.
,
-
,
'
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,
,
,
,
,
,
,
,
,
,
-
,
Now the question is in order to win should you turn down the
first card o r courteo usl y request your opponent to do so
An d
ho w s ho uld yo u cond u ct your pl ay ? Th e re ader will perh aps say
“ h that is easy en ough You must play first
an d turn down a
O
3 then wh ate ver yo ur Opponent does h e c annot stop your makin g
,
,
,
,
.
,
,
,
,
THE C A NTE RB U R Y PU ZZL ES
1 26
a
n
d
sto
p
your
m
king
se
v
enteen
twent
y
four
the
wi
nn
i
ng
a
r
o
e
n
t
t
o
u
hirty
h
ve
onl
y
to
secure
these
n
mbers
win
a
u
o
e
Y
n
o
t
s
a
a
thi
is
j
st
th
t
little
k
n
owledge
which
is
such
d
ngerou
a
u
s
But
thin g an d it pl aces yo u in the h ands of the sh arper
o
n
d
counts
seven
u
a
a
a
the
sh
rper
pl
ys
d
a
n
a
u
4
Yo pl y 3
y
u
a
n
score
s
d
a
count
ten
the
sh
rper
t
rns
dow
n
d
a
n
3
play 3
“
cou
n
t
seventeen
the
sh
a
r
p
er
d
a
n
a
pl
y
o
u
4
y
-
,
,
,
”
-
.
.
.
,
,
plays a and counts t went y o ne
you pl ay 3 and m ake your
twe n ty four
Now the sh arper plays the last 4 an d scores
twent y e ight
Yo u loo k in vain for another 3 with which to win for the y are
all turned down I
So yo u are compelled either to let him m ake the
thirty o ne o r to go yours elf be yond and so lose the game
Yo u th us see that your method o f cert ainl y winning bre aks
down ut terly by what may be c alled the method o f exh austion
-
-
.
-
.
,
-
,
.
”
,
.
THE C A NTE RBU R Y PU ZZL ES
I 28
81
.
The E ig ht Clowns
.
sa
w
n
o
his
i
lust
tion
represents
troupe
of
clowns
I
once
the
a
a
r
l
T
I
o
n
his
on
i
n
nt
E
ch
clown
bore
one
of
the
numbers
to
a
9
C t e
body After going t hrough the usu al tumbling j uggling an d other
a
l
l
a
nt
c
the
y
gene
ll
y
concluded
with
few
curious
ittle
n
u
m
eric
r
a
i s
a
.
,
.
,
,
tricks o ne of which was the rapid form ation of a number o f m agic
It occurred to me that if clown No I failed to appe ar
squ ares
(as happens in the illustration) this last item o f their perform an ce
might not be so e asy The re ader is as ked to discover how these
eigh t clowns m ay arr ange them selves in the form o f a squ are (one
place be ing vac ant ) so that every one of the three columns three
rows and each o f the two di agon als shall add up the s ame The
vacant place may be at any p art o f the squ are but it is N o I t hat
must be abs ent
,
.
.
,
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,
,
.
,
,
.
.
MI S CELLA N E O US
On ce
PUZZL ES
129
upon a time a knight went to consult a cert ai n farnous
Th e intervi ew h ad to do with an affair o f the he art ; b ut
wiz ard
i
m an o f m agic h ad foretold the most favour able issues
e
t
h
t
er
af
s c ert ain t o help hi s visitor s
and concocted a love potion th at wa
c ause the convers ation drifted on to occult subj ect s ge ne rally m
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An d art tho u learned also in the m agic o f n irmbers
asked
the knight
Show me but one sample of thy wit in these m atters
Th e o ld wi z ard took five blocks bearing numbers and pl aced
the m o n a shelf app arentl y at r andom so th at they stood in
‘
th e o rder 41 096 as shown in o ur ill ustration
Hé I t he n l to o k
in his han ds an 8 an d a 3 and h eld them together t o fo rm thé
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T HE C AN T E RBU R Y PU ZZLES
1 30
Sir K night tell me s aid the wi z a rd c anst thou multiply
o ne number into the other in thy mind P
the good knight replied
I should n e ed
Nay o f a truth
to se t o ut upon the t as k with pe n an d scrip
Yet m ark ye how right e asy a thing it is to a man l e arn ed I n
the lore of far Ar a by wh o knoweth all the magi c that is hid in
th e philosophy o f n umb e rs I
The wi z ard simply placed the 3 next to the 4 o n the shel f an d
It will be found th at thi s gives the answer
the 8 at the other end
—
q uit e co rrectly 3 41 0968 Very curious is it not ? Ho w m any
oth er two figure multipliers c an you fin d th at will produce the s ame
You m ay place j ust as m any bloc ks as y ou
e ffe ct P
o n the
shelf bea ring any fig ures yo u choose
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83
.
The R i bbon P roblem
.
we
t ake the ribbon by the ends and pull it o ut straight we
have the number 0 588 23 5 2 1 1 6
This numbe r has the peculi
94 7 47
ari ty
that if we multiply it by any o ne o f the numbers 2 3 4 53
If
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UZZ
LES
P
R
R
T HE C A N TE B U Y
S3 2
r he r t o
f
o
o
w
a
l
d
y
suggested
th
t
the
simpl
e
st
w
uld
be
a
y
a
One
t ake a smaller sh are th an the other two bec ause then t he c arpet ,
u
a
d
not
into
more
th
n
fo
r pieces
u
t
c
be
n ee
v
t
e
l
e
a
e
h
s
her
th
ee
e
s
y
w
ys
of
doing
thi
which
I
will
a
a
r
e are
T
reader for the present the amusement of findi ng for himself merely
o
n
a
n
t
o
t
e
r
a
y
ng
th
t
supp
e
the
c
be
ine
squ
re
feet
then
s
o
e
u
a i f yo
p
sa i
l ady m ay take a piece two feet squ are whole a nother a two feet
sq uare in two pieces an d the third a squ are foot whole
a
for
moment
be
entert
ined
a
u
f
f
this
generous
o
er
wo
ld
But
not
by the other two sisters who insisted th at the squ are c arpet should
‘
s
a
f
a
a
t
o
m
a
a
cut
th
t
e
h
should
g
et
squ
re
ex
ctly
the
me
ac
a
be so
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me
No w
.
d
l
w
a
ccording
the
best
Western
uthorities
the
y
ou
o
t
a
h ave found it n ecess ary to cut the ca rpet into seven pi eces ; b ut a
correspondent in Tokio assures me th at the legend is that they
did it in as few as six pieces and he wants to know whether such
a t hin g i s possible
Yes it can be done
Can you cut o ut the si x piece s th at will form three
m ats o f equal size
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85
.
Captai n Longbow
and
the Bears
.
emin ent and more o r less veracious traVelle r Capt ain
”
Longbow has a great grievance with the public He clairns th at
during a recent expedition in Arctic regions he actu ally reach e d the
Nort h P ole but c ann ot induce anybody to believe him Of course
t he diffi cul ty in such c ases i s to produce proof but he avers th at
future travellers when they succeed in accomplishing the s ame fe at
will fin d evidence on the spot He says that when he got there he
saw a be ar going round an d round the top o f the pole (which he
declares is a pole) evidently perplexed by the peculi ar fact that no
matt er in what direction he looked it was always due south
Cap
t in Lo ngbow put an end to the bear s medit ations by shooting
a
hi m and afterwards imp ali ng hi m in the m anner shown i n the
Th at
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M IS C ELLA NE O US PUZZLES
‘
1 33
illustration as th e evidence for future travellers to which I h ave
allude d
When the CaptaI n got o ne hundred miles so uth on his return
journey he h ad a little expe rience th at is somewhat puz z ling He
was s urprised one mor
nin g on looking down frOm an elevation
to see no fewer than eleven bears in his iIn me di ate vic init y ; But
wh at astonished him more th an anythi n g else was the curio us
fact that they h ad so placed themselves th at there were severi rows
of bears with fo ur bea rs In every row W
hether or not this was
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t h e res ult of pure ac cident he c annot sa y b iI t su ch a thing might
have h appened If the rea der tries to m ake eleven dots on a sheet
o f pa per so th at there sh all be seven rows of dots with fo u r dots I n
every row he will find some diffI CIIlty; b ut the capt ain s al leged
groupin g of the bears is quite possible Can you discover how
they were arr anged ?
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I
C ANTE RBU R Y
THE
34
PUZ ZLES
a
n
d
s
a
a
a
i
h
s
p
e
to
do
with
r
lw
y
route
i
n
these
d
ys
a
s
h
z
l
u
z
T i
T
h
e m ap of Engl and shows
much
tr
v
lling
shou
d
prove
useful
l
e
a
of
t wen ty four towns connect e d by a system of r ailways A resident
m
s
t
o
a
e
f
o
town
m
r
k
ed
A
the
t
o
the
propose
visit
ev
ry
a
t
a
e
at th
p
p
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o ne o f
the towns once an d only once and to
up
at Z
Thi s would be e as y en ough if he were able to cut across
co untry by ro ad as well as by rail b ut he is not
Ho w doe s he
pe rform the feat ? Take your pencil an d st arting from A pass
from town to town m aking a dot i n the towns yo u hav e vis it e d
an d se e if you can end at Z
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87
The
.
Chifu Che mulpo P uz z le
-
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Here is a puz z le that was once o n sale in the London shops
It represe nts a milita ry train—e u engi n e and eight cars The
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T HE C A NTE RBU R Y PUZZ LES
1 36
di sposed of a fif th of the remain der and gave a fifth o f an
Then wh at sh e h ad left she divided equally among
egg over
And strange to say sh e h ad not through
thirteen o f her friends
the puz z le
o ut all these t ransa ctions broken a single e gg fi Now
is to find the sm allest po ssi ble n umbe r of eg gs th at Mrs Co ve y
Can yo u s ay how m an y
c ould have t aken to market
sh e
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The
89
.
P ri mrose P uz z le
.
Select the n ame of any flower th at yo u think suitalble and th at
con tains eight letters Touch o ne o f the primroses with your
pencil and
over o ne o f the adjoining
an other o n
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,
,
which yo u m ark the first letter of your word Then touch another
a
a
v cnt flower an d again j ump over o n e in another direction an d
wn te down the second letter
Contin ue this (t aking the letters in
th ei r prope order until all the letters h ave been written down
)
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M IS C ELLA N E O US l PUZ ZLES !
over may be oc cupied
or
n ot
The
.
name
1 37
t ree may
of a
lso
a
be
.
Seven fri en ds named Adams Brooks Cater ; Do bson , E dwards
F ry an d Green were spending fifteen d ays together at the seaside
and the y h ad a round brea kfast t able at th e hotel all to themselves
It was agreed th at n o m an should ever sit down twice with the
sam e two neighbo urs As they can be se ated under these condi
tions in just fifteen ways the plan was quite practic able But co uld
the reader have prep ared an arran gement for every Sitting ? The
hotel proprietor was aske d to draw up a scheme but he miserably
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Sometimes people will Speak o f mere cou nting as o ne o f the
simplest operations in the world but o n occasions as I shall Show
it i s far from e asy Sometimes the l abour can be diminished b y the
use o f little artifices ; sometimes it is pr actic a lly im possible to m ake
the required enumeration without h aving a very clear he ad indeed
An ordin ary child b uying twelve post age st amps will al most in
stinctively say when he sees there are four along o n e side an d three
F our times t r ee are t welve ;
along the other
w
ile
tin
y
s
i
h
h
h ‘
brother will co unt them all I n rows I
etc I f the child S
ad d up the numbers I
2 3 up to 5 0 sh e
a d dition s um o f the fift y numbers
more u sed to ari thmetic al o e rations will se e
p
at a gl anc e th a
t by j oining the n umbersat the extremes th ere are
2 5 p airs of 5 1 ; therefore 2 5 x 5 1
I
But his sm art son o f
twenty m ay go one better an d say Why multiply by 2 5
ust
J
add two 0 s to the 5 1 an d divide b y 4 an d there yo u are l
hich
A tea merchant h as five tin tea boxes o f cubic al sh ape w
he kee ps o n his counter in a ro w as sho wn i n o ur illustrati o n
Every box has a pi cture o n each of its six sides so there are thirty
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T HE C AN TE RB U RY PUZZ LES
x3 8
pictures in all but o ne pict ure on N o I is repe ated o n No 4 and
There are
two o ther picture s on No 4 are repeated o n No 3
therefore only t went y seven different pictures The own er always
ke eps No I at o n e end o f th e ro w and never allows No s 3 an d 5
to be put side by side
tradesman s custome r h aving obtained this inf ormation
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thinks it
,
good puz z le to work o ut in how many way s
may be arranged o n the co unter so th at the order o f th
turns in front Sh all ne ver be twice alike
He found
o f th e count a tough little nut
Can you work o ut
wi thout gettin g your brain into a t angle
Of course
t
u
pic res may be in a row as it is all a que stion of their order
a
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The
92
.
The
F o ur P orkers
.
s
i
p g are so pl ac ed each in a se parate sty that altho ugh
e ver
o
n
e
f
o
t he thirt y six sties is in a st raight lin e eith r ho i
y
r
e
(
z on tall
y verti cally or di agon ally) with at lea st o ne of the pigs
fou
r
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U
ZZ
LES
P
R
R
T
A
N
E
BU
Y
T HE C
1 40
by
I
is the
me
sa
‘
’
to get rany
You will find it quite impo ible
ss
.
l r res ult
D
a
m
y
p
le
is
find
the
l
r
g
est
p
ssible
result
ivide
t
o
z
z
u
No w
o
a
a
a
o
u
d
a
s
block
n
o
two
gro
p
of
five
th
t
like
rr
n
g
e
u
n
a
n
t
s
i
y
e
th
y
sm al e
.
.
,
,
th em to form two multiplication sums th at S hall pro duce the same
all an d yet it
a
roduct
the
l
rge
t
mount
possi
b
le
h
t
is
T
a
n
a
s
a
d
p
is a nut th at requires some cracking
Of course fr actions are no t
allo we d no r an
z z le is quit e interest ing
tricks
W
h
atever
p
T
e
u
h
y
‘
P
aps it
e nough in the Sim
e
form
in
which
I
h
ve
given
it
erh
a
m
r
shoul d be added that the multi pliers ma
res
o
co
n
t
in
w
figu
a
t
y
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F
o
s
x
e
94
.
and
Geese
.
Here is a little puz z le of the moving counters cl ass that my
read ers will probably find en tert aini n
n
f
o
ke
di
a
gr
m
a
M
a
a
g
ay
con ve ni en t siz e similar to th at shown in o ur illustration an d
r
o
p
—
e
s
i
x
o
u
vid
c nters three m arked to represent foxes and three to
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M IS C ELLA NE O US PUZZLES
14:
represe nt geese P lace the gee se on the discs 1 2 an d 3 an d the
foxes o n the discs n umbe red 1 0 I I an d 1 2
B y movi ng o ne at a time fo x , and
No w the p uz z le is this
go
ose altern atel y along a straight li ne from o ne disc to the n ext
n d the geese on
z an d 3 a
o ne try to get the f oxes on I
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re a
ch
of
e ach other
,
or
,
,
e will be tro uble
ther
.
Thi s rule
,
u
o
y
find pre vents yo u moving the fox from I I on the first move as on
either 4 or 6 he would be within re ach of a goose It also prevents
yo ur mo ving a fox from I O to 9 o r from 1 2 to 7 If yo u pl ay
I O to 5 then y o ur next move m ay be 2 to 9 with a goose which
o
a
u
n
could
h
ve
pl
ye
if
the
n
o
t
f
o
o t previousl y gone from
a
a
d
x
h
d
y
10
It is perh aps unnec ess ary to say that onl y o n e fox o r o ne
goose can be o n a disc at the same ti me ” N ow wh at is the
sm allest n umber of mo ves necessary to make the fox es and geese
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C A N T ER B U R Y P UZ ZL ES
T HE
II
—
i
o
n
o
b
n
s
R
95
.
Crus oe
’
s
Table
.
s
t
i
s
d
a
r
r
I
C
R
curio
s
extr
ct
f
o
obi
n
son
usoe
i
y
r
m
a
u
is a
a
n
r
es
d
o
v
f
f
ou
d
i
n
the
moder
n
editions
the
Ad
e
n
tu
n
not to be
e
o
t
b
a
o
t
a
o
t
d
i
n
the
his
lw
y
s
seemed
me
pit y
a
s
a
h
ld
T
o
is mi t e
r
a
e
a
a
v
i
third
i
n
the
morni
n
g
the
wind
h
ng
b
t
d
du
ing
day
The
n
r
a
d
a
w
t
o
i
0
n
i
ht
went
do
n
the
shore
h
ping
f
nd
t
yp
e
rite
o
t
w
I
the
g
other u se ful things washed up from the wrec k o f the shi p i but all
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fell in my way was a piece o f timbe r with m an y
in it
My man F riday had man y times s aid that we st o od s adl y in ne ed
o f a sq ua re t able fo r o ur afternoon te a an d I bethought me h o w
this piece o f wood might be used for th at p u r pose
An d since
d uring the long time that F rid ay h ad n o w been with me I was no t
wanting to lay a found ation o f useful knowledge in his mind I told
h im that it was my wish to m ake the t able from the timbe r I h ad
fo und witho ut t here being an y holes in the top thereo f
Friday was sadl y put to it to say how thi s might be more
th at
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T HE C A N T E R B U R Y
44
PU ZZLES
p retty closely in o rder th at the y might get sh ade an d protection
from cold win ds 8 0 the y agree d to pl ant a lot o i young trees a
d ifiere n t number in ea ch orch ard in order to comp are res ults
One man h ad a single tree in his field another h ad two t rees ,
another h ad thre e trees another h ad fo u r trees another five an d
so o n the l as t m an h aving as m an y as fifteen trees i n hi s little
orchard Last year a very curiou s result was found to have come
Each o f the fifteen individual s discovered th at e very tree
abo ut
in his o wn orchard bore ex actly the same number o f apples
But
what was stranger still o n comp aring notes they found that the
tota l gathered in every al lotment was almost the same In fact
if the man with eleven trees h ad given o ne apple to the man who
had se ven trees an d the m an with fo urtee n trees had given three
an d thirteen trees ; th ey would all h ave
ith
ni
n
e
each to the men
w
had exactly the same
Now the puz z le is to disco ver h o w
ha ve had (the same i n every case) if th at li
bee n carried lo ut It is quite easy if y ou se t to work in the right
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way
.
