Brazos Valley Math Teachers' Circle

2008-09

Meeting 4 Part A

Two Person Games

Dr. Melanie Pivarski

Department of Mathematics
Texas A&M University

Two Person Games

• The Subtraction Game:
  • There are two players, each take turns subtracting a number (1,2,3,or 4) starting with 20.
    The person who reaches 0 wins. Who should go first? What is a good strategy?
  • The main conceptual idea is pattern recognition.
  • It's some practice with subtraction too; it can be modified to be a simple fraction game.
  • It can be modified to (1,2,3..k) starting with n. (Good for the quicker students)
• NIM:
  • Another two player game involving piles of tokens. What is the strategy?
  • The one pile version is extremely easy.
  • The two pile game is solvable (the ideas here are similar to the subtraction game, but in a different context).
  • Three or more piles are tricky-- the general solution involves binary representations. (Good for advanced students)

© Philip B. Yasskin, 2008-10.
Last updated Feb 15, 2010