George Pólya
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George Pólya |
In this spirit each student of my Fall '96 Mathematical Models and Applications (MAT 303) class has contributed a page describing some game/puzzle that they felt would be of use in the classroom. The students of the class were future K-8 teachers, so most of the problems are at that level. All comments/suggestions/corrections are welcome.
A magic trick involving 4 five pointed stars.
A two person game played on a small grid. Players are trying to avoid getting 3 in a line.
1 2 3 5 A two person game where the players take turns adding a 1,2,3,4 or 5 to a common sum. The same number can not be added on twice in a row and the player to take the sum over 37 loses.
A two person game played with a pile of sticks. Different rules are possible that allow a person to select 1, 2 and sometimes 3 sticks from the pile. Whoever takes the last stick is the winner.
You are asked to find a path starting at the upper left hand corner of a table of numbers and moving one jump to a 1, two jumps to a 2, three jumps to a 3, etc. until you reach the lower right hand corner. The path is not allowed to cross itself.
A puzzle that asks you to place circles at the head of sticks arranged in a star pattern.
A puzzle that asks you to plan the escape of a prisoner through a corridor partitioned by five doors.
A card game played with the 2, 3, 4, 5, 6, 7, 8, 9, 10 and Queen of one suit.
A two person game played on a grid. Players alternate building a path from the upper left hand corner to the black square located someplace in the grid.
A two person game where each player in turn draws a line using his own color between two of six points. A player loses when they complete a triangle in their color.
This is a dynamic Knight's tour puzzle. You try to visit all the squares and end up back where you started, but the squares disappear as time goes by.
This is a problem that asks you to do a random walk down a pyramid tree.
A two person game played on a piece of paper. Several dots (3 or more) are drawn on the paper and then players take turns connecting the dots by lines and adding a new dot in the middle of their line. No dot can have more than three lines coming out of it. The last player able to add a line is the winner. This game is usually called "sprouts".
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This is a two person game that is played on a grid. The players take turns coloring in one or two adjacent squares. The player to color the last square wins.
A puzzle using pool balls. You try to arrange the balls in a triangle so that the number on a ball is equal to the difference of the numbers on the two balls above it.
A puzzle that asks you to order the numbers 1..10 around a circle so that every adjacent pair of numbers have the same sum as the pair opposite them on the circle.
A collection of puzzles requiring you to move a knight around boards of various shapes, visiting every square on the board and ending up back at the starting point.
Several piles of sticks make up the game. Each player takes his turn removing sticks from the pile of their choice. The player who removes the last stick wins.
The jackals and the coyotes are trying to cross a river in a small boat. They need your help.
This is a two person game between a fox and a goose. The fox tries to catch the goose before he dies of hunger.
This is a puzzle that uses a grid containing numbers at its vertices and operations (+,/,*,-) on its edges. You are asked to find a path that takes you from the number in the upper left hand corner to the lower right hand corner, performing the operations on the numbers as you go, and ending up with a specified value.
This two person game uses a 3x3 grid and cards 1 .. 9. One player plays the even numbered cards and the other player the odd numbered cards. They each try to play the last card in a line of three cards that add to 15.
A popular puzzle from the 70's. You are to try to stack 4 cubes, whose faces are colored using four colors, so that the colors on each side of the 4 stacked cubes are four different colors.
A magic trick with numbers.
A two person game played on a small grid. Players are trying to avoid having consecutive numbers in adjacent cells.
A two person game played on a grid with some cells missing and one cell contains a smiley face. Players take turns coloring in rectangular areas of the grid. The player forced to color the smiley face loses.
A puzzle that asks you to find a tiling of a rectangular floor with 1X2 tiles that does not contain a fault line.
A game of chance. Players try to get a large score on several rolls of a pair of dice. They add the roll to their score, if they elect to stay in, but get a zero for that round if a one is rolled and lose their accumulated points from the previous rounds, if two one's are rolled. There are five rounds.
