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How can Mathematics be Recreational?
Think Big!
How can you cut a 3x5 card so that you can walk
through it?
Why Recreational Mathematics?
Historically many important mathematical concepts arose
from problems mathematical in origin.
Ideal for introducing topics covered in liberal arts
mathematics courses.
Something a bit different to do on a day when students
need something a bit different to do!
Types of Recreational Mathematics
Puzzles
Games
Others
Puzzles Puzzles require mathematics in order to solve them.
They have specific rules, but mathematical puzzles
don't usually involve competition between two or more
players. Instead, in order to solve the puzzle, the solver
must find a solution that satisfies the given conditions.
Logic puzzles fall into this category.
Games Rules, strategies, and outcomes can be studied and
explained by mathematics although players may not
use mathematics in order to play the game.
Others Curiosities and pastimes of non-trivial mathematical
interest
Optical Illusions
Videos
Brain Teasers
Cat's cradle and other string figures
Origami (many mathematical results, some deep)
Tower of Hanoihttp://www.mazeworks.com/hanoi/index.htm
Game consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.
The objective of the puzzle is to move the entire stack to another rod, obeying the following rules:
Only one disk may be moved at a time. Each move consists of taking the upper disk from one of the rods
and sliding it onto another rod, on top of the other disks that may already be present on that rod.
No disk may be placed on top of a smaller disk.
TangramsThe aim of the puzzle is to seamlessly arrange all the geometric pieces to form
problem figures. It is said that the Pythagorean theorem was discovered in the Orient with help of Tangram pieces...
The 7 polygons or 'tans' that form the Tangram are:• 5 right triangles: 2 small (hypotenuse of n/2 and sides of n/2√2); 1
medium (hypotenuse of n/√2 and sides of n/2); 2 large (hypotenuse of n and sides of n/√2). The large triangle is 4 times the size of the small triangle, but curiously its perimeter is only 2 times as big!
• 1 square (side of n/2√2).• 1 parallelogram/rhomboid (sides of n/2 and n/2√2).
Of these 7 pieces, the parallelogram (or rhomboid) is the only piece that may need to be flipped when forming certain shapes; in fact, it has no reflection symmetry but only rotational symmetry, and so its mirror image can only be obtained by flipping it over.
An Even Hundred Can you insert addition or subtraction signs among
the following digits to get an expression equal to 100?
123456789
An Even Hundred Solution
There are many are possible solutions
123 – 4 – 5 – 6 – 7 + 8 – 9 = 100
123 – 45 – 67 + 89 = 100
Make a Thousand
Try making 1000 with
Eight 8’s
Seven 7’s
Six 6’s
Make a Thousand Solution
888 + 88 + 8 + 8 + 8 = 1000
777/.7 – 77/.7 = 1000
666/.666 = 1000
7 pairs; 7 sums Using the numbers 1-6, create a three by two grid
where the seven pairs of adjacent squares have seven
different sums
3 8
4
5 11
7
610
1 3 2 6 4
Solution
CongruencyHow many different
ways can you cut a grid
4x4 in half along the
grid lines? Six different
polygonal shapes are
possible from the halves.
The Simple Solution . . .
Another solution . . .
Another solution . . .
Another solution . . .
Another solution . . .
Another solution . . .
Logic Puzzles Printable logic puzzles in pdf format found at
http://www.logic-puzzles.org/
Monthly Logic Puzzles that to not need to be printed
found at
http://www.puzzlersparadise.com/page1034.html
Strategy Games A strategy is a rule or decision making formula that
tells the player which choice to make at each turn.
Winning strategy – Strategy enables the player to win
no matter what moves his or her opponent makes.
Drawing strategy – Strategy does not guarantee a win
for a particular player but does guarantee that he or
she does not lose. The game can end in a draw.
Strategy Games What are the rules?
What constitutes a win or a loss?
What is a move?
Is it advantageous to go first?
What should be the opening move?
Types of Games Chance – The player’s fortune depends on roll of the
dice or the deal of the cards.
Chance-Free – Each player at each turn is free to choose any legal moves. Decisions are not made by chance.
Perfect Information- Each player is aware at all times of all aspects of the structure of the game.
Finite- The game must necessarily end or terminate in a finite number of moves.
Bounded – If there is a number “n” such that the game cannot last for more than “n” moves.
Nim Game of Nim, said to have originated in China
http://education.jlab.org/nim/index.html
The "classical" Nim game is a game by two players. It
consists of 16 matches. Two players alternately pick a
certain number of matches and the one, who takes the
last match, loses.
9 Cell Tic Tac Toe Directions: Each player has three markers. Alternate
turns putting own marker on any cell. When all six
markers have been placed on the board, players
alternate moving their own marker into an empty
adjacent cell either horizontally or vertically. The first
player to get three in a row is a winner.
Split, Strategy Game Game for two players
Play begins with a pile of 32 matchsticks or checkers.
Each player must separate any existing pile into two
unequal piles. For example, 4 chips must be split into
a pile of 3 and 1, not two and two. A pile of two can
never be separated. The first player who cannot make
a move is the loser.
Other Games Jeopardy
http://www.jmu.edu/madison/teacher/jeopardy/
jeopardy.htm
Other Power Point Games (Who Wants to be a
Millionaire, etc.)
http://teach.fcps.net/trt10/PowerPoint.htm
Optical Illusions . . . Escher
YouTube as a resource . . .
Pa & Pa Kettle due mathematics?
http://www.youtube.com/watch?v=OettgNpe4n4
Where does the extra man come from?
http://www.youtube.com/watch?v=4XbrUHMDTg0&feature=related
Brain Teasers Puzzles, games (speed games, memory games, problem solving
games), illusions, and logic games. You will need to create a free
account found at http://www.brainbashers.com/
Make your own puzzles (Pencil puzzle, Letter puzzles & Others)
found at http://www.creatievepuzzels.com/spel/speel1/sites.htm
Collection of brain teasers, and puzzles found at
http://www.internet4classrooms.com/brain_teasers.htm
String Games, Cats Cradlehttp://www.ifyoulovetoread.com/book/chten_cats1105.htm
Origami Wolfram Mathworld Origami found at
http://mathworld.wolfram.com/Origami.html
Using Origami to Teach Mathematics – Math on the
Street found at
http://math.serenevy.net/?page=Origami-
TeachingLinks
What have are you doing for FUN
in your classroom?
