A bandsaw project
making a new puzzle from an old one
Sam Loyd (1841 to 1911) was
a great puzzler. His little
books contain hundreds of
original ideas.
Here is one of his puzzles
“Dissect a Greek cross and re-arrange the
pieces to make a square. Do it with as few
cuts as possible”
Making a new puzzle from an old one
Here is Sam Loyd’s solution – only two cuts.
And a nice “Aha!” moment.
Interesting – but quite a lot of trouble for a
puzzle that will be used only once.
Can it be made better?
Making a new puzzle from an old one
But cut one of the
complicated pieces
in two (making five
in all).
Now several more
re-arrangements
are possible
And the woodwork
is a bit easier
Making a new puzzle from an old one
Make just one more cut (that makes six
pieces) and a whole range of new shapes
becomes possible
Making a new puzzle from an old one
With a six piece puzzle, the pieces are easy to
make and the number of nice shapes is over 30
Making a new puzzle from an old one
The basic triangle behind the cross to square
puzzle. Sides are 2, 1, and √5 (about 2.236)
Angles are 26 ½ and 63 ½ degrees
(but let's calculate these numbers)
Making a new puzzle from an old one
The sizes of the three triangles are in the ratio of 1 : 2 : √5.
(remember Pythagoras?)
They fit together in unusual ways
Use the "cosine rule" and the cos-1
button on the calculator to
calculate angles
cos(θ) = (a2 + b2 – c2) / 2ab
a = 1.0, b = √5 = 2.236, c = 2.0
cos(θ) = (1.0 + 5.0 – 4.0) / 2 x 1.0 x 2.236
= 2.0 / 4.472 = 0.4472
so θ = 63.43°
Cutting the pieces for the new puzzle – jigs for the bandsaw
The six pieces of the puzzle are cut
from sheet that is 60mm wide and
about 8mm thick. The angles of
the triangles are 63 ½ , 23 ½ and 90
degrees
Cutting the pieces for the new puzzle – jigs for the bandsaw
Several pieces 60mm wide and 8mm
thick can be cut at the same time.
The first jig is used to make the long cut
at 63 ½ degrees.
The others are used in sequence to
produce all the pieces.
Each jig is designed to be used with the
rip fence set accurately at 60mm
A puzzle made on the
router
The 6-piece "burr"
Burr puzzles all look alike
from the outside, the
complexity is in the details
of the cuts
This one is the simplest
Three identical pieces
Two identical pieces
One solid piece
Six-piece "burr" puzzles
Six blocks are needed for each puzzle – there are many ways of
cutting the internal notches.
In these pieces the notches go all the way through (so they can
be cut by a router). This is not always the case.
Six-piece "burr"
puzzles
Six blocks are needed for each
puzzle – in this case
25mm x 25mm x 75mm
There are four ways of making
router cuts in the pieces. Two
"outer" cuts (red and blue) and
two "inner" cuts (green and
yellow)
Six-piece "burr"
puzzles
The router jig has two
position for holding the
75mm pieces, one for an
"outer" cut and one for an
"inner" cut
The cover holds the two pieces
in place and prevents them
rising up while the router is
operating
The bottom is attached to a
dust extractor (not shown)
Six-piece "burr"
puzzles
The router sits on the cover
and is guided by the side
rails.
To get a good finish the sides
of each groove are pre-cut on
the bandsaw
A 12.5mm square end router bit is used
for making the grooves
Using the lathe and the
pillar drill
A cylindrical "burr"
Instead of square section pieces,
this puzzle has six cylinders and a
base.
They are turned on the lathe and
bored on the pillar drill
Six-piece
cylindrical
"burr" puzzle
After turning, the cylinders are
cross-bored (off-centre) in a jig to
form the semi-circular
depressions
As before there are
three identical
pieces, two
identical pieces and
a solid piece
Six-piece cylindrical
"burr" puzzle
The base is also turned and bored (offcentre) on the lathe
Using the base, the pieces may be re-assembled, like this
Puzzle Making for Woodworkers
Donald Bell
SFW Meeting, January 2011
Email : donald@marchland.org
Web site : www.bellwoodwork.com