Department of Mathematics
University of Illinois at Urbana–Champaign
www.math.uiuc.edu
2004
This calendar was designed by Tori Corkery for the Department of Mathematics at the University of Illinois at
Urbana-Champaign. Special thanks go to Sara Nelson, Lori Dick, Tess Rannebarger, Elizabeth Denne, Michael
Bush, and Professors Douglas B. West, Dan Grayson, and Joseph Rosenblatt for their help and support on this
project.
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 West Green Street
Urbana, Illinois 61801
office@math.uiuc.edu
www.math.uiuc.edu
Tel: 217-333-3350
Fax: 217-333-9576
Kalah
Kalah, also called mancalah, is the oldest known continuously played game in history. A Kalah
board was found carved into the stone pyramid of Cheops in Egypt. The commercial wooden
board game (at right) was first made available to the public in the 1950s by the Kalah Game
Company. The playing surface includes two rows of 6 depressions, with a larger storage area at
each end. Beans or seeds were included for use as counters in the game. According to the
Kalah Game Company “the game Kalah not only induces children to like
arithmetic, but also makes them think. The method of playing—distributing
counters one by one to the right—confirms the habit of moving from left
to right as when reading or writing. The rules are so simple that they can be
quickly explained to pre-school age children who usually start with only one
or two counters in each pit. Small children learn to count without using their
fingers; to distinguish units from multiples; and to acquire other mathematical concepts in a
natural way. Addition, subtraction, multiplication and division are all used in determining the
number of counters to be used in the twelve pits, or in computing the score. Calculation is also
required to anticipate where the last counter will land at the end of a single or series of plays.”
[Used with permission from www.ahs.uwaterloo.ca/~museum/countcap/pages/kalah.html]
Sunday
Monday
Tuesday
Wednesday
Thursday
1
Friday
2
Saturday
3
New Year's Day
4
5
6
7
8
9 10

11 12 13 14 15 16 17

2004
December
2
3
4
9 10 11
16 17 18
23 24 25
30 31
February
7
14
21
28
1
8
15
22
29
5
12
19
26
6
13
20
27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
18 19 20 21 22 23 24

Martin Luther
King Jr. Day
29
Department of
Mathematics
University of Illinois at U-C
1409 W. Green Street
Urbana, IL 61801
(217) 333-3350
office@math.uiuc.edu
25 26 27 28 29 30 31


www.math.uiuc.edu
 New Moon

 First Quarter
 Full Moon

 Last Quarter
Burr Puzzles
Jerry Slocum and Jack Botermans (Puzzles Old & New, Seattle:
University of Washington Press, 1992, page 66) indicate that a
Burr Puzzle is an interlocking geometric puzzle composed of
notched rods that poses a high degree of external symmetry. The
history of puzzles of this type date back to the 18th and 19th
centuries. The 6 piece wood puzzle pictured at left was available
as early as 1875, and when assembled creates a star shape. Slocum
and Botermans report that mathematicians have used computers
to determine that of the thousands of possible notched rods that
might be attempted to be used to create Burr Puzzles, only 369
shapes will do. However, it is to be noted that mixing and matching
of the 369 useable shapes results in the ability to create 119,979
different Burr Puzzles! [Used with permission from
http://www.ahs.uwaterloo.ca/~museum/puzzles/burr/index.html]
Sunday
Monday
Tuesday
3
Wednesday
4
Thursday
5
Friday
6
Saturday
1
2
8
9 10 11 12 13 14

7

St. Valentine’s
Day
15 16 17 18 19 20 21

2004
President’s Day
(observed)
January
4
11
18
25
5
12
19
26
6
13
20
27
1
8
15
22
29
2
9
16
23
30
3
10
17
24
31
7
14
21
28
1
8
15
22
29
March
2
3
4
9 10 11
16 17 18
23 24 25
30 31
5
12
19
26
6
13
20
27
7
14
21
28
Department of
Mathematics
University of Illinois at U-C
1409 W. Green Street
Urbana, IL 61801
(217) 333-3350
office@math.uiuc.edu
22 23 24 25 26 27 28


