Nim Stones

You take turns removing 1 or 2 stones from a pile.
Whoever takes the last stone wins!
The trick - if you leave your opponent a multiple of 3 (3, 6, 9, 12, ...), you win for sure.

Example

You take 16Opponent takes 15You take 23Opponent takes 24You take 133Opponent takes 12You take 2You win!Opponent takes 21You take 1You win!

For parents

What does this exercise practice?

Nim stones practice strategic forward thinking and discovery-based math without a formula - the child finds the rule of three themselves instead of memorizing it.

Common pitfalls

Without the rule of three, the safe move looks like guessing. It helps to think backward from small numbers of stones.

How to practice at home

Play the game with a partner using real pebbles, counters, or chestnuts, and discover the safe remaining numbers along the way.

← Back to the book overview