How to Trick Your Friends: The Peg Game

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This week we will show you how to play a game that you will never lose! For this you will need 12 pegs and a piece of material. Clip all 12 of these pegs in a line along the material.

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The rules of the game are simple:

  • There may only be 2 players.
  • Each player takes it in turns to remove 1, 2 or 3 pegs from the material.
  • The winner is person who removes the last peg.

If you follow 2 key steps then you can ensure victory every time. Firstly always let your opponent go first. The second step is to remove enough pegs so that the combined total of the pegs you remove and the pegs your opponent removed on their last turn adds up to 4.

For example if your opponent removes 1 peg then you will remove 3 but if your opponent removes 3 pegs then you should only remove 1 peg.

If you do this then no matter what happens the most pegs you will ever have on your last go will be 3 so you will always win!

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The Science

This game is actually based on good old times tables and more specifically the 4 times table. If each round adds up to 4 then the 12th peg will always be removed by the person finishing the round as 12 is a multiple of 4.

This means the game could be played with even more pegs as long as the total number of pegs is a multiple of 4.

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