NRICH: Last Biscuit

This is a game for two players.

This game follows on nicely from Have You Got It?

This is a game for two players. You can play against the computer or with a friend.
It is a version of a well known game called Nim.

Each player can take biscuits in one of two ways:

  1. By taking any number they like from just one jar or
  2. By taking the same amount from both jars.

The winner is the person who takes the last biscuit/s.

Play the game several times.
Can you find a winning strategy?
Can you always win?

Does your strategy depend on whether or not you go first?

By clicking on the purple cog you can enter the settings menu and change the number of biscuits in each jar.
Can you work out a winning strategy for any combination of biscuits?
Look for patterns in your winning moves and use them to find winning strategies.
Is it best to start the game? Always?

When you’ve found some winning moves, explain why they work.

Can you describe the winning strategy if the jars start by containing 100 and 50 biscuits?

Printable NRICH Roadshow resource.

Age 11 to 16 

Math Topics
Deductive Reasoning & Logical Thinking
Middle School, High School
6th Grade, 7th Grade, 8th Grade, 9th Grade, 10th Grade, 11th Grade

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NRICH (University of Cambridge)

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Type of Resource

Board/Card Game

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