When I pai d a visit to Peckh am rece n tl y I foun d e ve rybod y
asking
What h as happene d to Sam Solde rs the plum
ber
He
se e me d to be in a bad wa
his
wife
seriousl
y
nx
ious
b
out
a
n
a
d
a
as
w
y
the st ate o f his mind As he had fitted up a hot water app aratus
fo r me some yea rs ago which did not lea d to an explosion fo r at
l eas t three months (and the n o nl y d am ag ed the complexion o f
one o f the cook s followers
I
consider
ble
r
g
rd
i
r
a
e
f
o
h
m
a
d
h
a
)
The re he
to in quire
Mrs Solders w hen I call e d =
That s how he 3 been for t hree weeks He h ardly eats an ything
and ta kes no rest whilst his business is s o ne lected th at I d on t
g
h ow what is goin g to h appen to me an d the fi ve
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tearing his
hair like
a
mad
thin g
It s worr ying m e
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M ISCELLA N EO US PUZZ LES
1 45
I pe rsu aded Mrs Solders to expl ain m atters to me It see ms
that he h ad recei ved an order from a customer to make two rec t
an gular z i n c cisterns one with a to p and the other without a to p
Each was to hold ex actly
cubic feet o f water when filled to
the brim
The p rice was to be a cert ain amount pe r ciste rn in
cluding cost o f l abour No w Mr Solders is a thrift y man so he
n atur ally desired to m ak e the two ci st e rn s o f such dime nsio ns that
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the sm allest po ssible qu antity o f met al should be required This
was the little qu e stion th at was so worrying him
Can my ingenious readers find the dimensions o f the most
economical cistern with a to p and also the ex act proportions o f
s uch a ci stern witho ut a top e ach to hold
cubic feet o f water ?
By e conomical is meant the metho d that requires the smallest
possible quantit y o f met al No m argin n ee d be allowed fo r what
la dies would c all turnings
I shall show how I he lped Mr
Solders o ut o i his d ilemma He says : That little wrinkle you
gave me would be u se ful to o the rs In my trade
m077)
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T HE C A NTE RB U R Y PU ZZL ES
us
—
h
e
T
8
9
.
N elson Colu mn
.
Nelson celebration I was st andin g in Trafal gar Sq uare
He h ad for some time been
wit h a frie nd o f p uz z ling proclivities
gaz ing at th e column in an abstracted way an d seemed quite
unc onscious o f the c asu al rem arks th at I addressed t o him
Wh at are yo u dre amin g about
I s aid at l ast
Dun n g
a
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Two
fee t
he murmured
Some bo dy s Trilbys P I inquired
Fi ve times roun d
Two feet five times roun d I Wh at o n earth are ou sayi ng
y
Wait a minute he said beginning to figure something o ut
the back o f an en velope
I n o w detected that he was in the
t roes of producin a n ew proble m o f some sort
I
w
ll
k
n
g
o
r
e
f
ew
h
hi s me thod s o f workin at th ese thin gs
g
.
’
.
,
”
,
,
.
,
.
T HE C A N T ER B U R Y PU ZZL ES
148
—
markable coin cidences little thin gs agai nst the prob abilit y o f the
—
th at fill us wi th be
o ccurre nce o f which the odds are i mmense
wilderment
the t hree motor men in the illustration h as
j ust happe ned o n o ne o f these queer coincidences He is pointing
o ut to his t wo friends th at the three n umbers o n their c ars cont ai n
all th e figures 1 to 9 an d o and wh at is more rem arkable that if
th e numbe rs o n the first an d second c ars are multipli e d t o ge th e r
t he y will m ak e the num be r o n the third c ar That is 78 345 and
One
.
of
.
,
,
,
.
all
the
,
,
,
ten figures and 78 multiplied by 3 45 m akes
Now the rea der will b e able to fin d m an y simil ar sets o f
n um bers o f t wo three and five figures res pecti vel y th at h ave
t he sam e pe culi arit y
But there is on e set and o ne o nly in which
t he numbe rs have this addi tion al peculi arit y—th t the second
a
num e
is a m ultiple o f the first
In
other
word
i
f
s
co
u
ld
5
3
b
4
r
be d mded by 8 wit hout a remai nde r the n um b
e rs on the c ars
7
co
nt ain
,
,
,
,
.
,
.
,
,
,
M IS C ELLA N EO US PUZZLES
1 49
wo uld th em selve s fulfil this ext ra con dition Wh at are the three
n umbe rs th at we want ? R emem ber that they must have two
three and five figures re spectivel y
.
,
,
.
1 02
.
—A
Can yo u construct a
it sh all be magi c (th at
Revers i ble M ag ic S quare
.
square o f sixteen di fferent n um be rs so th at
is addi ng up ali ke in the four rows four
co lumns an d two di ag onals ) whether you turn the di agr am u pside
d own o f n ot P Yo u must not us e a 3 4 o r 5 as these figures will
not reverse ; but a 6 maybecome a 9 when reversed a 9 a 6 a 7 a 2
an d a 2 a 7
The I 8 an d 0 wi ll read the same both ways
Re
m ember that the const ant must not be changed by the re vers al
,
,
,
,
,
,
,
,
.
.
,
,
,
,
.
The
The above di agr am is the pl an o f an underground r ai lway
fare is uniform for any dist ance so long as you do no t go twice
along any portio n o f the line during the same jour n e y
No w a
ce rt ain passe nger
with plenty o f t im e o n his han ds g oes dail y
from A to F How m any di fferent rout es are there fro m which
.
,
.
,
,
.
F o r ex ample he can t ak e the short direct route
he may select
A B C D E F in a straight line ; o r he c an go o ne o f the long
rout es such as A B D C B C E D E F It will be noted that
i
he has Option al lines betwee n cert ain st ations , and hi s selec tio ns
Many readers
o f these le ad t o v ari ations o f the complete route
will fin d it a very perple xi ng littl e problem though its co nditions
,
,
’
,
,
,
,
,
,
,
,
,
‘
,
,
,
,
,
,
,
.
‘
.
’
,
are so
sim ple
.
I
T HE CAN TE RB U RY PUZZ LES
50
T
o
f
t
i
Simon
Softleigh
spe
n
t
most
his
life
between
oo
n
g
d
h
a
Mr
s
o
f
ea
w
as
enc
urch
Street
His
k
nowledge
the
there
h
F
d
Be e an
fore very li mi t e d So as he was t aking a holiday o n the south
f
o
r
i
n
a
o
t
he
tho
ght
this
splendid
opportunity
pic
k
g
up
a
w
as
u
c as
li ttle use ful inf orm ation He therefore proceeded to draw the
n ative s
I suppose said Mr Softleigh o ne mo rmng to a j o vi al weather
.
.
.
,
,
.
.
0
.
,
beaten skipper
yo u
.
,
hav e seen m an y wonderful sights on the rolling
seas
Bles s yo u sir yes said the skipper
F raps y ou ve never
seen a vanilla iceberg or a merm aid a h anging out her things to d r
y
o n th e equatori al li ne o r the blue winged sh ar k wh at fli es through
th e air in pur suit o f hi s pre y o r the se a sar int
p
Have yo u reall y see n a se a serpent P I thought it was nu
cert ain whether they e xis t e d
(1a
Yo u wouldn t say there was anything uncertin
’
,
,
,
.
-
,
-
-
,
-
"
.
’
'
[
T HE C A N T ERB U RY PUZZ L ES
2
5
much longer would the ladies h ave t aken ove r the ir n eedle
work task i f the si sters o f the curate refe rred to h ad play ed l awn
Of course we must
tennis instead o f attending the meetings ?
assum e that the l adies attended regul arl y an d I am sure th at the y
A mutu al kiss here counts as two Oscula
all worke d equ ally we ll
Ho w
,
.
rod
—The
Adventuro us S nai l
"
.
A simple version o f the pu z z le o f the climbi ng sn ail is familiar
We were all t aught it in the nu rsery and it was
to e ve rybod y
appare n tly intended to inculcate the simple moral t hat we sho uld
A
This is the popul ar story
ne ver sli p if we can help it
.
,
.
.
feet every night How long does it t ake to get to the
top
Of co ur se we are expec t e d to sa the an swer is twel ve d ays
y
because the cre ature m akes an ‘
actu al adv ance o f 1 foot in e v ery
w
n
t e ty four hours But the mod ern infant in arms is not t aken
m in thi s way He says correctly e nou gh th at at the e nd o f the
ping
back
2
.
,
,
-
.
.
,
,
M IS C ELLANE O U S PUZZ LES
1 53
the sn ail is 3 feet from the to p and there fore re aches
the summit o f its ambition on the tenth d ay for it would cease
to slip when it had got to the top
Let us however consider the origin al story Once u pon a
time two philo so phers were walking in their garden when o ne of
them espied a highly respect able member of the Helix Aspersa
famil y a pioneer in mount ainee ring in the act o f m aking the
perilous ascent o f a wall 2 0 feet high Judging b y the trai l the
gentleman calcul ated th at the sn ail ascended 3 feet e ach d ay
sleeping and slipping b ack 2 feet every night
said the philosopher to his fri end who was in
Pr ay tell me
the same li ne o f business how long will it t ake Sir Sn ail to climb
to the to p of the wall an d descen d the other side ?
Th e t0p o f the
wall as you know h as a sh arp edge so that when he gets there he
will instantly begin to desc end putting preci sely the same exertion
into hi s d aily climbing down as he di d in hi s climbi ng u p and
sleeping an d slippi ng at nig ht as before
This is the true version of the puz z le and my rea ders will
perh aps be interested in working o ut the exact numbe r o f days
Of course in a pu z z le o f this kind the d ay is always supposed to be
e qu all y divided into twelve hours d ayti me an d twelve hours night
ninth d ay
,
,
'
.
,
.
,
,
,
,
,
.
,
.
”
,
,
,
,
,
,
,
,
”
.
,
.
,
'
’
.
1 07
.
The F o ur P ri nces
.
Th e
dominions o f a cert ain Eastern mon arch formed a perfe ct ly
sq uare tract of country
It happen ed th at the king o ne d ay
disco vered th at his four sons were not only plotting agai nst each
other but were in secret rebellion against himself Aft e r co n
sultin g with his advi sers he decided not to exile the princ e s b ut to
co n fin e them to the four corners of the country where e ac h should
be given a tri angular territory of eq ual area beyond the boundaries
of which they would p ass at the cost o f their lives No w the
royal surveyor fo und himself confronted by gre at natural difii
culties owing to the wild ch ar acter of the co untry
Th e result
was th at while each was given ex actly the s ame area the four tri
.
.
,
,
,
-
,
.
,
.
,
,
THE C A N TE RB U R Y
1 54
P U ZZ LES
at
w
a
n
f
ng
l
r
districts
were
of
di
f
ere
t
sh
pes
some
h
a
ll
u a
a
z z le is to give the three
e
hown
in
the
ill
str
tion
pu
T
h
a
u
s
,
.
ment s fo r e ach o f the four dist ricts in the sm allest po ssible
-all whole furlongs
In other words it is required to
sm allest possible n umbers) four ration al right angl ed tri an gl es
equal area
.
,
-
.
1 08
.
—Plato
the Nin es
and
.
Both in ancient and in modern times the number mne has
We
considered to possess peculi arl y mystic q ualities
inst ance th at there were nine Mu ses nine rivers o f Hades and
that Vulc an was nine d ays falling down from he aven Then it
while
h as been confidentl y held th at nine t ai lors m ake a m an
we kn ow th at there are nine pl anets nine d ays wonders and th at
a cat has nine lives - an d sometimes nin e t ails
Most people are acqu ainted with some o f the curious properties
o f the n u
ber
n
ine
in
ordin
r
y
rithmetic
ex
mple
write
o
a
F
a
r
a
m
down a number cont ain ing as m any figures as you like ad d these
figure s together and deduct the sum from the first number No w
the sum o f the figures in this new number will alway s b e a multiple
o f nine
There was once a worthy m an at Athens who was not only a
cranky arithmetici an but also a mystic
He was deeply convin ced
o f the m agic prope rties o f the number n in e and was
e
petu
l
y
r
a
l
p
.
,
,
,
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’
,
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,
,
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,
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,
.
,
,
T HE C AN T E R B U R Y PU ZZLES
6
5
I t will
an d expired in nine minutes
o ut nin e teeth
be re d that nin e was hi s l uck y n umber It
.
,
was
.
e vi
In solving the above little puz z le only the most
Though the an swer
ari thmeti cal si gn s are necessa ry
sim ple wh e n yo u see it m an y re aders
in disc overing it Take your pencil and see if you can arrange
t hree nin es to represent twenty
,
.
,
.
.
1 09
.
—Nougkts
and
Crosses
.
Every child knows ho w to pl ay thi s game Yo u make a square
o f nin e cell s an d e ach o f the two pl aye rs pl ayin g altern ately puts
his mark (a nought or a cro ss as the case m ay be ) in a cell with the
obj ec t o f getting three in a line Whichever player first gets three
in a line wins with the exultin g cry
.
,
,
,
,
.
toe
My l ast go
Three j olly butcher bo ys
All in a ro w
Tit tat
,
,
,
”
.
It is a very ancient game But if the two pl ayers h ave a
fee t knowl e dge o f it o ne o f three thing s m ust alway s h
(r) The first player should win (2) the first player should lose
o r (3) the game sh ould always be dr awn
Which is co rrec t
.
,
.
110
—0v£d s G ame
’
.
.
H aving exami ned Noughts an d Crosses we will now co n
s ide r an e xt ensio n of the g ame th at is d istin ctl y mentioned i n t he
works o f Ovid It is in fact the p arent o f Ni ne Me n s Morris
refe rred to by Sh akespe are in A M idsummer N ight s Dream (Act ii
Scene
Each pl ayer has three counters which th ey p lay al ternately
o n to th e ni ne poi nts shown i n the di agr m
with the o bj ec t o f
a
gett i ng three in a li ne and so winning
But after th e six co unt ers
,
"
’
.
,
,
,
’
.,
,
,
.
M IS CELLA NE O US PUZ ZLES
1 57
played th ey then proceed to move (always to an adj acent
In the e xarnple below
un occupied point ) with the s ame obj ect
White pl ay ed first an d Bl ack has j ust pl ayed o n p oint 7 It is now
White s move and he will undoubtedly pl ay from 8 to 9 and the n
are
.
,
.
’
,
,
,
whate ve r Bl ack may do he will continue with 5 to 6 and
That is the simple g ame : Now if both pl ayers are e q ually
,
,
so
win
.
perfect
sho uld h appe n
Should the firs t player always
Or should the second pl ay er win P Or sho uld e ve ry game
draw ? One o nl y o f these things should always occ ur Which
,
.
it
rrr
.
—
Th
e
F armer s Oxen
’
.
A child m ay propose a problem th at a sage c ann ot answer
A f armer propounded the following question :
That ten acre
meadow o f min e will feed twelve bullocks fo r si xtee n wee ks or
e ighteen bullocks for eight weeks
Ho w m an y b ulloc ks could I
fee d o n a forty acre field fo r six weeks the grass growing regul arl y
all t he time
It will be seen that the sting lies in the t ail That st ead y
.
-
’
.
~
-
,
.
T HE C A NTE RBU R Y PU Z Z LES
1 58
growth o f the grass is such a re ason able point to be co nsidere d
yet to some readers it will c ause considerable perplexit y
s umed to be of
ss
is
cou
se
s
a
r
f
o
r
a
g
ness in every case when the c attle begin t o eat The difficult y
not so great as it appears if y ou properly att ac k the q uestion
—
,
.
,
,
.
.
,
112
.
— The Great Grangemoor Mystery
.
very we al thy man a reputed
millionaire residing in that be autiful old m ansion that has figured
He was a b achelor
so much in English history G range m o o r P ar k
spent most of the ye ar at home an d lived quietly e nough
Accordi ng to the evidence given o n the d ay preceding the night
‘
o f the crime he received by the second post a single
contents o f which evidently gave him a shoc k At ten
ni ght be dismissed the servants s aying th at he had so me
busine ss matters to look into and wo uld be sitting up late
would require no attend ance It was supposed that after all
gone to bed he had admitted some person to the house for
o f the serv ants was positive that she h ad he ard loud
at a very late hour
Next morning at a quarter to seven o cloc k o ne
se rvants o n entering the room foun d Mr Mowbr ay
floor shot through the he ad an d quite dead Now
the curious circumst ance o f the c ase It was c le ar that after
bullet had passed o ut o f the dead m an s head it h ad struc k the
clock in the room right in the very c entre of t he face an d actu
welded together the three b and s for the clock
th at revolved ro und the s ame di al as the ho ur
But altho ugh the three hands had become welded to ge t
as they s t ood in rel ation to e ach other at the moment
yet they were free to revolve round the swivel in one piece
had been st upidly spun ro und several times by the serv ants be
Mr Wiley Slyman was c alled upon the sp ot But they would not
move separately
Mr St anton Mowbray was
a
.
,
,
.
,
,
.
,
,
.
,
.
,
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,
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’
,
,
,
.
,
,
.
,
.
’
,
,
,
.
.
.
T H E C ANTE RB U RY PUZZ LES
1 60
Yo u will notic e
The matt er is sup remely simple
thre e band s appear to be at e q ual dist ances from o ne
The ho ur h an d fo r e a n ple is exactl y twent y m inutes
.
from th e minute han d—th at is the third o f th
You att ac h a lot o f im port anc e to
th e dial
servants have bee n re volvi ng the welde d han ds
no conse que nce what e ver ;
taneo usly as th e y are free o n the swivel
Give me a
of themselves into e q uili b rium
can te ll yo u be y o n d any do ub t the e xact ti m e th at the
fired
Mr Wiley Slyman t o o k fro m his p ock et a n ote boo k
to figure it o ut
I n a few mi nut es
a sli p o f paper o n which
th e crim e
The stranger
Mowbray s was con vict e d
but be fore he pai d the pen alty for his wic ke d act he admitted
Mr Slyman 5 st at em e nt o f the time was pe rf ec tly correct
Can yo u also gi v e the e xact time
,
,
,
.
,
,
,
.
”
.
.
,
.
,
.
’
,
,
’
.
.
