Nim Games

Description

Try these counting games with a friend. Can you figure out a strategy so that you can win no matter what your opponent does?

Levels

• Adults will find this activity interesting.

0 minutes

5 to 60 minutes

Topics

• subtraction
• multiplication
• division
• modular arithmetic

Goals

• Students will understand the strategic role of the ``winning numbers'' in counting games.
• Students will identify patterns in the winning numbers. Younger students will identify these patterns in terms of counting or subtraction. Older students will identify these patterns in terms of multiples and remainders.
• Students will adapt strategies learned in one game to slightly different games.
• Students will generalize strategies learned in similar games to a general strategy for games of this type.
• Students will increase their comfort level with expressing mathematical ideas by using relevant math terms to record their strategies.
• Some game variations can lead to deeper mathematical insights.

• counting

• multiplying
• division

Related Concepts

• modular arithmetic

Credits

• Some variations come from the files of Tatiana Shubin and Paul Zeitz.
• ``Cartesian Chase'' comes from Thinking Mathematically by Mason, Burton, and Stacey, page 162.
• Steve Dingledine contributed the ``Adding Up To 100'' variation.
• Phil Yasskin shared ``The Rolling Die'' game, which he saw at a Renaissance Festival.

Author

Amanda Katharine Serenevy