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You have a collection of nickels, dimes, and quarters. You and the
computer take turns removing coins (you go first). The only
restrictions are that each of you must, whenever your turn comes
around, *take at least one coin* and
*take only one kind of coin*.
For example, you might take 1 dime, or 7 quarters, but you cannot take a
dime and a quarter during a single turn.

The person who takes the last coin wins (though you can change this rule if you like; see Customizing below).

Can you beat the computer? It all depends how many coins you start with. Try playing the game starting from the situations below, then customize your own starting situations.

Go ahead and make your move. Can you beat the computer? I think you'll find it very difficult! Can you figure out what strategy the computer is using?N N N

Go ahead and make your move!N N N

Now try different starting situations by choosing different numbers from the popup menus below, then select "Start Game".

*Can you find a mathematical formula that tells you which
starting situations you can win from, and which you can't? And, in
those situations you can win from, can you find a mathematical
formula that tells you what moves to make in order to guarantee a
win?* Hints are available.

This page last updated: May 26, 1998

Original Web Site Creator / Mathematical Content Developer: Philip Spencer

Current Network Coordinator and Contact Person: Joel Chan - mathnet@math.toronto.edu

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