—Cutting
Wood Block:
An ec onomi cal carpe nter had a bloc k o f wood measuring
inches lo ng by four in ch es wide by t hree
dee p How man y piec es
by o ne in ch and a h alf by o n e in ch an d a quart er
o f it
It is all a question of how yo u cut them o ut Mos t
would have more wast e m ateri al left ove r than is necessary
many pieces could you get o ut o f the bloc k P
l
H a
.
a
,
,
.
.
H
4
.
-
The Tramp s
and
the Biscuits
.
Four me rry tramps bought borrowed foun d o r in some
mann r o bt ai ne d pos sess ion of a bo x o f biscuits which
e
,
,
,
,
M IS C ELLA N EO US PU ZZLES
man
161
pproache d the bo x devoure d exactly a qu arter o f
the numbe r o f biscuits except the o d d o n e left over which h e
threw as a bribe to their dog Later in the night a second man
awoke an d hit o n the same idea t aking a qu arter o f wh at rem ai ned
and giving the od d biscuit to the dog
Th e third an d fourth me n
di d preci sely the same in turn t aki ng a qu arter o f what they found
tr ee
,
o ne
a
,
.
,
,
.
,
.
,
giving the o dd biscuit t o the do g In the m orni ng they divided
what remai n ed equ all y amongst them and again gave the od d
bisc uit to the anim al Every man noticed the reduction in the
con ten ts o f the bo x b ut believi ng himself to be alone res po nsi ble
m ade n o comments Wh at is the smallest possible n umber o f
biscuits that there could have been i n the bo x whe n they first
‘
acquired it i
and
.
,
.
,
,
.
,
T HE C ANTE R B U R Y PU ZZLES
1 64
t ri angul ar numbe rs with fo ur stools an d for p yramidal numbe rs
wi th five stools In these c as e s there is always only o ne met hod
—
s
o
f
olution
th
t
is
piling
the
cheese
a
f
s
o
In the case o f three stools the first and fourth rows tell us that
e
i
n
1
T
h
2
che
s
s
ay be removed in 1 5 moves 5 in 3 1
m
e
e
7
7
4
se cond and fifth rows show th at with four stools 1 0 may be re
moved in 49 an d 2 1 in 3 2 1 moves Al so with five stools we fin d
from the thi rd an d sixth rows that 2 0 cheeses require 1 1 1 moves
But we also le arn from the t able the
an d 3 5 ch ees es 3 5 1 moves
necessary method of piling Thus with four stools an d 1 0 cheeses
the previous column shows th at we m ust m ake piles o f 6 an d 3
—
which will t ake 1 7 and 7 moves respectively th at is we first pile
th e six sm allest c h eeses in 1 7 moves o n o n e stool ; then we pile
then remove the
the next 3 cheeses o n another stoo l in 7 moves
nd
largest cheese in 1 move ; then repl ace the 3 in 7 moves ; a
finally replace the 6 in 1 7 : m aking in all the necessary 49 mo ves
Similarly we are told th at with five stools 3 5 cheeses m ust form
piles o f 20 1 0 an d 4 which will respect ively t ake 1 1 1 49 an d 1 5
mo ves
If the n umber o f cheeses in th e c ase o f four stools is n ot tri
an gular and in the case of five stools p yr amid al then there wi ll
be more than o ne way o f m aking th e piles and subsidi ary t ables
will be re quired This is the c ase with the R e ve s 8 cheeses But
I will le ave the re ader to work o ut for himself the ex ten si on o f
the problem
,
.
.
,
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’
.
.
.
.
2
.
The P ardon er s P uz z le
’
.
Th e diagram o n p age 1 65 will show
from the l arge black town and visited
how the Pardoner started
all the other towns o nce
and once onl y in fifteen st rai ght pilgrim ages
Se e No 3 20
The R oc k s Tour in A i n M
,
,
.
’
.
”
,
.
,
—
The
3
.
M i ller 3 P uz z le
.
’
.
The way to arrange the sacks o f flo ur is as follo ws - 2 , 78 1 56
39 4 Here each pair when m ultiplied by its sin gle n eigh bo ur
makes the n umbe r in the middle an d o nl y five o f the s ac ks nee d
,
,
.
,
,
m;
S O LUTI O NS
There
be
have
1 74,
j ust thre e other ways in which the y
are
bee n arr an ged (4 3 9 1 56 78 2 ; o r 3 5 8 1 74 29 6 ; o r 6
but the y all require the moving o f seven sacks
58
,
,
,
,
,
,
,
,
29 ,
.
,
The Knight de clared th at
marke d o ff o n his sh ield, with
,
as
a
m any as 575
rose at e ve ry co rner
.
be
Ho w this
C A N TE R BU R Y PU Z ZLES
THE
1 66
a
o
a
t
r
e
ult
is
chie
ed
be
re
i
d
b
y
efere
n
ce
the
ccomp
ny
a
l
z
a
m y
v
a
res
o
f
a
ar
e
66
—
h
n
d
a
di
gr
m
o
n
A
B
t
ere
squ
res
a
n
d
D
C
i
a
a
ing
J
A H I J
t h is s iz e to be fo rm e d ; the si z e A E F O gi v es 48
,
,
,
,
,
,
2
3
,
,
,
,
,
,
;
h m b 14 ; K O S D 16 ;
T
i
tot
l
number
is
thus
hese
e
a
2
T
h
r
u
C
t
5
5
7
4; Q
Q
p
groups have bee n treated as if each o f them represent e d a di fferent
siz ed square This is correct with the o ne exception that the
s o f the fo rm B N O P are ex actl y the same siz e as those
sq uare
o f the form K h m b
K
,
,
,
,
,
.
.
,
,
,
,
,
,
,
,
,
,
,
,
.
,
,
,
,
,
,
.
good lady explai ned that a hung that is made fast in a
barre l is like another bun g th at is falling o ut o f a b arrel because
The little
o ne o f them is i n secure an d the other is al so i ns ecure
re lationship pose r is readily understood when we are told th at the
paren tal co mm an d came from the father (who was also in the
ro om) an d not from the mothe r
The
.
.
.
pu z z le propounded by the j ovi al host o f the Tab ard I nn
o f Sou thwark h ad p rove d more popul ar th an an y other o f the
whole collect ion
I see my merry masters he cried
th at I
have sorely twist ed thy brains by m y little piece of craft Yet it is
b ut a simple m atter fo r me to put a true pi n t o f fine o ld ale in each
o f these two measures albeit o ne is o f five pints and the other o f
thre e pints without using an y other meas ure wh atever
The host o f the Tabard
I nn thereupon procee ded to explain
to th e pilgrims h o w this app arentl y im p ossible t ask could be done
He first fille d the 5 pint and 3 pint measure s and then tu rning the
tap all o wed the b arrel to run to w aste—a proc e eding ag ai nst which
The
”
.
,
,
,
.
,
”
,
.
.
-
-
,
,
,
T HE C A NTE R B U R Y PU ZZLES
168
one
e
a
t
i
n
i
f
a
s
tte
n
pro
rl
y
tched
It
l
o
st
ul
ted
f
ect
th
a
as
w
e
m
a
r
p
a
p
p
e
t
r
a
T
h
s
a
m
a
thr
e
pieces
us
as
s
ll
possible
illus
tion
e
t
b
m
e
o f th e
.
.
shows ho w to make the c uts and ho w to put the piece s together
while o ne o f the pieces cont ains only twelve o f the little sq u ares
,
.
—
T
e
h
9
,
C arpenter s P uz z le
’
.
The carpenter said th at he m ade a bo x whose intern al dimensions
were exactl y the same as the origin al block o f wood—that is 3 feet
by 1 foot by 1 foot He then pl ace d the carved pill ar in this bo x
and filled up all the vac ant s pace wi th a fin e dry san d which he
care full y shook do wn until he could get n o more i nto the bo x
Then h e remove d the pill a r t aking gre at care not to lose an y o f
the sand which o n being sh aken down alone in the bo x fille d a
space e qu al to o ne cubic foot
This was therefo re the quantity
o f wood that h ad bee n cut away
,
.
,
,
.
,
,
,
,
.
,
,
.
10
,
—The
P uz z le
f
o
the S qui re
’
s
Yeoman
.
The
illustration will show h o w three o f the arrows were removed
e ach to a neighbouring sq uare o n the signbo ard o f the Cheq uers
Inn so that still no arrow was in line with anothe r The bl ack
do ts indi cate the s q uares o n which the th ree arrows ori gin ally
sto od
,
.
.
S O LUTI O NS
As there are eighteen cards be arin g the letters CANTE RBURY
write the n umbers 1 to 1 8 in a circle as shown in
P ILG R I MS
the
Then write the first letter C
1
and e ac h
,
,
,
letter against the second number that
to be
vacant Thi s h as been done as far as the s econd R I f the re ader
completes the process b y pl acing Y against 2 P ag ainst 6 I against
1 0 an d so o n he will get the letters all pl aced in the followin g
order —C YAS NPTR E I R MBLU I R G which is the re quired arran ge
ment for the c ards C being at the top o f the p ack and G at th e
botto m
.
.
,
,
,
,
,
.
,
THE C A N TE R B U R Y PU ZZ LE S
1 70
—
The
12
.
M erchaut s P uz z le
'
.
pu z z le amounts to findin g the sm allest possible number th at
has ex actly sixty four divisors counting 1 an d the number itse lf as
The pilgrims might there
di viso rs The least n umber is
fo re have ridden in single file two an d two three an d thre e four
an d four and so o n in ex actly sixty four di fferent ways the last
ma nn er being in a single row of 7 560
The Merch ant was c areful to s ay th at the y were going over a
co mmon an d n o t to mention its si z e fo r it cert ai nl y would no t
be po ssible along an ordin ary ro ad I
To find how m an y diff erent numbers will di vide a given numbe r
”
=
b
c
N let N a§
where a b c
are p rime numbers
Then th e n umbe r o f di viso rs will be (p + r) (q + r) (r + r)
which includes as divisors 1 and N itse lf Thus in the c ase o f
my puz z le
This
-
,
,
.
,
,
,
,
-
,
,
,
.
,
,
,
,
'
,
,
,
.
.
3
=
6
0
2
,
5
7
P owers
x
3
3
3
x
3
Therefore 4
x
5
x
7
1
4
1
64
x 2 x 2
diviso rs
.
To
fin d the smallest number th at has a given number o f di visors
we must p roceed by trial
But it is import ant sometimes to note
whe ther o r no t the condition is th at the re shall be a gi ven number
o f di visors aud uo more
Fo r ex ample the sm allest n umber that
has se ven divisors an d no more is 6 4 while 2 4 has eight divisors
and might e qu all y fulfil the conditio ns
Th e stip ul ation as to
no more
was not necessary in the c ase o f m y pu z z le for n o
small e r number has more th an six t y four divisors
.
.
,
’
,
,
.
,
-
.
1 3 —The
.
M an of Law s P uz z le
’
.
The
fewest possible moves for getting the pri soners into their
dungeo ns in th e re quired numerical order are twent y six The
me n move in the followin g order —1 2 3 1 2 6 5 3 1 2 6 5
3 I 2 4 8 7 I 2 4 8 7 4 5 6
As there are never more than
-
.
,
.
.
.
.
.
,
,
,
,
,
,
,
,
.
,
,
,
,
,
,
,
,
,
,
,
T HE C ANTE RBU R Y PU ZZLES
1 7:
e
e
a
t
o
f
e
e
p
s
y
willing
to
eith
r
An
y
possibl
o
ar
t
w
d
an
a t
eat th e
s
mbi
n
tio
n
m
st
f
ll
i
n
to
the
following
group
e
o
f
o
n
a
u
(i Where
a
co
a
w
d
n
pie
is
dist
ib
t
d
entirel
y
mong the five first mentioned ;
u
e
r
e
r
e
a
th
a
e
a
whe
e
onl
y
the
ccommod
ting
p
ir
is
giv
n
pie
iii
a
o
f
n
;
o
e
r
(
)
ii
( )
where the other o f the p air is given pie ; (iv ) where both o f the
pair are given pie
1
0
ii
iii
iv
0
(
( ) 5 ( )
the eight participants A gre at
as 1 8 5 b y overlooking the f act
precisely the same eight guests would be
c l ass (ii ) though the a ccommod ating p air would
en tly o f the two dishes This is the point that U pset the
tions o f the comp any
.
,
.
.
.
.
.
.
.
,
.
,
.
.
,
,
.
.
16
The S omb ucmr s P uz z le
’
'
.
.
number that the Sompnour confided to the Wife o f Bath
was twent y nine and s he was told to begin her count at the Doctor
o f P hysic who will be seen in the illustration st andin g the s econd
o n her right
The first count of twenty nine f alls on the Shipm an
The second count falls on th e Doctor
who steps o ut o f the ring
Th e rem aining t h
who next steps o ut
o n the Cook
the Sompnour and the Miller Th e l adies would
therefo re h ave been left in possession h ad it not been for the
added
un fort u nate error o f th e goo d Wife An y multiple o f
to 2 9 would also h ave se rv ed the same pur pose begi nn ing the
co unt at the D oc tor
The
-
,
,
-
,
.
.
,
.
,
,
.
,
,
.
,
.
—
17
The
.
M ouk s P uz z le
’
.
The Mon k
might have pl a ced dogs in the ke nn els in two
san d n ine hundred an d twent y six di fferent w a ys so th at
sh o uld be ten dogs on every side
Th e numbe r o f do gs might
from twenty to fort y an d as long as the Monk k ep t
within thes e limits th e thing was always possible
The gen e ral so lution to this pu z z le is difficult
-
,
.
,
.
.
S O LUT I O NS
fo r
11
dogs
on
17
e very side of the square the number of di fferent
,
where
‘
u
I ou
3
3
68 71
2
3 811
48
1,
where u is even i f
,
n
we
is odd
,
an d
count only tho se
rrangements that are fundament ally diffe rent But if we count
all re ve rsal s an d reflections as di fferent as the Monk himself did
a
.
,
,
then 11 dogs (odd o r even) maybe pl aced in
wa ys
m ust
.
In order that there may be 72 dogs o n every side the number
n o t be less than 2 11 nor gre ater th an 471 but it ma
be
a
n
y
y
,
,
An e xtension o f the princ iple in vo l ved in this puz z le is given in
“
“
No 42 Th e Riddle o f the P ilgri ms
Se e also The Eight Villas
an d
A Dormitory Puz z le in A i n M
”
”
.
.
,
.
18
.
— The S hipman
.
’
s
P uz z le
.
sixt y four different ways in
m ade her ten annual vo yages
without ever going over the same course twi ce in a ye ar Every
ye ar she must n ec essa ril y end her te nth voyage at the islan d from
which she first set o ut
Th e are just two hundr d
whi ch the shi p M agdaleu might h ave
e
er
an d
-
.
.
19
of
.
—The
P uz z le
Chertsey was
c
orrect
.
The
curiously
1
T HE C A NTE RBU R Y PUZZ LES
74
form
a
See
pe rfec t square
also
p
.
.
How this is done
in A i u M
31
.
is
shown in the illust ra
.
f
f
H ere we have in deed a knotty problem Our text books tell
us that all Spheres are similar an d th at simil ar so lids are as the
There fore as the circumferences
cu be s o f corresponding lengt hs
o f th e two phi als were on e foot and two feet respectively an d the
cu be s o f o n e an d two added together m ake nine what we h ave to
fin d is two other numbers whose c u bes added together m ake nin e
Now this litt le ques
These n umbe rs clearly must be fraction al
tio n has reall y engaged the attention o f le arned men fo r two hun
dre d and fift y ye ars ; but although Peter de F erm at showed in the
se ven teen th cent u ry h o w an answer m ay be found in two fraction s
with a den omin ator o f no fewer th an twenty o n e figures not only
b y his method th at I h ave seen
are all the pu blishe d answers
in acc urate but nobod y h as ever published the mu ch sm aller result
i t t 3
n
Th e c u bes o f W
a
d
th at I n ow print
11
m
ad de d tog et her m ake ex actl y
o f a foot are the me asurements o f the circumferen ces o f the
phi als that the Doctor required to cont ai n the same quantit
liquid as those produced An eminent actu ary an d another
res po ndent h ave t aken the tro uble to cube o ut these numbe r
s
they both find my res ult quite correct
If the phi als were o n e foot an d three feet
respe ctively then an answer would be that the cubes
an d
added together m ake ex actl y 2 8
See also NO 6 1
W
Th e S ilver Cu bes
Given a known c ase for the ex pression o f a number as the sum
o r diffe rence o f two c u bes we c an
by formul a derive from it an
infini te n umber o f other c ases alte rn atel y positive an d negative
3
3
u
s
Th
Fermat s tarting f rom the known case 1
e
w
which
2
9 (
will call a fundament al case ) first obt ained a negative solution in
20
-
.
Thc P uz z le
the Doctor
o
P hysi c
o
.
-
.
,
.
,
,
.
,
.
-
,
,
,
,
-
.
7
.
,
.
,
.
.
,
.
,
,
,
.
,
,
T HE C A NTE RBU R Y PU Z ZLES
1 76
be lieve d to be th e max imum number o f rows possible ; an d though
a
e
a
ca
ith
pre
e
n
t
k
nowledge
I
nn
ot
rigorousl
y
demonstr
t
th
t
s
o ur
w
fift e en rows cannot be beaten I have a stron g pi0us Opinion
a
a
f
o
s
m
h
t
it
hi
he
t
nu
ber
rows
obt
i
n
ble
t
h
e
i
s
t a
g
-
,
.
22
nswer
n umbe rs
The a
the
.
—The
F rankli n
'
s
P uz z le
.
this pu z z le is shown in the illustration where
to 3 0 in the ten
the six te en bottles all
to
,
st raight direc tion s The trick consists in th e fact th at al th ough
the six bottles (3 5 6 9 1 0 and 1 5 ) in whi ch the flowe rs have
bee n pla ce d are no t removed yet the sixt ee n ne ed not oc cupy
e x actl y the sam e position o n th e t able as be fo re
The s qu are is
in fact formed o ne step fu rther to the le ft
,
.
,
,
,
,
,
,
.
,
,
.
23
.
—The
S qui re
’
s
P uz z le
.
