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Nim-7 for Two

Stage: 1 and 2 Challenge Level: Challenge Level:1

Here’s a game to play with a grown-up! This is a basic form of the ancient game of Nim.

How do you play?
You'll need a grown-up to play with.
You will also need seven objects, such as counters or blocks.

Place the 7 counters in a pile and starting with the grown-up, take turns to take away either one or two counters.
The person who takes the last counter wins.
Swap who goes first, and keep playing until you work out a winning strategy.

Does it matter who has the first turn?
What happens when there are three counters left?
How can you win at this game?
What happens when you start the game with more counters?

There are more Nim-like games here.
Notes for grown-ups

This game offers a motivating context in which children can improve their logical thinking skills. It is a low threshold high ceiling game.

Easier version: record a game and look back together at key moments.
Harder version: try starting the game with different numbers of counters.

Repeat the game, aiming to find a winning strategy, then talk together about how it was found.

There's a classroom version of this game here.