Game of Nim

The Game of Nim is a strategic game in which two players take turns removing objects from distinct heaps. On each turn, a player must remove at least one object (more than one object can be removed) provided it/they all come from the same heap. The goal of the game is to avoid being the player who has to remove the last object.

You can play an online version of the game here - recommended if you want to understand and enjoy the rest of this post!

We brought out our trusty numbered tokens (recall the Cups and Downs activity) and used them to have kids play the game in teams of 3. The team size was intentional on our part as we wanted members of each team to rotate between the roles of players (2) and observer (1). The role of the observer was to deduce any patterns he/she observed while studying the game played between his/her two teammates.

After giving our students a good amount of time to play and experiment with the game, we asked each team to share their observations with the class. Their inferences and conjectures took us down the road of binary arithmetic and understanding a strategy that would ensure victory. We came to the conclusion that two factors determine who wins the game - the number of sticks in each row and who starts the game.

The kids were keen on exploring what would happen when restrictions were placed on the maximum number of sticks that could be removed in a move so we let the topic flow for a longer time than intended as they investigated more patterns and strategies!