Math Club Nim
Math concepts: logic, patterns, divisibility
Number of players: 2
Equipment: 10 tokens, any sort, mix or match
Place the pile of tokens (pebbles, toothpicks, beans, pennies, dry cereal, etc.) on the table between the players.
How to Play
Allow the youngest player choice of moving first or second; in succeeding games, allow the loser of the last game to choose. On your turn, remove one or two tokens from the pile. You must take at least one token on your turn, but you may not take more than two.
Whoever takes the last token is the winner.
1 – Change the number of tokens in the starting pile.
2 – Allow players to take one, two, or three tokens per turn.
3 – Make the last token “poison.” Whoever takes it loses the game. This changes the strategy significantly, and it allows for an interesting endgame. My students (especially the boys) love to act out dramatic death scenes when they lose.
Players must always agree before starting whether the person taking the last token will win (traditional) or lose (the “poison” variation).
In math club, we start by playing a few games on the chalkboard, the whole class against the teacher. (I give them at least two opportunities to win before I move in for the kill.) Then the kids pair off to play several games against each other, taking turns on who goes first. If anyone thinks he knows the pattern to the game, I let him challenge me — and no “free” chances, this time!
- I let the student choose whether to go first or second. If he muffs that choice, I know he is just guessing.
- If he can’t beat me, he needs to go back to his partner and experiment with different strategies.
- If the student beats me, I add two tokens to the pile. That changes the strategy of the game slightly. If he can still beat me (when I allow him choice of first or second move), then I am pretty sure that he has the game figured out. Time to move on to the “poison” version.
Nim is a favorite game at our math club meetings, but it is like Tic-Tac-Toe in that once you know the trick, you can usually win (unless the other player knows, too). That is boring. For a greater challenge, try the multiple-pile version.