The po rtrait may be dr awn in a sin gle lin e because it cont ains
only two points at which an od d n um ber o f lin es m ee t but it is
absolutely necessary to be in at o n e o f these poin ts an d e n d at
g
the other
One point is near the outer extremit y of the King s
left eye the o th e r is belo w it o n th e left chee k
,
’
.
.
S O LU T I O NS
17
'
7
five hundred silver pennies might h ave been pl aced in the
four b ags in accordance with the st ated con ditions in ex actly
di ffe r
ent ways If there h ad bee n a th ousan
d
coins
there
“
would be
ways It 15 a difficult problem m the partition
o f numbers
I have a single form u
l a for the solution of anyn umber
o f coins in the ca se o f fo ur b ags but it was e
xtremely h ard to con
S truct an d the best method 1s to find the twelve separ ate formulas
for the di fferent con gruences to the modulus 1 2
The
,
,
.
.
.
,
,
.
o
“
~
O
25
The P arson
.
’
s
P uz z le
.
A very little ex amin ation o f the origin al drawing will have
shown th e reader th at as he will h ave at first re ad the c onditio ns
We have therefore to
the pu z z le i s quit e impossible o f soluti on
,
,
.
12
T HE C A N TE RB U R Y PU ZZ L ES
1 78
loo k fo r so me loophole in the a ct ual conditions as they we re worded
If th e Parso n could get round t he source o f the river he could then
cross e very bridge once and once only on his way to church as
Th at this was no t prohibited
s hown in the anne x ed illustr atio n
Though the pl an showed all the bridge s in
we sh all soon find
his pari sh it only showed p art o f the parish it sel f It is no t
st at e d th at the river did no t t ake its rise in the p arish and since
it leads to the o nl y possible solution we must assume th at it did
It shou ld be noted
The an swe r wo uld be therefore as shown
that we are cle arly prevented from considering the possibili t y o f
u
o
u
a
e
tting
ound
the
mo
th
f
the
river
bec
se
told
it
join
d
w
e
ar
e
r
e
g
while no parish e ver
t he sea some hundred miles to t he south
e xtended a hundred miles
.
,
,
.
.
.
,
,
,
.
.
,
,
,
,
—
26
The
.
Haberdasher s P uz z le
’
.
The illustration will
be
sq
show how the tri an gular piece o f clot h may
cut in to four piec es that will fit togethe r and fo rm a pe rfec t
Bisec t AB in
making EF eq ual
uare
to F
and
.
to
EB
;
in E ; produce
AE
bisect AF i n G an d descri be the
THE C A N T E RBU R Y
1 80
PUZZLES
prac tical form as it was m ade in polished m ahogany with brass
b
e
e
a
t
h
e
n
g
s
use
by
cert
n
a
u
diences
It
will
s
en
th
t
four
a
i
f
r
e
o
i
h
piece s form a sort o f ch ai n an d th at when they are closed up i n
one di re ction they form the tri angle and when closed in the oth e r
direc tion they form the squ are
,
.
,
,
.
—
The Dyer s P u zz le
27
’
.
.
correct answer i s
diff erent ways Th e general
2
formula for six fie urs de lys for all squ ares gre ater th an 2 i s S I m pIy
this : Six times the squ are o f the number o f combin ations of 11
things t aken three at a time where n represents the n umber o f
—
—
eur
de
lys in the side o f the square Of course where u is even
h
s
the rem ainders in rows an d columns will be even and where rt is
o d d the rem ainders will be o d d
F o r further solution see No 3 5 8 in A i n M
The
.
-
-
,
,
.
,
.
28
.
The
Great
.
.
,
D i sp ute between the F ri ar
.
and
the S omp n ou r
.
In this little pro blem we attempted to show how by sophistic al
rea soning it may app arently h e proved th at the di agonal o f a
square is o f pre cisely the s ame length as two o f the sides Th e
puz z le was to di scover the fall ac y bec ause it is a v ery obvious
fallacy if we ad mit th at the shortest dist ance betwee n two poi nts
is a straight line But where does the error come in
Well it is perfectly true th at so long as our z igz ag path is
fo rmed o f steps parallel to the side s o f the square th at p ath m ust
be o f the same length as the t wo sides It does not m atter if yo u
h ave to use the most powerful microscope obt ain able ; the rule is
always t rue if the path is m ade u
steps
in
th
t
a
But
f
a
w
o
y
p
t he error lies in the assumption th at such a z ig z ag p ath c an ever
become a straight line Yo u may go o n increasi ng the number
o f step s infinite l —th at is there is no limit wh atever theoretic ally
y
to the number o f steps th at c an be m ade —but o u can never reac h
y
a straight line by s uch a method
In fact it is j ust as much
a
j ump to a straight lin e if you have a billion steps as it is at
,
,
.
,
.
,
.
.
.
,
.
S O LUT I O NS
181
the very outset to pass from t h e two sides to the di agon al It
would be j ust as absurd to say we might go on dropping m arbles in to
a b asket u ntil they become sovereigns as to sa
we
incre
se
c
a
n
a
y
the number of o ur s teps un til they become a straight hn e There
is the whole thin g in a nutsh ell
.
.
.
—
29
Chaucer s
P uz z le
’
.
.
Th e
surf ace o f water or other liquid is always spherical and
the greater an y S phere is the less is its convexity Hence the top
diameter of any vessel at the summit o f a mo unt ain will f orm th e
b ase of the segment of a greater sphere th an it would at t h e bo tto m
This sphere ; being greater must (from wh at h as been alre ad y said )
be less convex or in other words th e Spherical surface o f the
water must be less above the brim of the vessel and consequently
it wi ll hold less at the top of a mount ain than at the bottom The
re ader is therefore free to select any mount ain he likes in It aly
o r else where
,
.
.
,
,
,
,
,
.
i
'
Yeoman
'
f
The general form ula
The number of di fferent ways is
for su c h arr an gements when the n umber o f letters in the shnte nce
is 2 71
I
an d it is a p alindrome without di agon al re adin gs
is
M?
up
I thin k it will be well to give here a formula for the general
sol ution of e ach of the four most common forms of the di amond
letter puz z le By the word line I mean the complete di agon al
Thus in A B C an d D the lines re spectively cont ain 5 5 7 and 9
letters A h as a non p al indrome line (the word bei ng BOY) an d
1
the general solution for such c ases where the line cont ains m
let t ers is
Where the line is a single p alindrome with
i ts middle letter in the centre as in B the general formula is
Th is is the form of the R at c at cher s P uz z le an d
therefore the expres sion th at I h ave given above In c ases C an d
D we h ave do uble p alindromes but these two repre sent very
30
-
.
The P uz z le
the Canon
o
’
s
.
,
,
,
.
.
.
,
,
,
,
,
,
,
-
,
.
,
,
,
,
,
'
’
-
,
.
,
T HE C A N T ERB U RY PU ZZL ES
1 82
1 let t ers the
differen t t ypes In C where the lin e c ont ains 4n
general e xpre ssion is
But D is by far the m ost diffi
cul t case o f all
I had be tter he re st ate that in the di amonds under considerati on
—
these h ave to be dealt with
no di agon al rea dings are al lowed
ii
s pe ci all y in c ases where they are possi b le an d admitt ed ;
( )
a
m
a
o
a
w
a
s
iii
re
dings
b
ck
rd
rea din gs m ay st art an ywhere ;
g
y
( )
an d fo rwards us ing letters more t h an once in a single rea ding but
This l as t co n
no t the same letter twice i n imm e di ate success ion
dition will be underst oo d i f the reader gl ances at C wher e it is
impos sible to go forwards and bac kwards in a reading with out
—
re pea ti ng the first 0 touche d
a procee din g which I have said is
I n the case D it is ve ry differen t an d thi s is what
no t allowed
accounts fo r its great er difii culty
The formul a fo r D is this
.
,
,
.
.
.
'
,
,
.
,
.
,
.
(
n
5)
x
8
x
where the n umber o f letters i n the line is 4”
give n th ere are therefore 400 re adi ngs fo r u
Se e also Nos 25 6 257 and 258 in A i n M
.
,
,
.
1
2
.
I n the
.
.
L
LE L
LEV E L
LEV EV E L
LEV E LEV EL
LEV EV EL
LEV EL
LEL
L
m
e xam
e
P U ZZ LI N G T I M E S AT SO LVAM H ALL CAST L E
S I R H U GH E ! P LAI NS HI S P ROBLE M S
fri ends of Sir H ugh de F o rtib us were so perplexed over
many o f his strange p uz z les that at a gathering o f his kins men and
ret ainers he undertoo k to expl ain his posers
said he
some of the riddles th at I have put
Of a truth
THE
”
.
”
,
,
for th
atly t ax the wit o f the unlettered kn ave t o re d e ;
gre
would
yet Wi ll I try to Show the m anner thereof in such way that all m ay
have underst anding
Fo r m any t here be wh o c an not o f themselves
.
"
.
13 4
S O LU T I O NS
1
85
do all these things b ut will ye t study t h em to their gai n when they
be given the answers an d will t ake pleasure therein
,
”
,
32
.
—The Game of Band Ball
y
-
.
.
Hugh expl ained I n answer to this puz z le th at as the nine
holes were 3 00 2 50 20 0 3 25 2 75 3 50
an d 400 y ards
apar t if a m an co uld al w ay s strike the b all in a perfectl y str aight
lin e and send it at will a di st an c e of eithe r 1 2 5 yards o r 1 00 y ards
he might go ro und the whole course in 2 6 s trok es Thi s is clea rly
correct for if we cal l the 1 2 5 s tro k e the drive and the 1 00 stroke
the appro ach he co uld pl ay as follows
Th e first hole c o uld be
re ached in 3 appro aches the second in 2 drives the third in 2
appro aches
the fourth in 2 appro aches an d I drive the fifth in
a
drives
1
b
a
c
w
rd
a
ppro
ch the sixth in 2 drives and I
a
n
d
k
a
3
appro ach
the seventh in 1 drive an d I appro ac h the eighth in
s
T
ar
ppro
che
here
thus
a
e
6
a
drives
a
n
d
the
ninth
hole
i
n
2
3
4
strok es in all and the fe at c annot be performed in fewer
Sir
,
,
,
,
,
,
,
,
,
,
.
,
-
,
,
,
,
,
,
,
,
.
,
.
,
—
Tilti ug
33
.
at
the Ri ng
.
“
By my hal idame ! excl aimed Sir Hugh
if some o f yo u
v arlets had been put in ch ains which for their sins they do truly
,
,
deserve then wo uld they well know m ayh ap that the length of
an y ch ain h aving like rings i s equal to the inner width of a ring
multiplied by the numberof rings and added to twice the t hi ckness
of the iron whereof it is m ade It m ay be S hown that the inner
width of the rings used i n the tilting was o ne in c h and two thirds
,
,
,
’
.
-
THE C A NTE RB U RY PUZZ L ES
1 86
thereo f and the numbe r of ring s Stephen Mal et did win was three
and those th at fell to Henr y de Gourn ay would be nin e
1 in
6 ln
The kni ght was quite correct for 1 § in x 3
1 6 in
Thus D e Gourn ay be at Mal et
an d 1 } in x 9 + 1 in
by six rings Th e drawing showing the rings m ay assist the reader
in verifyi ng the answer and help him to see why the inner wi dth o f
a lin k multiplied b y the number of lin k s and added to twice th e
t hickness of the iron gives the exact length It will be noticed that
every link put on the chai n lo ses a length equal to twice the thick
nes s o f the i ron
,
,
”
.
.
,
.
,
.
.
.
.
.
.
.
—
Th
34
e
.
N oble D emoiselle
.
Som e here hav e asked me continued Sir H ugh how they
may find the cell in the D u ngeon o f the D eath s head wherei n the
noble maide n was c ast B eshrew me ! but tis eas y with al whe n
o
In attempting to pass
y u do but kno w how to do it
,
,
’
-
’
.
.
every door once and never more you m ust t ake hee d th at
cell ha th two doors o r four which be even numbers except mo
c ells
whi ch have but three Now certes y ou c annot go i n and
ut o f any place passing through all the doors o n ce an d n o more
o
i f the num ber o f doors be an odd n umber
But as there b e but
two such odd cells y et m a we by b egi nn i ng at the o ne and endi n
y
g
at t he other so m a ke o ur j ourne y in m an y w ys with succ
a
e ss
a
I pr y yo u albeit to m ark th at onl y o ne of these o dd cells lie th o n
,
,
,
,
,
.
,
,
,
,
.
,
,
,
,
.
,
THE C A N T E R B U R Y PU Z Z LES
1 88
that they do ad d u p to twenty and three in all the twelve lines
o f th ree th a t are u pon the b utt
I think i t well here to s upplement the sol ution o f De F o rt ib us
with a few rem arks o f my own Th e nineteen numbers m ay be
ay
so a rr anged th at the lines will add up to an y nu m ber we m
exc epting 3 0 In some
c hoose to s elect from 2 2 to 3 8 inclusive
ca ses there are several di fferent solutions b ut in the c ase of 2 3
I give one o f these
To obt ain the second
t h e re are only two
sol ution exch ange respectively 7 1 0 5 8 9 in the ill ustr ation
wi t h 1 3 4 1 7 2 1 5 Also exch ange 1 8 with 1 2 an d the other
numbers m ay rem ain unmoved In every inst ance there must be
an even number in the centra l pl ace a n d an y such number from
Every solution has its complement ary Thus
2 to 1 8 may occur
if for every number in the acco mp any in g drawing we s ubstitute
the di fference between it an d 20 we get the solution m the c ase of
Simil arly from the arr angement in the origin al drawi ng we
37
m ay at once obt ai n a solution for the c ase of 3 8
hat s
”
.
.
.
,
,
'
.
.
,
,
,
,
,
,
.
,
,
,
,
,
.
,
.
.
,
,
.
,
,
.
36
.
—The
D omon K cap
’
In this c ase Sir H ugh h ad gre atly perplexed his chief builder
by dem anding th at he sho uld m ake a window me asuring o ne foot
0"
r
an d divided b y b ars into eight lights
side
h
avi ng all
eve y
the i r sides equal Th e illustration will show how this was to be
,
‘
.
S O LU T I O NS
1 89
done It will be seen th at if e ach side of the window me asures
one foot then e ach of the eight t ri angul ar lights is six in ches o n
every side
said De F ortib us slyly to the
Of a truth m aster builder
I did n o t tell thee th at the window must be square as
architect
it is most cert ain it never co uld be
s
.
,
.
,
,
,
,
.
—
The
37
.
Crescent
and
”
the Cross
.
By the toes of St Moden excl aimed Sir Hugh de Fo rtibus
‘
when this puz z le was brought up my poo r wit hath never shaped
It
a more cunning artifice or an y more bewitc hing to look upon
c ame to me as in a vision an d Ofttimes
m arvelled at the
.
,
f
,
.
,
its excee ding di fficult y My m asters and ki nsmen
it is done in this wise
Th e worthy knight then poi nted o ut that the crescent was o f
—
the two dist ances a to b
a p art icul ar an d somewh at irregul ar form
an d c to d being st r aight lines an d the arcs ac an d bd being pre
c i s e ly similar
He showed th at if the c uts be m ade as in F igure I
the four pieces will fit together an d form a perfect square as shown
in F igure 2 if W e there only regard the three curved lines B y
no w m aking the straight cuts al so shown in F igure 2 we get the
t e n pieces that fi t together as in F igure 3 an d form a perfectly
oss The proportio ns o f the crescent and
symm etric al Gree k c r
.
,
”
.
,
,
.
,
.
,
,
,
.
,
T HE C A N TE RB U R Y PU Z Z L ES
1 90
origi nal illustration were correct and th e solution
can be de monstrated to be absolutel y exact and not m erel y ap
proxim at e
I ha ve a s olu ti on in considerably fewer piec es b ut it is far
mo re difficult to underst an d th an the above method i n whi ch the
problem is simplified by introducing the intermediat e sq uare
o
th e
cr ss
in th e
,
.
'
,
,
.
—
T
h
e
8
3
Amulet
.
.
pu z z le was to place your pencil on the A at th e top o f th e
amulet and coun t in h o w m an y di ff erent w ays yo u could trac e o ut
t h e word
Abrac adabra downwards always passing from a
letter to an adj oining o ne
The
,
.
A
B B
R R R
A A A A
C O C C C
A A A A A A
D D D D D D D
A A A A A A A A
B B B B B B B B B
R R R R R R R R R R
A A A A A A A A A A A
No w
m ar k y e fine fellows s ai d Sir Hugh to so me who had
be sought him to expl ai n that at the very first st art there be two
ways ope n whiche ver B y e select there will be two several ways
o f proc ee ding (
twice times two are four) whichever R y e sel ect
there be two ways o f going o n (t wice times four are eight ) and so
on
i
ach letter in order fro m A down w ards ma
n
t
l
the
end
E
so
y
u
be reach ed in 2 4 8 1 6 3 2 etc ways Therefore as there be
ten lin es o r steps in all fro m A to the bottom all y e n ee d do is to
m ultiply ten 2 s together and truly the result 1 024 is the an swer
thou dost seek
,
,
,
,
,
,
.
,
,
,
,
,
.
,
,
.
'
,
’
,
,
,
"
.
39
Thoug h
it is
.
The S na il
on
the F lag stafi
’
.
the re was no n ee d to t ake down an d meas ure the st
un doubt e dly nec es sary to find i ts heigh t be fore th
T HE C A NTE RB U RY PUZZLES
1 92
~
in in ches o f the side o f that squ are so the acc urac y o f the
can be checked almos t at a gl ance
Sir H ugh de F o rtib us m ade some
on the occ asion th at are not altogether uninterest i ng to d ay
,
.
-
.
F riends
an d
ret ai ners he s aid
if the strange o ffsp ri ng
my poor wit about which we h ave held ple asan
hat h m ayh ap h ad some sm all in teres t for ye
serve to c all to min
be se t with enigm as
and al beit such as
st and ing y et there
,
,
,
.
,
S O LU T I O NS
1 93
come after us will ever strive for the answer Whe ther success
do attend or do n o t attend our l abo ur it is well th at we m ak e the
attempt ; for ti s tr ul y good an d honour able to tr a n the mind an d
the wit an d the fan cy of man for out of such doth iss ue all m anner
o f g ood in way s unforeseen for them th at do come af ter us
do
.
,
i
’
,
,
,
.
