Euclid’s Game on a Hundred Chart

Math concepts: subtraction within 100, number patterns, mental math
Number of players: 2 or 3
Equipment: printed hundred chart (also called a hundred board), and highlighter or translucent disks to mark numbers — or use this online hundred chart

Set Up

Place the hundred chart and highlighter where all players can reach them.

How to Play

• Allow the youngest player choice of moving first or second; in future games, allow the loser of the last game to choose.
• The first player chooses a number from 1 to 100 and marks that square on the hundred chart.
• The second player chooses and marks any other number.
• On each succeeding turn, the player subtracts any two marked numbers to find and mark a difference that has not yet been taken.
• Play alternates until no more numbers can be marked.

Endgame

The player who marks the last number wins the game.

For Advanced Students

When you play Euclid’s game on paper, circle the original pair of numbers. Collect several finished game boards. Compare the pattern of the numbers marked on each game.

• Can you explain why some games have few numbers marked and others have many?
• If you knew the first two numbers, would you be able to predict how many squares would be marked in the end?

For a hint, check out this page at Amby’s Math:

• Greatest Common Factors

Comments

I first discovered Euclid’s game at Alexander Bogomolny’s outstanding website, Cut the Knot. You can play a Java version online here:

• Euclid’s Game

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This is post #3 in my Hundred Board Series.

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Have more fun on Let’s Play Math! blog:

• Hundred Chart Nim
• 20 Things to Do with a Hundred Chart
• The Game that is Worth 1,000 Worksheets
• In Honor of the Standardized Testing Season…
• The Puzzling Pythagorean Pebbles