29
www.math.uiuc.edu
 New Moon

 First Quarter
 Full Moon

 Last Quarter
Billiards
Billiards evolved from a lawn game similar to croquet played sometime during the
15th century in Northern Europe and probably in France. Play was moved indoors to a
wooden table with green cloth to simulate grass, and a simple border was placed
around the edges. The balls were shoved, rather than struck, with wooden sticks
called "maces". The term "billiard" is derived from French, either from the word
"billart", one of the wooden sticks, or "bille", a ball. The game was originally played
with two balls on a six-pocket table with a hoop similar to a croquet wicket and an
upright stick was used as a target. During the eighteenth century, the hoop and
target gradually disappeared, leaving only the balls and pockets. Billiard equipment
improved rapidly in England after 1800, largely because of the Industrial Revolution.
By 1850 the billiard table had essentially evolved into its current form. Real billiards
can involve spinning the ball so that it does not travel in a straight line, but the
mathematical study of billiards generally examines collisions in which the reflection
and incidence angles are the same. The analysis of billiards involves sophisticated
use of ergodic theory and dynamical systems. For more history about billiards, see
the website at http://www.poolroom.com/articles/history.html.
Sunday
Monday
1
Tuesday
2
Wednesday
3
Thursday
4
Friday
5
Saturday
6

7
8
9 10 11 12 13

14 15 16 17 18 19 20

2004
St. Patrick’s Day
Spring Begins
February
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
1
8
15
22
29
2
9
16
23
30
3
10
17
24
21 22 23 24 25 26 27
29
April
4
11
18
25
5
12
19
26
6
13
20
27
7
14
21
28
Department of
Mathematics
University of Illinois at U-C
1409 W. Green Street
Urbana, IL 61801
(217) 333-3350
office@math.uiuc.edu
28 29 30 31


www.math.uiuc.edu
 New Moon

 First Quarter
 Full Moon

 Last Quarter
Tower of Hanoi
The French mathematician Edouard Lucas invented this puzzle in 1883 and
called it La Tour d'Hanoi (The Tower of Hanoi). A fanciful legend is told about
the tower where “in the temple of Benares there was a brass plate on which
stood three diamond needles. While creating the world, God placed 64 gold
disks, from large to small, on one of these needles... The priests, in
accordance with the laws of Brahma, removed one disk at a time to one of the
other needles. The disk on top of which the priest places his can never be
smaller than the one going on top of it... only one disk at a time can be moved.
Once the tower has been transferred from one needle to another, everything
will turn to dust and the world come to an end with a big bang.” In
mathematical terms, for this puzzle the number of moves required to transfer
just 3 disks is 7 moves or (2x2x2-1). With 64 disks it would require (2 to the
64th power minus one) moves. It is estimated that at one move every second,
this would take nearly 6 billion centuries! [Used with permission from
http://www.ahs.uwaterloo.ca/~museum/puzzles/tower/index.html]
Sunday
4
Monday
Tuesday
5
6

Wednesday
Thursday
7
Friday
Saturday
1
2
3
8
9 10
Daylight Savings
Time Begins
Palm Sunday
Passover
Good Friday
11 12 13 14 15 16 17

2004
7
14
21
28
1
8
15
22
29
2
9
16
23
30
3
10
17
24
31
March
2
3
4
9 10 11
16 17 18
23 24 25
30 31
May
4
11
18
25
5
12
19
26
6
13
20
27
5
12
19
26
Easter
6
13
20
27
18 19 20 21 22 23 24

7
14
21
28
1
8
15
22
29
Department of
Mathematics
University of Illinois at U-C
1409 W. Green Street
Urbana, IL 61801
(217) 333-3350
office@math.uiuc.edu
Earth Day
25 26 27 28 29 30


www.math.uiuc.edu
 New Moon

 First Quarter
 Full Moon

 Last Quarter
Nim
The ancient game known today as Nim is thought to be Chinese in origin. A
full analysis was published in 1901 by Charles Leonard Bouton (associate
professor of mathematics at Harvard University) in which he described a
mathematical strategy for playing the game. It is Bouton who is
responsible for the modern name, Nim. The game of Nim is for two players.
Several stones (or matchsticks, paper clips, tokens, etc.) are placed in
several piles—the precise numbers are agreed upon by the two players. A
move for either player consists of removing some stones (at least one)
from just one pile. The winner is the one who takes the last stone. The
development of the winning strategy involves group theory, and the
strategy itself involves binary notation for the numbers.
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
1
2
3
4