TH E M E RR Y M O N KS O F RID D LE W E LL
—
i
d
l
e of the F i sh p ond
e
R
d
1
T
h
4
-
.
.
N U M BE R the fish b askets in the i ll ustration from 1 to 1 2 in the
di rection th at B rother Jon ath an i s seen to be going St arting
from 1 proceed as follows where I to 4 me ans t ake the
from b asket No 1 an d tran s fer it to b asket No 4
1 t o 4 5 to 8 9 to 1 2 3 to 6 7 t o 1 0 1 1 to 2 an d
the las t revol ution to 1 m aking three revol utions in a ll Or
c an proceed t hi s way
1
to
1
1
1
1
0
to
to
to
8
0
o
2
t
6
t
2
3
4
5
7
g
It is e asy to s olve in fo ur revolutions but the solutions in three
are more di fficult to di s cover
.
,
,
,
.
.
,
,
,
,
,
,
.
,
,
,
,
.
,
,
,
.
—
h
e
2
T
4
R i ddle
the P i lgrims
f
If it were not for the Abbot s conditions th at the num be r of
gu es ts in any room may not exceed t hree an d th at every room
must be occ upied it would h ave been possible to accommodate
eit her 24 2 7 3 0 33 3 6 3 9 or 42 pilgri m s But to accommodate
2 4 pilgrim s so th at there s h all be twi c e as m an y sleepin g on th e
upper floor as o n the lower floor an d eleven persons o n e a ch side
of the b ui lding it wi ll be found neces sary to leave some of t
rooms empt y If on the other h and we try to put up 3 3 3 6
o r 42 pilgrims we s h all find th a t in every c ase we are obliged
place more th an three pers ons in some of the rooms Thus
know that the n umber of pilgrims origin al ly anno unced
it will be remembered it was possible to accom modate un
.
o
.
’
,
,
,
,
,
,
,
.
,
,
,
.
,
,
,
,
.
,
194
,
T HE C A N TE R BU R Y P UZ ZLES
1 96
—
The
44
e
i
n
W
f
The question was : D id Brother Benj amin t ake more wine
the bottle th an w ater from the j ug ?
Or did he t
from the jug th an wine from the bottle ? He (1
same quantity o f wine was transferred from the
was t aken from the j ug
Let us assume th at the
a quarter o f a pint
There was a pint of wine in the bottle and a
pint of water in the j u g After the first m anipul ation the bottle
cont ains three quarters o f a pint o f wine an d the j ug o n e pint of
water mixed with a quarter o f a pint of wine Now the second
transaction con sists in t aking away a fifth of the contents of the j ug
that is o ne fifth of a pint of water mixed with one fifth of a qu arter
o f a pint o f win e
We thus le ave behind in the j ug fo ur fif t h s o f
a q uarter o f a p int of wine— th at i s one fifth o f a pint — while wen
i
“
l
tran sfer from the j ug to the bottle an equ al qu an tit y (o ne fifth oi
a pint o f w ater
)
—
T
h
e
i
l
R
d
d
e of the C ellarer
5
4
Riddle of the S ack
.
o
.
.
.
.
-
,
,
.
-
-
,
-
.
-
,
-
.
.
.
T ere were 1 00 pints of wine in the c ask and on thi rt y occasions
John the Cell arer h ad stolen a pin t an d repl aced it with
water
After the first theft the wine left in the c ask
h
.
,
S O LUTI O NS
1
97
a
pints
fter
the
second
theft
the
wine
in
the
c
sk
wou
d
be
a
l
;
99
i
u
pints
the
sq
re
of
a
0
0
a
di
v
ided
b
y
fter
the
third
theft
1
(
fi
99
)
0 59
3
1
there woul d rem ain 3 6 5 56 (the cu be o f 99 divided by the squ are
o f 1 00 )
after the fo u rth theft there wo uld rem ain the fo u rth power
u be of 1 00 ; an d after the thirtieth t h eft
of
divided
by
the
c
99
th ere would rem ain in the cask the thirtieth po wer of 99 divi ded b y
the twenty ninth power of
This by the ordin ary method of
c alcul ation gives us a n umber composed o f 5 9 figures to be divided
by a number composed of 5 8 figures 1 But by the use of logarithms
it m ay be quickly ascert ained that the required quantity is very
93
nearly 73 1 0 5 pints of wine left in the c ask Cons equently the
cell arer stole ne arly
pints Th e monks doubtless omitted
the answer for the re ason th at they h ad no t ables of logarithms
an d did not c are to f ace the t ask of m aking th at long an d tediou s
calcul ati on in order to get the quantity to a nicet y as the wily
cellarer h ad stipul ated
B y a simplified process of c alc ul ation I have ascert ained that
the ex act qu antity of wine stolen wo uld be
l }
2
9
-
.
.
,
,
.
,
2 6 02 9962 66 1 1 7 1 95 772 6 998 49076 83 2 85 05 77473 2 3 73 76473 2 3 55 5 65
2 999
A man wh o would in volve the mon astery in
fift y eight decim als deserved severe punishment
pints
.
-
fraction
a
of
.
—The
the Crusaders
f
Th e correct answer is th at there would h ave been
Crusaders wh o co uld form them s elves into a square 776 by 776 ;
the y co uld form 1 1 3
an d aft er the str anger j oined their rank s
—
men th at is 73 by 73 Or 1 1 3 x 73
squ ares of
—
so
c alled P elli an Equation re
This is a p artic ul ar c ase o f the
S pec tin g which see A i n M p 1 64
6
4
.
R i ddle
o
.
,
,
?
.
,
,
.
.
.
—
e of S t E dmonds ba ry
idd
l
R
T
h
e
47
.
.
Th e reader is aware th at there
Now
site whole numbers
.
,
are
.
prime n umbers an d compo
c an not be a prime number
,
T HE C A N T ERB U RY PUZ ZL ES
198
becau se if it were the onl y possible answers would be those pro pos ed
by Brother Benj amin an d rej e c ted by F ather P eter Also it c annot
have more th an two factors or the an swer would be indetermin ate
As a m atter o f fact
equ al s 2 3 9 x 46 49 (both primes ) an d
since e ach cat killed more mi c e t h an there were c ats the answer
m ust be 2 3 9 c ats See al so the Introduction p 1 8
Tre ated generally thi s problem consists in finding the factors
.
.
,
,
,
,
.
,
.
.
.
,
if
n umbers of the form
an y, o f
,
“
10
1
9
Amusante
es
o
Luc as in his L Ari thmé ti qa e
l
n
um
b
er
v
a
f
g
c urious t ables which he obt ained from an a rithmetic al tre atise
c alled the Talkhys by Ibn Alb ann a an Arabi an m athem atici an
an d astronomer of the first h al f of the thirteenth cent u ry
In the
P a ri s N ation al Library are sever al m an uscripts de aling with the
Talkhys an d a co m ment ary b y Alkalacad i who died in 1 48 6
Among the t ables given by Lu c as is one giving all the factors of
n umbers of the above form up to n = 1 8 It s eems almost in co n
c e ivab le th at Ar abi ans of th a t d ate co u ld find the
n = 1 7 as given in my Introdu ction
But I re ad Lu c as as st ating
that they are given in Talkhys though an e m inent m ath e m a
tic ian re ads him differently an d suggests to me th at the y were
discovered by Lu c as himself This c an o f co urse be settled by
an ex amin ation of Talkh s b ut this has not been possible during
y
the war
Th e diffic ult y lies wholly with those c ases where n is a prime
number If n = 2 we get the prime 1 1 Th e factors when n = 3 5
1 1 an d 1 3 a re re s pe c tively (3
an d
1
(4
a
I
h
ve given in these p ages the f actors where
5
3
( 79
n = 7 an d 1 7
Th e f actors when n 1 9 2 3 an d 3 7 are
!
there are an y When n 2 9 the fac to rs are
’
,
,
,
,
,
.
,
.
,
.
,
.
,
,
.
,
,
,
.
.
.
,
,
,
:
.
,
.
,
Mr Osc ar H O pp e
.
d ti
kh
in t h e I n tro
te io us wo r
d
i ngs
of
uc
on,
,
he
e su c c e e
th e So ci e ty fo r
,
k i f m m
v tig t th
p v g th umb
N e w Yo r
w as le d t o in
e
in ro in
of
dd
1 4 th
Fb
e
,
n or
es
a e
e n
ru ary 1 9 1 8
.
s
e
th at ,
ft
a
e c as e o f n
er
to b e
a
e r re a
di g
n
my
ft
1 9 , an d a
p im
r
e
.
He
er
s ub
,
P UZ Z LES
T H E C A NTE RBU R Y
200
white discs move in the directions o f the h ands of a cloc k an d the
white figures o n bl ack discs the other way Th e followi ng are the
n umbers in the order in which they move Whether you h ave to
m ak e a simple move or a le aping move will be cle ar fro m the posi
Th e moves enclosed
t ion as yo u never c an h ave an altern ative
in brackets are to be pl ayed five times over : 6 7 8 6 5 4 7 8
1
I
6
2
z
2
0
6
1
1
1
2
8
0
6
1
3
5
3
s
4
4
)
(
5 4 3
7
9
9
,
.
.
.
,
,
,
.
.
.
.
.
.
1
1
1
0
8
,
(7
9
6 5 4 3 2 8 9
,
,
.
.
,
,
1 0, 1 1
,
1
,
.
.
.
.
.
8
7
9
,
,
,
.
6 5 4 3
,
,
.
.
.
,
.
.
,
.
,
,
,
.
8
7
9
2, 1 2,
,
,
,
,
,
.
,
.
1 0, 1 1 ,
a
1
We
thus
h
a
ve
m
de
1
8
3
4
moves within the conditions the bl ack frogs h ave ch anged pl aces
with the whi te ones an d 1 an d 1 2 are side by side in the positions
stipul ated
—
Th e general sol ution in the c ase of thi s pu z z le is 3 n + 2 n 2
moves where the n umber of frogs of e ach colo ur is n Th e law
governing the sequence of moves is e asily discovered by an ex
n
a
d 4
amin ation of the s impler c ases where ri = z
3
If inste ad of 1 1 an d 1 2 ch anging pl aces the 6 an d 7 must
interch ange the expression is n + 4n + 2 move s If we give it the
value 6 as in the ex ample of the F rogs R ing the number of moves
would be 62
F o r a general sol ution o f the c as e where frogs of o n e colour
reverse their order le aving the bl ank sp ace in the s ame position
an d e ach frog is allowed to be moved in either direction (le aping
o f co u rse over his own colour
se e
e Gr asshopper P u z z le
in
T
h
)
A i n M p 1 93
,
,
,
,
,
,
1 0, 1 1 ,
,
,
,
2 , 1 0, 1 1
,
2
.
,
,
.
’
.
,
,
,
.
,
,
,
2
.
,
’
,
,
.
,
,
,
,
.
.
,
,
.
.
TH E ST RAN G E E SCAP E O F TH E
KI N G S
’
S
T
E
E
R
J
ALTHO U G H the king s j ester pro mi sed that he would the reaft e r
m ake the m ann e r thereof plain to all there is no reco rd o f his
having ever done so I will therefore submit to the reader my o wn
views as to the prob ab le solutions to the mysteries involved
’
”
,
.
.
49
.
The Mysteri ous Rop e
.
When the j ester divided his rope in h alf it does not follow
th at he cut it into two p arts each h alf the origin al length o f the
rope No do ubt he simply unt wisted the stran ds and so divided
it into two ropes e ach of the origin al length but o ne h alf the thick
n ess He would thus be able to tie the two together and m ake a
rope nearly twice the origin al length with whi c h it is quite co n
ce i vab le th at he m ade good his esc ape from the dungeon
”
,
,
.
,
-
,
,
.
,
.
50
,
—The
U nd ergroun d M az e
.
How did the j ester find his way o ut o f the m az e in the dar k P
He h ad sirnply to grope his way to a wall and then keep on walk
ing without once removing his left h and (or right h and) from the
wall St arting from A the dotted line will m ake the route clear
when he goes to the left If the re ader tries the route to the right
in the same way he will be eq ually successful ; in fact the two
routes unite and cover every p art of the walls of the m az e except
—
those two det ache d p arts on the left h and side o ne piece like a
.
,
.
,
-
201
T HE C A NTE RBU R Y
2 02
P UZZLES
U and the other li ke a distorted E This rule will apply to the
m aj ority o f m az es an d p uz z le gardens ; but if the centre were e n
,
.
closed b y ah isol ated wall in the form o f a split ri ng the j ester
would sim ply h ave gone round and round this ring
See the article Maz es and How to Thre ad Them in A i n M
,
.
”
,
,
1
5
.
.
.
,
— The S ecret Lock
.
p uz z le ent ailed the findin g o f an English word o f three
letters e ac h letter being found o n a different di al No w there
is n o Engli sh word compo sed o f con sonants alone an d the only
vowel appearing anywhere on the di als is Y No English word
be gins with Y an d h as the two other letters conson ants an d all the
words o f three letters ending in Y (with two conson ants) either begin
with an S or h ave H L or R as their second letter But thes e
four conson ants do not appe ar Therefore Y m ust occur in the
middle an d the only word th at I c an find is P Y!
an d there
can be little doubt th at this was the word
At any r ate it solves
o ur p uz z le
Thi s
.
,
,
,
.
,
,
.
,
.
,
,
.
.
52
—Crossi ng
.
the
,
M oat
.
doubt some o f m y readers wi ll smile at the st atement th at
in a bo at o n smooth w ater c an p ull hi mself across with
a
the tiller rope ! But it is a fact If the j es ter h ad fastened the
end o f hi s rope to the stern of the bo at an d then while st andi ng
in the bows h ad given a series of violent j erks the bo at would have
been propelled forw ard Thi s has often been put to a practic al
test an d it is said that a speed of two or three miles an ho ur m ay
be att ained See W W R ouse B all s M athemati cal R ecreations
No
man
.
,
,
,
.
,
’
.
.
.
.
3 04
T HE C A N T E R BU R Y
54
If
.
—Bridg ing
PUZZLES
the D i tch
.
The solution to this pu z z le is best explain e d b y the illustration
he had pl aced his eight pl anks in the m anner shown ,
.
,
the angle o f the ditch he would h ave been able to cross without
much trouble The king s j ester might thus have well overco me
all hi s difficulties an d got safel y away as he h as told us th at he
succ e eded i n doi ng
,
’
.
,
.
TH E SQ U I R E S C H RI ST M AS P U ZZ LE P ARTY
’
H OW TH E VARI O U S TRI CK S
WERE
D ON E
THE record o f one of Squire D avidge s an nual
P uz z le P arties
mad e by the old gentlem an s young lady relative who had often
spent a merry Christm as at Stoke Co urcy Hall does not cont ain
’
,
’
,
,
the solutions o f the mysteries So I wi ll give my own answers to
th e p uz z les an d try to m ake them as cle ar as possible to those who
may be more o r less novices in such m atters
.
.
55
.
—The
Three Teacups
.
Miss Charit y Loc ky er clearly m ust have h ad
tric k up her
sle eve an d I thi nk it highly prob able th at it was conceived
She proposed that ten l umps o f sugar
o n the following lines
should be placed in three te acups so that there should be an o dd
a
,
.
,
number o f lumps in every cup The illustration perhaps shows
a
u
i
o
n
u
iss
h
rity
s
nswer
the
fig
res
the
c
ps
ind
c
te the
n
d
a
a
M
C a
number o f l umps that h ave been separ ately placed in them By
pl acing the c up th at holds one lump inside the one that holds
two lumps it can be correctly st ated th at every cup cont ains an
On e cup holds seven lump s another holds
o dd number o f lumps
It is e vident
o ne lump while the t hird c up holds three lum ps
.
’
,
.
,
,
.
.
,
2 06
C A N T E RBU R Y
THE
PU ZZ LES
th at if a cup cont ains another cup it also cont ains the content s
of th at second c up
There are i n all fifteen di fferent solutions to this pu z z le
Here
.
.
two numbers in a triplet represent respe ctively t he
number of lumps to be placed in the inner an d o uter o f the two
c ups th at are pl aced one inside the other It will be noted that
the outer cup of the pair m ay itself be empty
Th e first
.
.
56
.
—The
E leven P e nni es
.
It is rather evident th at the trick in this pu z z le was as follows
F rom the eleven coins t ake five
then add four (to those alre ady
t aken away) and yo u le ave nine—in the second heap o f those
removed l
—
T
he
57
.
Chri stmas Gees e
.
sent ex actly 1 0 1 geese to m arket Jabe z first sold
Mr J asper Tyler h alf of the flo c k an d h al f a goose over (that is
s
F
or
gee
e
le
ving
he
then
sold
rmer
Avent
1
a
a
a
C
S H f
5
third of wh at rem ained an d a thi rd of a goose over (th at i s 1 6 +
or 1 7 geese le aving 3 3 ) he then sold Widow F oster a quarter of
—
—
a
a
s
8
wh at rem ained and three qu rters of goo e over (th at is H 2o r
he
next
sold
Ned
ollier
a
fi
fth
of
wh
a
t
he
C
geese
le
a
ving
2
i
4)
9
th
a
t
is
h ad left an d gave him a fifth of a goose for the missus
(
1
geese
le
vin
g
He
then
too
k
these
b
c
k
to
his
r
a
a
o
4
5
9
42
m aster
—
l
e
d
b
u
a
k
N
ers
e
h
T
C
m
h
8
5
F armer R ouse
.
.
,
-
,
,
3
1
,
,
-
,
,
,
,
.
'
.
.
little j est on the part o f Maj or Trench ard is another trick
puz z le and the face of the rog uish boy on the extreme right with
This
,
,
T HE C A NTE R B U R Y PUZZ LES
20 8
twe n ty o ne b ut I h ave not counted them I h ave recorded
fo urtee n o f these and possibly there are m ore An y o ne o f these
would se rve o ur purpose except for the condition th at the tenth
hot pudding Thi s was
stro ke sh all end at the ste am n
-
-
-
.
.
,
,
.
—
(1q
to stop a plur alit y o f solutions c alled b y the m ak er o f
chess problem s coo ks
I am not aware o f more th an o ne solu
tion to this pu z z le ; but as I may not have recorded all the tours
I c ann ot mak e a positive st atement o n the point at the time o f
”
.
,
6o
.
Under the M istletoe Bough
.
