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Nim
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.
Age 11 to 16
Challenge Level
Last Biscuit is a game for two players.
Each player can take biscuits in one of two ways:
- By taking any number they like from just one stack or
- By taking the same amount from both stacks.
The winner is the person who takes the last biscuit/s. Choose some different amounts of biscuits for each pile, and play a few games against a friend.
Look for patterns in your winning moves and use them to find the winning strategy.
When you've found some winning moves, explain why they work.
Can you describe the winning strategy if the stacks start by containing 100 and 50 biscuits?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.