In the game Heaps (also called Nim), players set up three groups. These groups can be actual objects (use piles of erasers or pennies) or just written numerals.

Here are three “groups”, labeled A through C, with their starting numbers.

A | B | C | Move |
---|---|---|---|

3 | 2 | 2 | The starting groups |

Players alternate turns, subtracting *any* number from a single group. You have to subtract at least one. You cannot subtract from more than one group. The goal is to make the other player subtract the last number.

A | B | C | Move |
---|---|---|---|

3 | 2 | 2 | The starting groups |

1 | 2 | 1 | Player 1 subtracts 2 from Group A |

1 | 0 | 1 | Player 2 subtracts 2 from Group B 👀 |

0 | 0 | 1 | Player 1 subtracts 1 from A |

0 | 0 | 0 | Player 2 subtracts 1 from C, losing the game |

After a few rounds, students should start to spot patterns and formulate strategies. You can help prod them along by asking them to review a completed game and look for the big mistake. I’ve marked the big mistake above with 👀.

I’d want students to develop a big idea; **a strategy that they can follow to guarantee a win each time**. And, as with The Game of 100, I’d demand that they beat **me** twice before winning a fabulous prize (so that I can check if they *really* figured out the strategy).

Now, the beauty of this game is that you can easily change the number of groups, the number *in* each group, and even the number of players. These changes will slightly adjust the strategy, allowing students to think more about how to win the game.

Enjoy and do check out the entire category of paper and pencil strategy games at Byrdseed.TV!

And, gosh, do share this computer from 1940 that could play Heaps (and win!)