Fibonacci Nim

Last week we started playing a game that starts out with two players and a pile of stones. The players take turns taking away handfuls of stones, and whoever takes the last stone wins. The first player may take as many stones as they like, but not the whole pile. After that first move, each player may take up to twice as many stones as the last person took. Passing is not allowed.

A sample game might go like this: we start out with 10 stones. Player A takes 2 stones, leaving 8. Player B may take up to 4 stones, but decides to take only 3, leaving 5. Player A may now take up to 6 stones, so Player A takes the remaining 5 and wins the game.

Depending on the number of stones in the initial pile, either Player A can always win if they play brilliantly enough, or Player B can always win if they play brilliantly enough. After the kids figured out who should win depending on the number of stones, I revealed that the name of the game is Fibonacci Nim.

I won't say more than that, in case someone wants to play you in this game!