Every body was found to h ave kissed everybody else once un der
the mistletoe with the following additions an d exceptions : NO
m ale kissed a m al e ; no m an kiss ed a m arried wom an except his
o wn wife ; all the b achelors an d boys kissed all the m aidens an d
girls twice ; the widower did not ki ss anybody and the widows
did not kiss each other Every kiss was returned and the double
pe rformance was to coun t as o ne kiss I n m aki ng a list o f the
,
,
.
,
.
mp ny
S O LU T I O NS
we
209
le ave o ut the widower
took no part in the osculatory exercise
co
a
,
c an
al
together bec ause
,
.
M
a
rried
co
u
ples
7
3
12
10
Widows
B ac helors and Boys
Maidens an d Girl s
Tot al
P
ersons
39
Now i f every o ne o f these 3 9 persons kis sed everybody else
once the number of kisses would be 741 ; an d if the 1 2 b achelors
an d boys e ach ld sse d the 1 0 m aidens an d girls onc e again we m ust
ad d 1 20 m aking a tot al of 8 6 1 kisses
But as no m arried m an
kissed a m arried wom an other th an his own wife we must deduct
1
1
k
2
a
isses
no
m
le
kissed
nother
m
le
we
must
deduct
as
a
a
;
4
7
kisses ; an d as no widow kissed another widow we must deduct 3
ki sses We h ave therefore to deduct 42+ 1 71 + 3 21 6 kisses
from the above tot al o f 8 61 an d the result 645 represents exactly
the number o f kisses th at were actu ally given under the mistletoe
bough
,
,
,
,
.
,
.
,
,
.
,
,
,
,
9
,
.
61
.
—The
S i lver Cu bes
;
There IS no limi t to the
give two cubes whose s um
n umber of di fferent dimensions th at will
sh all be exactly seventeen cubic inches
Here is the answer in the sm allest possible numbers One of the
silver cubes m ust m easure
inches along each edge and the
inch
If
the
re
ader likes to undert ake
other must m easure T
hi s?
the t ask o f cubing each number (th at is multiply e ach number
twi c e by itself) he will find that when added together the contents
Th e
exactly equal seventeen c ubic inches Se e also No 20
P uz z le of the D octor of P hysi c
.
.
,
.
,
,
.
”
.
.
,
TH E AD VE N T U RE S O F TH E P U ZZ LE CLU B
—
62
The
.
Ambiguous P hotograp h
.
by o ne the m embers o f the Club succeeded in disco v erin g
the ke y to the mystery of the A mbiguous P hotogr aph excep t
Churto n who was at length persu aded to
give it up
Herbert
B ayn es then pointed o ut to him th at the co at th at Lord Marksfo rd
was c arrying over his arm was a l ady s co at bec ause the buttons
are o n the left side wherea s a m an s co at always h as the buttons
Lord Marksfo rd would not be likely to
o n the right h and side
walk about the streets o f P aris with a lady s co at over his arm
unless he was accom p an ying the own er He was therefore walking
with the l ady
As they were t al ki ng a wai ter b rought a telegram to Bayn es
Here yo u are he s aid after reading the message
A wire
D on t bother about photo
from D ove y :
F ind l ady was the
gentlem an s sist er p assing through P aris Th at settles it Yo u
might notice that the l ady was lightly cl ad an d therefore the co at
might well be hers But it is clear that the rain was only a sudden
shower an d no doub t they were close to their destination and she
did no t think it worth while to put the coat o n
ONE
,
”
.
,
’
,
’
,
-
.
’
.
.
.
”
.
,
,
’
.
’
’
.
.
,
,
.
,
,
”
.
—
The
63
.
Corn i sh Clifi Mystery
r
.
the Cornish Cliff Mystery was very
simple when he gave it Yet it was an ingenious trick that the
two crimin als adopt ed an d it would h ave completely succeeded
h ad not o ur friends from the P uz z le Club accident ally appe ared on
Melville s explan ation
’
of
.
,
210
THE C A N TE RBU R Y PUZZLES
212
Mystery may b e trac ed without
p ath e ver crossing
E went to the north o r t
,
an y
It depends whether the b Utle r
o f the gamekeeper s cott age an d
south o r the north o f the h all But it will be found that the
persons who co uld h ave appro ached Mr Cyril H astings wit
,
,
’
,
.
.
c ro ss ing a p ath we re the butler E an d the m an C It was
e ver a fact th at the butler retired to bed five minutes before
night where as Mr H astings did n o t le ave his fri end s hou se
midnight Therefore the cri min al must have bee n the man
entered the park at C
,
,
,
.
,
,
’
.
,
.
.
—
66
The
Buri ed Treas ure
.
.
field must h ave cont ained between 1 79 an d 1 80
acres
be more ex act
H ad the meas urements
then
an d 4 f urlongs respe ctively from s u cce ssive corners
2
ac res in are a
field would h ave been
One method of solving this problem is as follows F ind the
o f tri angle AP B in term s of x the side of the squ are
Do
the result = xy D ivide by x an d then square an d we h ave
2
2
val ue o f y in terms o f 96 Simil arly find v al ue of 2
2= 2
2
o f x ; then so lve the eq u ation y + z
3 which will come
2=
4—
2
—
=
=
the form x 20x
Therefore
1
0
6
x
+ J 3 17
37
squ are f urlongs very ne arl y an d as there are ten acres
square furlong this equal s
If
acres
tive root o f the equation we get the are a o f th
acres in which
The
.
,
,
,
.
.
.
,
.
,
'
.
,
:
.
,
,
,
.
,
,
.
.
S O LUTI O NS
2 13
field as in D i agram 2 But this solution is exc luded by the
Th e words
di tion th at the tre asu re was buried in the field
,
.
.
were The document
st ates cle arly that the field is
an d th at the treas ure l s buried in it
,
”
.
TH E P R O F E SSO R S P U ZZ LE S
’
67
.
—The
Coi nage P uz z le
.
THE poin t o f this p uz z le turns o n the fact th at i f the m agic
sq u are were to be composed o f whole n umbers addin g up 1 5 in
all w ays the two m u st be pl aced in o n e of the corners
0 th
fractions must be used an d these are supplied in the pu z z le by t
,
.
,
employment of sixpe nces an d h alf crowns I give the arrange
ment requiring the fewes t possible c u rrent English coins—fifte e n
It will be seen th at the amount in e ach corner is a fraction al one
the sum re quired in the tot al being a whole number o f shillin gs
-
.
.
,
.
68
.
—The
P ostage S tamps P uz z les
.
first o f these p uz z les is b ased on a simil ar prin ciple tho ugh l
it is re all y m uch e as ie r bec ause the condition th at nine of the
Th e
,
,
214
T HE C A NTE R B U R Y PUZZ LES
2 16
st amps
p esent in circul tion
—
these
d
§
ld 2d
1
a
n
d
d
1
0
3
d
d
d
d
6
1
o
d
2
s
6d
3
5
4
£
£5
9
In the first sol ution the numbers are in arithmetic al
—1 1 5 2 Z S 3 3 1 4 45 5 But an y nine numbers will form
m agic squ are i f we c an write them thus
.
,
.
,
at
r
.
,
,
a
,
,
,
,
,
.
.
,
,
are
,
1d
,
.
,
1
.
,
.
,
.
1
2
7
13
8
3
9
14 15
where the horiz ont al di fferences are all alike and the vertic al dif
fe re n ces all alike but not necess arily the s ame as the horiz ont al
This h appens in the case o f the second solution the numbers o f
which may be written
.
,
,
Also in the c ase of the sol ution to N o
num bers are in shillin gs
.
67
,
the Coin age
Pu z z le
,
the
,
2
2
S
4S 5
7
7h
3
st
8
If there are to be nine difierent numbers 0 may occur once (as
in the sol ution to No
Yet o n e might con stru ct s quares with
negative numbers as follows
,
.
,
69
.
—The
F rogs
an d
Tumblers
.
It is perfectly true as the P rofessor s aid that there is onl y on e
solution (not counting a revers al ) to this p uz z le The frogs th at
j ump are George in the third hori z ont al ro w ; Ch ang the artful
looking b atr achian at the end o f the fourth row an d Wilhelmin a
,
,
.
,
,
S O LU T I O NS
the fai r creature in the seventh ro w George j umps downwards
to the second t u mbler in the seventh row
h
ng
only
C
a
who can
;
le ap short dist ances in consequence of chronic rheumatism removes
somewh at u nwillingly to the gl ass j ust above him—the eighth
in the third row ;
with all the sp rightline ss o f
.
,
,
O O O O O O O O
O O O O O O O O
O O O O O O O
,
o q
o
z
d
O
O
d
d
o o o
O O O O
0 0
6
0
0
0 6 0 0 0 0
0 0 0 0 0
he r
0 0
youth and se x performs the very credit able s alt atory fe at of
leapn to the fo urth t umbler in the fourth row In their new
positions as shown in the ac comp anying di agram it will be found
that of the eight frogs no two are in line vertic ally horiz ont ally
o r di agon all y
,
.
,
,
,
,
.
—
Romeo
uli et
j
Thi s is r ather a di fficult p uz z le thou gh as the P rofessor t e
“
m arked when H awkhurst hi t o n the solution it is j ust one of
those puz z les that a person might solve at a gl ance by pure l uck
Yet when the solution with its prett y symmetric al arran gement
is seen it looks ridic ulously simple
It will be found th at R omeo re aches Juliet s b alcon y aft er
V isiting every ho use once an d only once
an d m aki ng fourteen
tu rnings not countin g the turn he m akes at st arting These are
70
.
and
.
,
,
,
.
,
,
,
.
,
’
,
,
.
218
T HE C A N T E RBU R Y P UZZ LES
the fewest turnings poss ible an d the problem
by the route shown o r its revers al
,
c an
onl y be sdlve d
.
1
7
— Romeo s S econd J ourney
’
.
.
I n order to t ake hi s trip through all th e white squ ares onl y
with the fewest possible turnings R omeo would do well to adopt
,
the ro ute I have sh own by me ans of which only sixteen t u rnings
Th e P rofessor in forms me that
are re q uired to perform the fe at
,
.
M I SCE LLAN E O U S P U ZZ LE S
—
e
a
l
T
G
a
e
o
K
es
m
h
73
f
y
To win at thi s game you must sooner or l ater leave your o p
po nent an e ven n umber o f similar grou ps Then wh atever he
does in o n e group yo u re pe at in a simil ar group Suppo se for
ex ample that yo u le ave him these groups 0 0 00 0 000 Now
if he knocks down a single you knock down a single if he kn ocks
down two in o n e triplet yo u kn ock down two in the other triplet
if he kn ocks down the central kayle in a triplet you kn ock down
the centr al one in the other triplet In this way you must e ventu ally
win As the game is st arted with the arr an gement 0 0000000 00 00
the first pl ayer c an alw ays win but only b y knocking down the
sixth o r tenth kayle (counting the one alre ady fallen as the second)
an d thi s le aves in either c ase 0
000
000000 0 as the order o f the
groups is of no import ance Wh atever the second pl ayer n ow
does this c an al ways be resolved into an e ven number o f equal
groups Let us suppose th at he knocks down the single one ; then
we pl ay to le ave hi m 00
Now wh atever he does we
0000000
can afterw ards le ave him either 000
We kn ow
000 or 0
00
000
wh y the former wins an d the l atter win s also ; bec ause however
he m ay pl ay we c an alw ays le ave him either 0 0 or 0 0 0 0
o r 00
00 as the c ase m ay be
Th e complete an al ysis I can no w
leave for the am u sement of the re ader
.
.
,
,
.
.
,
.
,
,
,
,
,
.
,
.
,
,
,
.
,
.
.
,
.
,
,
,
,
,
,
.
.
—
e
e
T
B
r
o
k
h
n Ches sboard
74
.
.
The ill ustration will show h ow the thirteen pieces can be put
to ge ther so as to construct the perfect bo ard and the re ve rse prob
,
S O LUTI O NS
22 1
lem of c utting these p articul ar pieces o ut will be found equally
entert aining
Comp are with No s 2 93 an d 294 in A i n M
.
.
.
—
e
T
S
i
d
e
p
h
r
5
7
~
.
an d
.
the F ly
.
thi s problem was much discussed in the Dai ly M ai l
from 1 8th Jan uary to 7th F ebru ary 1 905 when it appe ared to
cre ate gre at p ublic interest it was act ual ly first propounded by
me in the Weekly D i spatch of 1 4th June 1 903
Im agine the room to be a c ardbo ard box Then the bo x m ay
be cut in various different ways s o th at the c ardboard m ay be laid
flat on the t able
I show fou r of the se ways an d indi c ate in every
case the rel ative positions of the spider an d th e fly an d th e straight
ened course which the Spider must t ake wit h out going off the
c ardbo ard These are the four mo st favourable c ases an d it will
be fou nd that the shortest route is in N0 4 for it is only 40 feet in
length (ad d the squ are of 3 2 to the squ are of 2 4 an d extract the
square root ) It will be seen that the spider act ually p asses al ong
five of the six side s of the room 1 H aving m arked the route fold
the bo x u p (removing the s ide the Spider does not use ) and the
If the
appe ar ance of the shortest co u rse is rather s urprising
Tho ugh
,
,
.
.
,
.
,
,
,
.
.
,
.
,
,
.
T HE C AN TE RBU R Y
222
PU ZZ LES
S pider h ad t aken wh at most persons will consider ob viously the
shortest route (th at shown in No
he would h ave gone 42 feet 1
feet in length an d R o ute NO 3 is
R o ute NO 2 is
feet
.
.
.
,
.
I
le ave the re ader to discover which are the shortest routes
when the spider an d the fly are 2 3 4 5 an d 6 feet from the ceili ng
an d the floor respectivel y
,
,
,
,
.
6
7
.
—The
P erp lexed Cellarman
.
Brother John g ave the first m an three l arge bottles and one
sm all bottleful of wine an d one l arge an d t hree sm all empty bottles
To e ach o f the other two men he g ave two l arge an d three sm all
bottles of wine an d two l arge an d one sm all empty bottle E ach
o f the three then receives the s ame q uantit y o f wine an d the s ame
nu mber o f e ach si z e of bottle
.
,
.
,
,
.
T H E C A N T E R BU R Y PU ZZ LES
224
pigs in their s impli c ity an d ignorance of the p ec uli arities o f
D utch hogs e ach went a fter the wrong anim al
Th e li ttle prin c iple involved in this p uz z le is th at known to
chess pl ayers as getting the oppo s ition
Th e rule in the c a se
of my puz z le (where the moves resemble rook moves in chess with
the added c ondition th at the rook m ay only move to an adj oining
squ are) is s imply this Where the number of squares on the s ame
row between the man o r wom an an d the hog is odd the hog can
never be c aptured where the number of squ ares is even a c apture
is possible The number of squares between Hendric k and the
blac k hog and between K atrii n an d the white hog is 1 (an odd
number) therefore these individuals c annot c at c h the anim al s
they are facing But the number between Hendrick an d the white
ho g an d between K atrii n an d the bl ack one is 6 (an even number )
therefore they may easily c apture those behind them
’
.
,
”
-
.
,
,
,
.
,
,
,
,
.
,
,
,
.
,
,
,
.
—
i
t
o ne Game
r
h
T
h
e
T
79
y
-
.
.
By leading with a 5 the first pl ayer can al ways win I f your
opponent pl ays another 5 y ou pl ay a 2 an d score 1 2 Then as
often as he pl ays a 5 you pl ay a 2 and if at any st age he drops
If after
o ut o f the s eries 3 1 0 1 7 2 4 3 1 you step in and win
your lead o f 5 he pl ays anything but another 5 you m ake 1 0
o r 1 7 an d win
Th e first pl ayer m ay also win b y le ading a 1 or
It is however well worth the
a 2 but the pl ay is complic ated
re ader s study
—
The Chi nes e Rai lways
80
.
.
,
,
,
,
,
.
,
,
,
,
.
.
,
,
,
’
.
.
.
pu z z le was artfull y devised b y the y ellow man It is n o t
a m atter for wonder th at the represent atives of the five countries
interest e d were bewildered It would have puz z led the engineers
a good deal to constru ct those circ uitous routes s o th at the various
trains might run with s afet y D i agr am 1 shows directions fo r the
five systems o f lin es so th at no line sh all ever cross another an d
t his appears to be the m ethod th at would require t he shortest
possible mile age
This
.
.
.
,
.
,
S O LUTI O NS
225
re ader may wish to know how m any di fferent solutions
there are to the puz z le To thi s I sho uld answer that the number
'
Th e
.
case o f line A alone then one route would be Di agram 2 anoth er
If 3 is different from 2 as it nu
3 another 4 an d another 5
doubtedly is then we must regard 5 as different from 4 But a
th e
,
,
,
,
.
,
,
.
'
the four di agrams 2 3 4 5 in succe ssion will Show that
we m ay continue this windin g U p process for ever ; an d as there
will always be an unobstructed way (however long and c irc uitous)
from st ations B an d E to their respective main lines it is evident
that the numbe r o f rout es for line A alone is infinite Therefore
the num ber o f complete solutions must also be infinite if railway
lines li ke o the r lines h ave no breadth ; an d ind e te rmi nate unless
glance
at
,
,
,
,
,
,
.
.
,
,
,
l5
T HE C ANT ER B U R Y PU ZZ LES
2 26
are told the gre ate st num ber o f parallel
it is possible
If some clear condition restricting
to construct in cert ain places
these windings up were given there would be no gr eat diffic ulty
we
li nes t hat
.
,
”
,
of
,
the kind the n umber would I c alculate be little short
thousan d surprising though it may appear
,
,
,
,
of
two
.
81
.
—The
E ight Clowns
.
is a little novelty in m ag ic squares These s qu ares may be
formed with numbers tha t are in arithmd ical progression o r that
If a square be formed o f the former
are n ot i n such progression
cla ss o ne place m ay be lef t v ac ant but onl y under particular con
In the case o f o ur puz z le there would be no difficulty
di tio ns
in m aking the m agic square with 9 missing ; but with 1 missing
6
it
is
n
t
po
sible
u
t
a
2
d
B
a
a
n
o
s
t
8
th
is
using
3
5
(
4
7
9)
gl ance at the origin al illustration will show th at the numbers we
have to de al with are no t actually those j ust mentioned The
clown that has a 9 o n his bod y is portrayed j us t at th e moment
when two b alls which he is j uggling are in mid air The pos itions
o f these b alls cle arl y convert his figure into the recurring decim al
9 Now since the recurring decim al 9 is equ al to g an d there
fore to 1 it is evident that al though the clown wh o be ars the figure
1 is absen t the m an who bears the figure 9 by this simple artifice
Th e
h as fo r the occ asion given his figure the v al ue o f the number 1
troupe can consequently be grouped in the following m anner
This
.