5
6
7
8
9 10 11 12 13 14 15

2004
Mother’s Day
April
4
11
18
25
6
13
20
27
5
12
19
26
7
14
21
28
6
13
20
27
7
14
21
28
June
1
2
8
9
15 16
22 23
29 30
1
8
15
22
29
2
9
16
23
30
3
10
17
24
3
10
17
24
4
11
18
25
5
12
19
26
Department of
Mathematics
University of Illinois at U-C
1409 W. Green Street
Urbana, IL 61801
(217) 333-3350
office@math.uiuc.edu
www.math.uiuc.edu
16 17 18 19 20 21 22

23 24
30
25 26 27 28 29


31
Memorial Day
 New Moon

 First Quarter
 Full Moon

 Last Quarter
Nine Men’s Morris
This photograph was taken in August 1996 at a hill temple near
Khejarala, Rajesthan, India. Carved into the rock is the board for
the game "Nine Men's Morris." Each player has nine stones which
they put onto the board alternately one at a time. When all the
stones are on the board players take turns to move a piece along a
line to a neighboring empty point. When a player achieves three in
a row an opposing stone is removed but it may not be taken from
an opposing three in a row. If a player is reduced to two pieces or
is blocked and unable to move, that player has lost the game. What
is the maximum number of pieces which can be on the board
without any forming a row? Investigate for other size boards.
[From http://atschool.eduweb.co.uk/ufa10/game2.htm]
Sunday
Monday
6
7
Tuesday
Wednesday
Thursday
Friday
1
2
8
9 10 11 12
3

4
Saturday
5

13 14 15 16 17 18 19

2004
Flag Day
May
2
9
16
23
30
3
10
17
24
31
4
11
18
25
5
12
19
26
6
13
20
27
7
14
21
28
1
8
15
22
29
1
8
15
22
29
2
9
16
23
30
3
10
17
24
31
20 21 22 23 24 25 26


July
4
11
18
25
5
12
19
26
6
13
20
27
7
14
21
28
Department of
Mathematics
University of Illinois at U-C
1409 W. Green Street
Urbana, IL 61801
(217) 333-3350
office@math.uiuc.edu
Father’s Day
Summer Begins
27 28 29 30
www.math.uiuc.edu
 New Moon

 First Quarter
 Full Moon

 Last Quarter
Peg Solitaire
Though the origins of Peg Solitaire are unknown, there is evidence that it
existed as early as 1697 from an engraving by Claude-Auguste Berey that shows
Princess de Soubise playing the game. The famous German mathematician
Gottfried Wilhelm Leibniz wrote about the game for the Berlin Academy in
1710. The most common objective of the game is to leave a single peg by
jumping and removing pegs. Mathematical study using group theory has shown
that there are only five locations where one can leave that single peg. There
are however a variety of ways to play and other configurations on the board (a
triangle, a cross, etc.) that enables the devising of a variety of puzzles on the
same board. More information about peg solitaire and group theory can be
found at http://www.cut-the-knot.org/proofs/PegsAndGroups.shtml.
Sunday
4
Monday
5
Tuesday
6
Wednesday
7
Thursday
Friday
Saturday
1
2
8
9 10

3

Independence
Day
11 12 13 14 15 16 17

2004
6
13
20
27
7
14
21
28
1
8
15
22
29
2
9
16
23
30
June
1
2
8
9
15 16
22 23
29 30
August
3
4
10 11
17 18
24 25
31
3
10
17
24
4
11
18
25
5
12
19
26
5
12
19
26
6
13
20
27
7
14
21
28
Department of
Mathematics
University of Illinois at U-C
1409 W. Green Street
Urbana, IL 61801
(217) 333-3350
office@math.uiuc.edu
18 19 20 21 22 23 24
25 26 27 28 29 30 31



www.math.uiuc.edu
 New Moon

 First Quarter
 Full Moon

 Last Quarter
Soma Cube
The Soma Cube's discoverer Piet Hein, a Danish poet and inventor,
first envisioned the cube while attending lectures on guantum physics
in 1936. The Soma Cube has been sometimes viewed as a threedimensional version of the Tangram Puzzle. This comparison is because
both types of puzzles are made up of seven pieces which can be used
to construct numerous shapes. The puzzle can be used to help develop
skills in visualizing spatial relationships. The Soma Cube is made of 27
cubes which are glued in seven individual arrangements: six pieces
consisting of 4 small cubes and one of 3 small cubes. The aim of this
game is to assemble a 3 x 3 x 3 cube. This can in fact be done in 240
different ways! [Used with permission from
www.ahs.uwaterloo.ca/~museum/puzzles/soma/index.html]
Sunday
1
Monday
2
Tuesday
3
Wednesday
4
Thursday
5
Friday
6
Saturday
7

