The Game of 100

Objective

Students will develop a winning strategy for this simple math game.

This very old game requires no supplies, but I recommend students use paper and pencil so they can review their game later.

• Both players add to a shared total.
• The shared total starts at 0.
• On their turn, a player may add from 1 to 10 to the shared total.
• The first player to reach 100 first.

Sample Game

• Total starts at 0.
• Player 1: Adds 10, total is 10.
• Player 2: Adds 7, total is 17.
• P1: Adds 8, total is 25.
• [time passes], total is at 75.
• P1: Adds 10, total is 85.
• P2: Adds 6, total is 91. 👀
• P1: Adds 9, total is 100, Player wins!

The key moment to have students analyze is denoted with 👀. Player 2 made a critical error, which guaranteed a loss. What could Player 2 have done differently to guarantee a win?

For more information, see The Game of 100 on Wikipedia