,
.
,
,
.
,
,
,
,
,
,
,
.
,
.
-
.
.
.
.
,
,
,
,
,
.
7
4
8
2
3
.
5
6
9
'
Every column every row and each o f the two diagon als
This is the correct solution to the pu z z le
ad d U p to 1 2
,
,
.
.
—Thc Wiz ard s Anim ate
i
Th s puz z le is both easy an d difficult for it is a v ery s
m atter to fin d o ne o f the multipliers which is 86 If we m
82
’
.
.
,
,
.
no
w
THE C A NT ER B U RY PUZ ZL ES
228
the 43 inthis way Th e onl y m ultiplier o f 3 that produc es an 8 in
the digits pl ace is 6 I therefore multiply 73 by 6 an d get 43 8 o r
a
fter
rej
ecti
g
the
Now
divid
d
by
8
e
s
a
n
le
ve
the
3
4
73
To this I ad d the 6 men
rem ainder 43 an d the dividend is
x 8 3 the ex ample given o n p age 1 2
tio n e d above an d ge t
9
In trying the even n umbers there are two c ases to be con
Srd e re d
Thus t aking 8 6 we m ay s ay th at if 60000 etc when
divided by 76 le aves either 22 o r 60 (bec ause 3 x 6 an d 8 x 6 both
we get a solution
prod uce
But I rej ect the former o n i nspe c
tion and see that 60 divided by 76 i s 0 le aving a rem ainder 60
the other example
It will be found in
Therefore 8 x
the c ase o f 7 1 th at 1 000 00 etc divided by 6 1 gives a rem ainder
x
6
1
a
2
fter
producing
the
long
ividend
the
b
eginning
d
2
a
t
4
4 (7
7)
o f this article with the 7 added
The other multipliers fail to produce a solution so 83 86 an d
r
r
the
onl
y
three
possible
multipliers
hose
who
f
mili
r
1
a
T
e
a
e
a
a
7
with the prin ciple o f recurring decim als (as somewhat explained in
“
my nex t note o n No 8 3 Th e R ibbon P roblem ) will underst and
the conditions under which the rem ai nders repeat themselves after
cert ain peri o ds an d will only find it necessary in t wo o r three c ases
to m ake any lengthy divisions
It clearly follows th at there
an u nlimited number o f multiplic ands for each multiplier
.
.
,
.
,
,
,
.
'
.
,
,
.
,
,
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,
,
.
.
.
,
,
,
.
,
,
,
.
.
,
,
.
.
—
The R i bbon P roblem
83
.
.
solution is as follows : P l ace this r ather lengthy
on the ribbon 0 2 1 276 5 95 74468 08 5 1 063 8 29787 2
r
6
It
be
multiplied
by
numbe
up
to
1
m
a
a
n
3 7
y
y
t o give the s ame order o f figures in the ring
Th e
vi o usly given c an be m ultiplied by an y number up to
the limit 9 in order to put readers o ff the scent The
t wo numbers are simpl y the recurring decim als th at
an d £7 respectively
Multipl y the one b y seventeen an d
by forty seven and you will get all nines i n e ach c ase
3
In tr ansforming a v ulgar fraction s ay 1 7 to a
Th e
,
.
.
.
.
-
.
,
,
,
,
S O LU T I O NS
2 29
fraction we proceed as below adding as m any noughts to th e
dividend as we like unt il there 15 no rem ainder or until we get
a recu rring series of figure s or u ntil we h ave c arried it as far as
we require since every addition al figure m a never e n ding dec imal
carri e s us nearer and nearer to ex actitude
,
,
,
,
-
,
.
)
17
1 00
85
9
.
Now sinc e all
o f 1 0 c an onl y cont ain f actors o f the
powers o f 2 an d 5 it cle arly follows th at your decimal never will
come to an end if an y other factor t h an these occurs in the de
nomin ator o f your vulgar fraction Thus l
an d § give us the
exact decim al s 5 25 an d 1 25 } and 33; give us 2 and 04
3
give us 1 an d 05 : bec ause the denominators are all
1 1, an d ”
compose o f 2 an d 5 factors But if you wish to convert
i
or }
your divi s ion sum will never end but you wi ll get these
decim als 3 3 3 33 etc
etc and 1 42857 1 42 857 1 42857
1 66666
in t he first c ase the 3 keeps on repeating for ever
an d ever ;
in the second c ase the 6 i s the repeater and in the
l ast case we get the rec urring period of 1 4285 7 In the c ase o f
3
i
d
a
i
ibbo
n
roblem
e
fi
n
d
the
circul
tin
per
o
w
n
P
T
h
e
R
g
1 7 (
,
,
.
,
.
d
.
a
,
.
,
7
.
,
,
.
.
.
.
,
.
,
,
,
.
,
.
.
.
,
,
,
.
to be 05 88 23 5 2941 1 7647
Now, in th e division sum
.
.
bo ve
a
,
the
succ e ssi ve remainders
are
THE C A NTE R B U RY
230
PUZZLES
etc an d these n umbers I have inserted around
the inner ring of the di agram It will be seen that every num ber
from 1 to 1 6 occurs on c e an d th at if we multiply o ur ribbon number
by any o ne o f the numbers in the inner ring its position indic ates
exactly the point at which the product will begin Thus if we
multiply b y 4 the product will be 2 3 5 etc if we multiply b y 6
1
,
1 0 , 1 5 , 1 4,
6
4
9
,
,
.
,
,
.
,
.
.
,
,
,
,
We can therefore multiply by an y numbe r from 1 to
the desired result
The kernel of the p uz z le is this : An y prime number with the
exception o f 2 and 5 which are the factors of 1 0 will ex actly
divide without rem ainder a n umber consisting of as m an y nines as
the number itself less one Thus 999 999 (Six 9 s) is divisible by 7
six teen 9 s are divisible b y 1 7 eighteen 9 s by 1 9 an d so on This
is always the c ase though frequently fewer 9 s will s uffice ; fo r o n e
r
f
o
1
1
u
r
u
l
i
s
divisible
b
y
b
y
six
b
y
1
when
ribbon
r
e
t
o
w
o
3
3
9
consecutive m ultipliers bre aks down an d another law co m es in
Therefore since the 0 an d 7 at the ends of the ribbon may no t
etc
2
5
3
1 6 an d get
,
.
.
,
,
:
,
,
’
,
.
,
’
’
,
,
.
’
,
,
,
,
.
,
T HE C A N T ERB U R Y PU ZZL ES
2 32
If with t he t hre e e qu al squ ares we form the rect angle I BBA
then the mean proportion al o f the two sides o f th e rect angle will
P roduce AB to C
o f a square o f equ al are a
be the
,
_
.
BC
,
q ual to BD
Then place the po int o f the compasses at E
a
midw
y be twee n A an d C) an d describe the arc AC I am show
(
ing the quite gener al method fo r conv er ting rect angles t o squares
but in this p articul ar c ase we may o f course at once pl ace o ur
compasses at E which req uires no finding P roduce the line BD
cutting the arc in F an d BF will be the required side of the square
Now m ar k o ff AG an d D H e ach equ al to BF an d m ake the
cut I G an d al so the cut H K from H pe rpendicul ar to I D The
six pieces produced are numbered as in the di agram o n l ast pag e
I t will be seen th at I h ave here given the reverse method first
N to cut the three sm all squ ares into six
pi eces to form a l arge square In the case
o f o ur p uz z le we c an proceed as follo ws
Make LM equ al to ha lf the di agon al
ON
D r aw the line NM an d drop from
L a pe rpendicul ar on NM Then LP
will be the side of all the three sq uares
of combined are a equ al to the large
squ are Q NLO
Th e re ader c an no w
c ut o u t withou t di ffi c ult y the s ix pieces
as shown in the numbe red squ are on the l ast p age
e
.
.
,
,
,
,
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,
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,
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.
.
.
.
,
.
S O LUTI O NS
—
C aptai n
8
Longbow
and
2 33
the
Bears
.
It might have struc k the reader that the story of the be ar
1m paled on the North P ole h ad no connection with the problem
th at followed As a m atter o f fact it is essential to a sol ution
Eleven bears c annot possibly be arranged to form o f themselves
seven rows o f bears with four bears in every row But it is
a
m at ter when Capt ain Longbow informs us that they
.
.
.
8
so placed the mselves that there were seven rows o f fo ur
F o r if they were grouped as shown in the di agram s o that
t hree of the be ars as indicated were in line with the North P ole
that imp aled anim al wo uld complete the seventh ro w o f fo ur
which c annot be obt ained in any other way It obviously does not
aff ect the problem whether this seventh row is a hundred miles
long or a h undred feet so long as they were really in a st raight
line —a poin t that might perhaps be settled by the c apt ain s pocket
compass
—
The E ngli sh Tour
86
h ad
,
,
,
,
,
.
,
’
.
.
.
It was required to show how a resident at the town m arked A
might visit every o ne o f the towns once and only onc e and finish
,
,
T HE C A NTE R B U RY PU ZZLES
2 34
up his tour at Z This pu z z le conce als a little trick After the
solver h as demonstrated to hi s s atisfaction th at it c annot be done
in accordance with the conditi ons as he at first understoo d them
he should c arefully examine the wording in order to fi nd some
This would be e asy enough if he were able to
flaw It was said
c ountry b y ro ad
as well as b y rai l b ut he is no t
cut
.
.
,
,
.
,
”
~
No w
.
,
,
lthough he is prohibited from cutting across country b y
road nothing is said about his going by Se a lEI f therefore
c arefully loo k again at the m ap we shall find that two towns and
two onl y lie o n the se a co ast When he reaches o ne of these
towns he t ake s his departure o n board a coasting vessel and sa ils
to the other port The annexed illustration shows by a dark
line the complete route
This p roblem should be comp ared with No 2 5 0
Th e Gr and
Tour
in A i n M
It can be sirnplified in practically an
a
,
,
,
,
,
,
,
.
.
,
,
.
.
”
,
'
.
.
,
T HE C A NTE RBU R Y PU ZZLES
2 36
j ump from 3 to I an d write it down o n I and so o n The second
word c an be inserted i n the s ame order Th e solution depends on
findi ng those words in which the second an d eighth letters are the
s ame and also the fourth an d sixth the s ame because th ese letters
in terch ange without destroying the words MA R I TI MA (or
pink) would also solve the pu z z le if it were an English word
Comp are with No 22 6 in A i n M
.
,
.
,
,
.
.
.
.
H ere
is the way of
.
rrangi ng the seven men
a
w
o
u
o
c
w
m m
o m
m o
m o
m c
m w
o m
m w
m o
o
m
u m
w m
w o
o w m
m o m
m c o
o
m w
u m o
w m e
m m u
o
m w
m mo
m w m o c
a n m c
w
w u a w O
c
course at a circul ar t able A will be next to the man at the
end of the line
I first gave this problem for six persons o n ten days in the
D aily M ai l for the 1 3 th an d 1 6th O ctober 1 90 5 an d it
since been disc ussed in various periodic als by m athem atici ans O f
course it is easil y seen that th e m axim um num be r o f sitti ngs fo r
Of
,
,
.
,
,
.
,
n
persons
is
W
ways
.
The com parati vel y easy method
S O LUTI O NS
237
case s where n is a prim e 1 was first di scovered by
Ernest Bergholt I then pointed out the form an d construction of
a solution th at I h ad obt ained for 1 0 persons from which E D
Bewley fo und a general method for all even numbers The odd
numbers however are extremely diffi c ult and for a long time
n o progress could be m ade with their solution the only numbers
th at could be worked being 7 (given above) and 5 9 1 7 and 3 3
these l ast four being all powers of 2 1
At last however
u
c
u
f
u
l
tho
gh
not
without
m
h
dif
ic
ty) I di scovered a subtle method
(
for solving all c ases and h ave written out sc hedules for every
number up to 2 5 inclusive Th e c ase of 1 1 has been solved al so
by W Nash P erh aps the re ader will like to try his h an d at 1 3
He will find it an extraordinarily h ard nut
The solutions for all c ases up to 1 2 inclusive are given in A
i n M pp 2 05 2 06
fo r solvin g all
.
,
.
.
.
,
,
,
,
,
.
,
,
,
,
,
,
.
.
.
.
.
.
.
.
,
.
,
91
.
The F i ve Tea Ti ns
.
twelve ways of arran ging the bo xes without consider
in g the pict ures If the thirty pict ures were all di fferent the
But the necessary deduction s for c ase s
answer wou ld be
where ch anges of boxes m ay be made without affecting the order
an d the b oxe s m ay therefore be
of pict ures amount to
di fferent
arr an ged in accordance wi th the condit i on s in
ways I will leave my re aders to discover for the mselves how the
figure s are to be arrived at
There
are
.
,
,
.
.
n umber of ways in which the four pigs m ay be placed in
the thirty six sties in accord ance with the conditions is seventeen
inc ludi ng the example that I gave not counting the reversals and
i
s
c
n
h
a
e
in
his
reflection s of the s e arr angement s as di fferent
J
quotes the
An alys e M athemati que an feu des Boheas
s t atement th at there are j ust twenty one sol utions to the lit t le
problem on which this p uz z le is based As I h ad myself only
recorded seventeen I ex amined the m atter ag ain an d foun d that
Th e
-
,
,
.
,
-
.
,
,
“
T H E C A NTE R B U R Y PUZZLES
238
he was in error an d doubtless h ad mist aken reve rsals for di fferent
arr angements
Here are the seventeen answers Th e figures indic ate the ro ws
an d their positions show the col umns
Thus 1 0 4603 m e ans that
we pl ace a pig in the first row of the first column in no row o f the
s econd column in the fourth row of the thi rd column in the si xth
ro w o f the f ou rth column in n o row o f the fi
column
in
t
h
a
n
d
t
h
e
f
third row of the s ixth column The arrangement E is that which
I gave in diagram form
,
,
,
.
.
,
.
,
,
,
,
,
,
.
A
B
.
.
C
.
D
.
E
F
.
.
G
H
I
.
.
.
1 04603
1 3 600 2
1 405 02
1 405 20
1 6002 5
1 603 04
2 0 1 405
2 0 1 605
2 05 1 0 4
It will be found th at form s N an d Q are se mi s ym m etric al with
reg ard to the centre an d therefore give onl y two arrangements
e ach by reversal and refle ction that form H is qu arter s ymmetric al
an d gives o nl y four arr angement s ; while all the fo urteen others
ield
by
revers
al an d reflection eight arr angements each
T
here
y
fore the pigs may be plac ed in (2 x 2) (4 x 1 ) (8 x 1 4) 1 20
di fferent ways b y reversing an d reflecting all the seventeen forms
Three pigs alone m ay be placed so th at every st y is in line with
a pig provided th at the pigs are not forbidden t o be in line with
o n e another ; but there is onl y o ne way of doin g it (if we d o no t
count reversals as different ) as follows 1 0503 0
-
,
-
,
.
.
,
.
,
93
Arrange the blocks
x
1
9 5
me
sa
64
:
an d
x
2
73
80 ,
.
—
The N umber Blocks
form the two multiplic ation sums
the prod uct in both c ases wi ll be the
so as
and
.
to
T HE C A NTE R B U R Y PU ZZLES
2 40
puz z les are the same thi ng in di fferent dres s Now co m pare
p age 1 41 with D i agr am B and it will be see n that by disent angli ng
the strings I h ave obt ained a simplified di ag ram without altering
the e ssen ti al relations bet ween the buttons o r discs The re ader will
now satisfy himself without any diffic ult y th at the puz z le requires
eleven moves fo r the foxes and eleven for the geese He will see
th at a goose o n 1 o r 3 m ust go to 8 to avoid being ( me m
ove from
If we
a fo x an d to ena ble the fox o n 1 1 to come o n to the ring
—
—
—
a
pl y 1 8 then it is cle arly best to play 1 0 5 and no t 1 2 5 fo r
the foxes When they are all o n the circle the n they sirnply
promen ade round it in a clockwise direction t aking c are to reserve
—
—
It is thus rendered ridi c u
8 3 an d 5 1 2 for the fin al moves
lo usly e asy b y this method
See also no tes o n solutions to Nos 1 3
two
.
,
.
.
.
,
.
,
’
.
,
,
.
.
.
an d
85
.
—
i
o
n
s
n
R
o
b
95
.
Crusoe
f
s
Table
.
‘
The di agram s hows h ow the pieCe o f wood should be cut in t wo
pi e ces to form the s qu are t able to p A B C D are the corn ers o f
-
.
b vious to the
th at is disc arded
o
.
,
,
whi ch the piece E fits into the piece F will
ey e of the reade r The shaded part is th e wood
The way in
be
,
.
S O LUTI O NS
241
The
number m ust be the le ast common m ultiple of 1 2 3 etc
up to 1 5 th at when divided by 7 leaves the rem ainder 1 by 9
lea ve s 3 by 1 1 leaves 1 0 by 1 3 leaves 3 an d by 1 4 le aves 8 S uch
a n umber i s 1 20
The next n umber is
b ut as we h ave no
—
a
record of tree especi all y a very young one— bearing anything
like s uch a l arge number of apples we may t ake 1 20 to be the only
answer th at is accept able
,
,
,
,
,
,
,
,
.
,
,
,
.
.
,
.
—
T
l
h
e
P
er
p
e
x
e
d
P
l
u
m
b
e
r
97
.
.
Th e
rect angul ar c losed cistern that sh all hold a given quant ity
of water an d yet have the s mal lest pos sible surface of met al m ust
be a perfe c t c ube— t h at i s a ci stern every s ide of which is a square
For
c ubic feet of w ater the intern al dimen s ions will be
1 0 ft x 1 0 ft x 1 0 ft
an d t h e z inc req uired will be 60 0 sq uare feet
In the c ase of a ci stern without a top the proportions wi ll be ex
ac tly h a lf a c ube
exact proportions as ked fo r
These are the
in the s econd c ase The exact dimen sion s c annot be given b ut
ft is a close approxim ation The cistern
will hold a little too much water at which the buyer will not
compl ai n an d it will involve the plumber in a trifling lo ss not
worth con sideri n g
—
l
u
n
o
n
o
m
N
e
l
s
8
T
h
e
C
9
.