8
9 10 11 12 13 14
15 16 17 18 19 20 21

2004
July
4
11
18
25
5
12
19
26
5
12
19
26
6
13
20
27
1
6
7
8
13 14 15
20 21 22
27 28 29
September
1
2
7
8
9
14 15 16
21 22 23
28 29 30
2
9
16
23
30
3
10
17
24
31
3
10
17
24
4
11
18
25
Department of
Mathematics
University of Illinois at U-C
1409 W. Green Street
Urbana, IL 61801
(217) 333-3350
office@math.uiuc.edu
22 23 24 25 26 27 28


29 30 31

www.math.uiuc.edu
 New Moon

 First Quarter
 Full Moon

 Last Quarter
Chess
One of the earliest mentions of Chess in puzzles is by the Arabic mathematician
Ibn Kallikan who, in 1256, poses the problem of the grains of wheat, 1 on the first
square of the chess board, 2 on the second, 4 on the third, 8 on the fourth, etc.
One of the earliest problems involving chess pieces is due to Guarini di Forli who
in 1512 asked how two white and two black knights could be interchanged if they
are placed at the corners of a 3 x 3 board (using normal knight's moves). Wellknown chess problems include the Knight's Tour of the chess board studied first
by De Moivre and Montmort who solved the problem in the early years of the
18th century after the question had been posed by Taylor. Euler, in 1759
following a suggestion of L. Bertrand of Geneva, was the first to make a serious
mathematical analysis of it, introducing concepts which were to become important
in graph theory. Another famous chess board problem, posed by Franz Nauck in
1850, is the Eight Queens Problem. This problem asks in how many ways 8 queens
can be placed on a chess board so that no two attack each other. [From
http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Mathematical_games.html]
Sunday
Monday
5
6

Tuesday
7
Wednesday
Thursday
Friday
Saturday
1
2
3
4
8
9 10 11
Labor Day
12 13 14 15 16 17 18

2004
1
8
15
22
29
2
9
16
23
30
August
3
4
5
10 11 12
17 18 19
24 25 26
31
October
3
10
17
24
31
4
11
18
25
5
12
19
26
6
13
20
27
7
14
21
28
6
13
20
27
Rosh Hashanah
7
14
21
28
19 20 21 22 23 24 25


1
8
15
22
29
2
9
16
23
30
Department of
Mathematics
University of Illinois at U-C
1409 W. Green Street
Urbana, IL 61801
(217) 333-3350
office@math.uiuc.edu
Autumn Begins
Yom Kippur
26 27 28 29 30

www.math.uiuc.edu
 New Moon

 First Quarter
 Full Moon

 Last Quarter
Cardan’s Rings
Around 1550 Jerome Cardan, an Italian mathematician specializing in the theory
of algebraic equations, described the Chinese ring puzzle, a game consisting of a
number of rings on a bar. Cardan’s Rings appear in the 1550 edition of his book
De Subtililate. The rings were arranged so that only the ring “A” (see diagram at
left) at one end could be taken on and off without problems. To take any other
off the ring next to it towards “A” had to be on the bar and all others towards
“A” had to be off the bar. To take all the rings off requires (2n+1 - 1)/3 moves if
n is odd and (2n+1 - 2)/3 moves if n is even. This problem is similar to the Towers
of Hanoi—in fact Edouard Lucas, the inventor of the Towers of Hanoi, gives a
pretty solution to Cardan's Ring Puzzle using binary arithmetic. [From
www-gap.dcs.st-and.ac.uk/~history/HistTopics/Mathematical_games.html]
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
1
2
8
9
10 11 12 13 14 15
16
3
4
5
6

