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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 7 to 16
Challenge Level
Can you win this game by getting the last bug into the snail's mouth?
This is a game for two players. You could use the interactive below to play against the computer, or a friend. There is also a game board available here.
Four bugs are placed on certain spots on the snail.
Take it in turns to move any bug, moving out towards the snail's mouth (the star). You can move a bug any number of spots but bugs cannot jump on or pass each other.
When a bug reaches the snail's mouth (the star), it is out of the game.
The winner is the player who gets the last bug into the snail's mouth.
Play as many times as you like.
Can you find any strategies that might help you to win?
You might wish to change the settings to make analysing it easier.
Could it make a difference who goes first?
NRICH is part of the family of activities in the Millennium Mathematics Project.