,
.
.
.
.
.
,
.
.
,
,
.
.
.
If you t ake a sheet of p aper an d m ark it with a di agon al line
as in F igure A you Will find th at when y ou
roll it i nto cylindri c al form with the line o ut
side it will appe ar as in F igure B
It wi ll be seen th a t the Spiral (in one com
a
t
rn
is
merely
the
hypotenuse
of
l
u
e
t
e
)
p
right ang led tri angle of which the length an d
width of the paper are the other two sides
In t h e p uz z le given the lengths of the two sides of the trrangle
Th ere fo r the
are 40 ft (one fifth of 200 ft ) an d 1 6 ft 8 in
,
,
,
.
,
-
,
.
,
-
.
{
.
.
.
l
g
T HE C AN T E RBU R Y PUZ ZL ES
242
hypotenuse is 43 ft 4 in The length of the garl a
nd is there fore
five times as long—2 1 6 ft 8 in A curio us feature o f the puz z le is
the fact th at with the dimensions given the result is exactly the
sum o f the height and the circumference
.
.
.
.
.
99
—The
.
Two E rrand Boys
.
All th at is necess ary is to ad d the two dist ances at which they
meet to twice their di fference Thus
640 = 1 760 yards
o r o n e mile which is the dist ance re q uired
Or put another way
three times the first dist an c e less the second dist an ce will always
a
ive
the
nswer only the first dist an ce should be more t han two
g
thirds o f the second
.
,
.
,
,
,
,
.
1 00
.
—0n
the Ramsgate S ands
.
ff
ust
six
di
erent rings may be formed without bre aking the
J
conditions Here is o ne way o f effec ting the arrange m e nts
.
.
1
L
ir
1
A
B
C
D
E
F
G
A
G
E
G
I
K
A
A
D
G
J
M
E
I
M
A
A
F
K
G
M
M
H
B
I
D
C
F
I
L
D
H
L
C
C
H
M
E
J
F
L
E
K
D
J
K
F
H
J
L
E
H
K
G
B
K
B
F
J
B
G
L
D
I
J
C
I
B
H
i
u
s
x
oin
the
ends
h
ve
the
rings
a
n
d
o
a
J
y
Luc as devised a simple mech anic al method for ob t aining the
1 children
n ri ngs th at m ay be formed under the conditio ns by 211
.
.
1 01
.
—The
Three M otor Cars
-
.
only set o f three n umbers o f two three and five figures
respectively th at will fulfil the required conditions is 27 x 5 94 =
These three numbers cont ain all the nine digits an d 0
without repetition ; the first two numbers multiplied together m ak e
the third and the second is exactly twenty two t imes the first If
The
,
,
,
,
,
-
,
.
THE C A NTE RBU R Y PUZ Z LES
2 44
“
irrespective o f routes
Thus the
direction BCDE gives
nine ro utes bec au se there are three ways of getting from B to
C an d t hree wa ys of getting from D to E
direc tion
But the
therefore yields o nl y one route
E BCE a dmits of no v ari ation
.
,
”
,
,
.
.
2
I
two line directions
three line
6
-
I
-
I
2
9
four line
12
-
6
3
2
6 fiv e
-
line
36
36
2
line
seven line
2 si x
2
7
-
12
2
3
4
-
Tot al
We thus see that there are j ust
is the correct answer to the puz z le
1 04
.
-
The S kipp er
6 40
6 40
di fferent routes in
all,
.
an d
the S ea S erp en t
-
.
E ac h of the three pieces was c le arly three c ables long But
Simon persi sted in as suming th at the c uts were m ade tran sversely
o r ac ro s s an d th at therefore the complete le n gth was nine c able s
Th e s kipper however expl ained (an d the point is q uite as ver ac ious
as the rest of his y arn ) th at his c uts were m ade longit udin ally
straight from the tip of the nose to the tip of the t ail
Th e c o m
l
ac
e
t
length
as
therefore
only
th
r
ee
bles
the
s
a
me
as
e
h
e
w
c
a
p
pie c e Simon was not asked the ex act length of the serpent b ut
how long it must h ave been It m ust h ave been at le ast three
c ables long tho ugh it might h ave been (the skipper s st atement
ap art ) anythi ng f rom th at up to nine c ables
according to the
direction of the c uts
.
,
.
,
,
,
,
.
,
.
’
,
,
.
S O LUTI O NS
—
1 05
The
.
2 45
D orcas S oci ety
.
If there were twelve l adies in all there would be 1 3 2 ki sses
among t h e l adies alone le a ving twelve mo re to be exc h anged with
the c ura te six to be given by him an d s ix to be received There
fo re of the twelve la dies six would be hi s s i sters Consequently
if twelve c o uld do the work in four an d a half months s ix ladi es
would do it in twice the time— fo ur and a h alf m onths longer
which i s the c orrect an swer
At first s ight there mi ght appe ar to be some ambiguity abo ut
the words
Everybody kissed everybody else except of c ourse
Might this not be held to imply
the b ashful young man him self
th at all the l adies immodestly ki ssed t he c urate although they
were not (exc ept th e sisters) ki ssed by hi m in ret urn ? No be
c au s e in th at c ase it wo uld be fo und th at there must have been
twelve gi rl s not one of whom was a Sister which is contrary to the
conditions If ag ain it should be held th a t the si sters might not
acc o rding to the wording h ave ki ssed their brother alth ough he
ki ssed them I reply th at in th at c ase there must h ave been twelve
gi rl s all of whom m ust h ave been hi s sisters And the reference
to the l adies who might h ave worked exclusively of the sisters shuts
o ut the possibilit y of this
,
,
a
.
'
,
,
.
,
,
.
,
,
,
,
”
.
,
,
,
,
,
.
,
,
,
,
,
,
.
,
.
1 06
.
— The Adven turous S nail
.
At the end of s eventeen d ays the sn ail will h ave climbed 1 7 ft
an d a t the end of i ts eighteent h d ay time t ask it will be at t h e to p
It inst antly begins slipping while sleepi ng an d will be 2 ft down
the ot her s ide at the end of t h e eighteenth d ay of twe nt y four hours
How long will it t ake over the rem aining 1 8 ft
If it slips 2 ft
at nigh t it c le arly overcome s the tenden c y to slip 2 f t during th e
d aytime in climbing up In rowing up a river we h ave the stream
If the
ag ain s t us b ut in c oming down it is with us an d helps us
snail can climb 3 ft ; and overcome the tenden cy to slip 2 ft in
twelve hours ascent it could with the same exertion crawl 5 ft a
-
.
.
,
-
.
.
.
.
.
,
.
,
.
’
,
.
2 46
THE C A N TE RBU R Y PUZZLES
on the level Therefore in going down t he same exe rtion
carries it 7 ft in twelve hours—th at is 5 ft b y person al exertion
and 2 ft by slip
This with the night slip gives it a descending
progress of 9 ft in the twent y four hours It can therefore do
the rem ainin g 1 8 ft in exactly two days and the whole j ourney up
and down will t ak e it ex actly twent y d ays
d ay
.
,
,
.
.
,
.
.
_
,
,
-
.
.
.
,
,
,
,
,
.
1 07
.
—The
F our P ri nces
.
Whe n Montucla in his edition o f Oz anam s Recreations i n
M athematic s d eclared th at
No more th an three right angled
tri an gles equal to each other c an be found i n whole numbers but
we may find as m any as we choos e i n fractions
he curiously o ver
looked the ob vious fact th at if you give all your sides a common
denomin ator and then c ancel th at denomin ator y ou have the
required answer in i ntegers l
Every reader should kn ow that i f we t ak e an y two n umb ers m
2
2
2
2
and n then m + n
m
n
an d 2mn will be the th ree sides o f a
ration al right angl e d tri an gle
Here m and n are c alled gen eratin g
num bers To form three such tri an gles of equal area we use the
followi ng s imple form ul a where m is the greater n um ber
’
,
-
,
,
,
,
,
,
-
,
,
,
-
.
.
,
,
mn + m
2
+n
2=
a
2
—
m
n
b
Z
a
2=
2 mn + n
c
N ow i f we form three tri angles from the followin g p airs o f
gener ators a and b a an d c a an d b + c they will all be of equal
area
This is the little problem respecting which Le wis Carroll
says in his di ary (see his Lif e and Letters by Collingwood p
over a tempting problem sent me
Sat up l ast night till 4 am
from New York to find three equal rational sided right angled
tri angles
I found two
but could n of fi nd three !
The following is a subtle formul a b y me ans o f which we may
always fin d a R A T equ al in area to an y given R A T
Let z =
hy potenuse b = b ase h = height a = area of the given tri angle ; then
,
,
,
,
,
.
.
,
,
-
-
,
’
.
.
,
.
.
.
,
,
.
.
PU Z Z LES
T HE C A N TE RBU R Y
2 48
1 09
.
— N oughts
and
Crosses
.
solution is as follows Between two pl ayers who thoroughly
Neither player
underst and the pl ay every g ame sho ul d be dr awn
co uld ever win except through the blundering of his opponent If
No ught (the first pl aye r) t akes the centre Cross m ust t ake a corner
or Nought m ay be at him with cert ai nty If No ught t akes a corner
o n his fir s t pl ay Cross m ust t ake the centre at once or again be
be aten with cert ainty If No ught le ads with a s ide both pl ayers
must be very c areful to prevent a loss as there are numerous pit
f all s But Nought m ay s afely lead anything an d sec ure a draw
and he c an o nl y win through Cross s bl u nders
Th e
.
.
,
,
.
,
,
.
,
,
,
.
’
.
—Ovi d s Game
The sol ution here is : The first pl ayer can al w ays Win pro
But a good vari a
vi d e d he pl ays to the centre on his first move
tion of the game is to b ar the centre for the fi rst move of the first
pl ayer In th at c ase the second pl ayer should t ake the centre at
once This sho uld always end in a draw but to ensure it the first
pl ayer m ust pl ay to two adj oining corners (such as 1 an d 3 ) on h is
fir st an d second moves Th e game then requires gre at c are on
both sides
1 10
’
.
.
,
.
.
.
,
.
.
111
.
— The
F armer s Oxen
’
.
Sir Is aac Newton h as shown us in his U n i versal Ari thmetic
th at we m ay divide the b ullocks in e ach c ase in two p arts—one p art
to e at the incre ase an d the other the ac c um ul ated grass The first
will v ary directly as the si z e of the field an d will not depend on the
time the second p art will also vary directly as the si z e of the field
an d in addition inversely with the time
W e find from the f armer s
st atements th at 6 bullocks keep down the growth in a 1 0 acre
field an d 6 bullo c ks e at the gr as s on 1 0 acres in 1 6 weeks There
fore ii 6 b ullocks keep down the growth on 1 0 acres 2 4 will keep
down the growth o n 40 acres
,
,
.
,
,
,
’
.
-
.
,
,
,
.
S O LU T I O NS
Again we find th at if 6 bullocks
acre s in 1 6 weeks then
e at
,
10
2 49
the accumul ated gr ass on
,
the gr ass
cres in
10 a
8
48
40
8
1 92
0
4
2
64
0
4
6
1 2 e at
on
Add the two res ult s together (2 4 +
m ay be fed on a 40 acre me adow for
regul arly all the time
-
weeks
,
find that 8 8 oxen
weeks the grass growing
an d
6
we
,
.
1 12
—The Great Gran emo or M ster
g
y
y
.
.
We were told th at the bu llet th at killed Mr St anton Mowbray
stru c k the very centre of th e clock face an d in st antly welded to
gether the hour min ute an d second h ands so that all revolved
in one piece The p uz z le was to tell from the fixed rel ative posi
tions of the three h ands the ex act time when the pistol was fired
We were also told an d the illustration of th e cloc k f ac e bore
th at th e hour an d minute h ands were ex ac tly
o u t the s t atement
twen ty divi sion s ap art the thi rd of th e c irc umferen c e of th e di al
Now t h ere are eleven time s in twelve ho urs wh en the hour h and
is ex actly twenty divi sion s ahe ad of t he minute h and an d eleven
times when the min ute hand is ex actly twenty divi sion s ahe ad of
the hour h and Th e illustration showed th at we h ad only to c o n
If we st art at four o clo c k an d keep on
s ider the former c ase
—
s e eleven time s t h e
se
we
s
ll
get
the
C
h
a
a
l
l
111
2
a dding I h 5
7
—
—
l ast being 2 h 5 4 min 3 2 se c Anot h er addition b rings us b ack
to four o clock If we now ex amine the clock f ace we s h all find
t h at the se c onds h and is nearly twenty two divi sions be h ind th e
minute h and an d if we look at all o ur eleven times we sh all find
that only in the l ast c as e given above is th e seconds h and at this
dist ance Therefore the shot must h ave been fired at 2 h 5 4 min
5
e e to
s
min
2
u
a
a
t
s
e
t
e
ex
ctly
or
t
ot
er
2
c
h
h
a
w
5
3 11
75
y
p
t h ree o clock This is the correct an d only possible answer to the
pu z z le
.
,
,
,
.
.
,
,
,
.
,
,
.
’
.
3
3 1
.
.
,
.
,
,
8
1 1
-
.
.
.
’
.
,
-
,
.
.
.
8
.
,
’
.
.
,
,
.
1
.
T HE C A N T E RB U R Y
250
—
1 13
Cutti ng
a
PUZZ LES
Wood Block
.
the cubic contents are s ufficient for twent y five pi
only twent y four c an act ual ly be cut from the block F irst red
the len gth o f the block by h alf an inch The smaller piece cut
constit utes the portion th at c annot be used Cut the l arger pi
into three sl abs e ach o ne an d a qu arter inch thick and it will
found th at eight blocks m ay e asily be cut o ut o f each sl ab without
an y further w aste
Though
-
-
.
.
.
,
,
.
114
.
—The
Tramps
and
the Bi scui ts
.
sm allest number o f biscuits must h ave been 1 02 1
which it is evident th at they were o f that mi ni ature descript
th at finds favour in t h e n ursery The general solution is that
a
n
where
is
n
m
n men the n u mber m ust be
(
y
E ach m an will receive m (n
1 bisc u its at the fin al divi s ion
tho ugh in the c ase of two men when m = 1 the fin al distribution
onl y benefits the dog Of course in every c ase e ach man ste als an i
n th o f the n um be r o f bisc uits after g i vin g the o dd o n e to the d o g
The
,
.
,
,
.
.
,
,
,
.
I N D E!
2 52
C k P zzl Th 3 6 17 1
C i h Cli ff My t y Th 9 9 210
C t P bl m M v i g 24 3 5
’
oo
u
s
e,
e,
s er
o rn s
o un e r
ro
,
s,
e
e,
n
o
7 7 , 124 , 1 35 , 13 6 , 14 1
u
e, 39
o ut
o u n ti n
,
69 ,
,
,
.
C
g
P zz l
C
t
d th Cr
Th 63 18 9
C i g Ri v P bl m 82 8 3
C u d Th R iddl f th 74 19 7
14 2 240
C
R bi
B T bl
Cu b S u m f Tw 174 209
9 2 209
Th S i l v
re sce n
ro
er
ro s s n
e rs ,
r sa
o s s,
e
an
a
,
.
e
rs -
o
r,
D m l R
g
D m ll
bl
Di m d Le tt Pu zzl 18 1
D igi t l A ly i 228
Puzzl 18 26 90 103
o
r
o
e s an
c e s,
r
’
er
on
s s,
na
a
e s,
148 , 15 4
Di
u
,
Nu
or of
174
Ph y
mb
si c ,
,
n o ur,
41, 49 ,
,
.
Fi d 170
Th e P u zz l e f th 4 2
To
n
e,
K e e p Win d o w Th 62 188
D
S i ty Th 15 1 245
D m it y P uzzl Th 70
D un g
Th D t h h d 60
D g
Th N i
35
Dy
Puzzl Th 50
e,
,
oc e
e,
,
e on ,
e o n s,
ea
s,
o
rra n
7 8 , 201
Ex
’
n
The , 78
,
r,
e
.
F ll y f S q u r s Di g n l 5 2
F m Ox n The 15 7 24 8
a
ar
a e
o
ac
’
er s
e
,
a
,
,
.
s,
e
.
,
,
.
.
,
,
a
ro
,
,
,
,
121
.
My t y Th 15 8 249
d
G up P o b l m C m b i ti
C o m b in tio
d Gro u p P b l m
r
s er
e,
,
,
o n an
na
o
s,
e
ro
n an
a
H b d h Pu zzl Th 49
H g C t h in g t h 124 223
19 8
H pp O
H t Puzzl Th 28 166
a
e r as
o
s,
’
’
e,
er s
s c a r,
.
e,
e,
s
e,
e,
a c
e,
bl C k
e
’
as
s
La
e t,
n is c h ,
23 7
an e se
La di e s
J
.
e
s
.
1 78
,
.
.
,
.
,
dy
6 7, 19 1
.
,
o
,
a
,
.
St
7 8 , 201
ran
g
.
C rpe t
th e
an d
a
,
ran
g E
e
sc a
p
e
of
Ki n g
t he
,
.
e
G m
K ayle e , Th e a e o f 118 , 220
e nn e s , Th e N i n e , 3 9
K
l
Kin g s J
.
,
.
e ste r,
7 8 , 201
’
ni ht s P u
St
ran
g E
e
s ca
pe
.
K g
13
.
e s t e r,
’
’
a
rs
e
G ran ge m o or
23 1
.
.
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.
puzzl
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th e
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i t o f i n e n ui ty an d in tricac ;
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”
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.
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gh t t b h igh ly p p l
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l
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t b
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—
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”
uch i n re ue s t
The M orn i ng L ea der
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ro
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oo ,
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”
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at th e e n d
M a n c hester G u ardi a n
k p
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en o
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whi h i
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k il f l i v t
N
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an
.
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.
n o
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as c o
ra n -
n
er
it ;
so
e of
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fo r in e n io us e rso n s wh o w an t e
o
e nt
”
i t a un an t sco e
Yorksh i re P ost
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.
g
.
d ity
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a
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ra
atic
Th e
b kg u d
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ac
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ro
s
o
n