7

2004
5
12
19
26
6
13
20
27
7
14
21
28
1
8
15
22
29
September
1
2
7
8
9
14 15 16
21 22 23
28 29 30
November
2
3
4
9 10 11
16 17 18
23 24 25
30
Columbus Day
(observed)
3
10
17
24
4
11
18
25
5
12
19
26
6
13
20
27
Department of
Mathematics
University of Illinois at U-C
1409 W. Green Street
Urbana, IL 61801
(217) 333-3350
office@math.uiuc.edu
www.math.uiuc.edu
Saturday
17 18 19 20 21 22


24
25 26 27 28 29

23
30
31
Daylight Savings
Time Ends
Halloween
 New Moon

 First Quarter
 Full Moon

 Last Quarter
Rubik’s Cube
This puzzle was invented by the architect and teacher Ernö Rubik in
Budapest, Hungary in the 1970s as an aid to help his students recognize
spatial relationships in three dimensions. The same puzzle was apparently
designed independently by Terutoshi Ishige, an engineer in Japan. A
patented copy was manufactured in Hungary and became available in Europe
in 1978, and became widely available during the 1980 Christmas season in
North America. It is really a group theory puzzle, although not many people
realize this. The cube consists of 3 x 3 x 3 smaller cubes which, in the
initial configuration, are colored so that the 6 faces of the large cube are
colored in 6 distinct colors. The 9 cubes forming one face can be rotated
through 45º. There are 43,252,003,274,489,856,000 different
arrangements of the small cubes, only one of these arrangements being the
initial position. Solving the cube shows the importance of conjugates and
commutators in a group. [Used with permission from
http://www.ahs.uwaterloo.ca/~museum/puzzles/rubik/index.html]
Sunday
Monday
1
Tuesday
2
Wednesday
Thursday
3
4
Friday
5

Saturday
6
Election Day
7
8
9 10 11 12 13

Veterans Day
14 15 16 17 18 19 20


2004
October
3
10
17
24
31
5
12
19
26
4
11
18
25
5
12
19
26
7
14
21
28
1
8
15
22
29
2
9
16
23
30
6
13
20
27
December
1
2
7
8
9
14 15 16
21 22 23
28 29 30
3
10
17
24
31
4
11
18
25
6
13
20
27
Department of
Mathematics
University of Illinois at U-C
1409 W. Green Street
Urbana, IL 61801
(217) 333-3350
office@math.uiuc.edu
21 22 23 24 25 26 27

Thanksgiving
28 29 30
www.math.uiuc.edu
 New Moon

 First Quarter
 Full Moon

 Last Quarter
Go
Go is thought to have originated in China between 4,000 and 5,000 years ago. By the time of
Confucius (around 600 B.C.), Go had already become one of the "Four Accomplishments" (along with
brush painting, poetry and music) that must be mastered by the Chinese gentleman. It passed into
Korean and Japanese culture as a result of trade and other contact between countries in the first
millennium A.D. Go remained a pastime for the wealthy and educated classes. The earliest Go players
in North America were probably Chinese workers toiling on the intercontinental railroad in the mid1800s. Go first came to the attention of Westerners in the early 1900s when a group of German
mathematicians and game players stumbled upon it, including Otto Korschelt and Edward Lasker, a
cousin of the legendary chess player Emanuel Lasker and himself a well-known chess master. With
Lee Hartmann (editor of Harper's magazine) and a few others, Lasker formed the American Go
Association in New York in 1937. The game’s complexity arises from the huge number of possibilities
for board positions (said to be 10 to the 750th power). A full-size Go board must have a grid of 19
horizontal and 19 vertical lines. The grid contains 361 intersections. The round stones (180 white
and 181 black) are placed on the intersections, not the rectangles. More information is available
from the American Go Association at www.usgo.org/index.asp.
Sunday
5

Monday
6
Tuesday
Wednesday
7
Thursday
Friday
3
Saturday
1
2
8
9 10 11
4
Hanukkah
12 13 14 15 16 17 18



2004
7
14
21
28
1
8
15
22
29
2
9
16
23
30
3
10
17
24
31
November
2
3
4
9 10 11
16 17 18
23 24 25
30
January
4
11
18
25
5
12
19
26
6
13
20
27
5
12
19
26
6
13
20
27
7
14
21
28
1
8
15
22
29
Department of
Mathematics
University of Illinois at U-C
1409 W. Green Street
Urbana, IL 61801
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