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10 October, 06:08

5 people enter a racquetball tournament in which each person must play evert other person exactly once. Determine the total number of games that will be played

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  1. 10 October, 10:08
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    This is the "handshake problem", namely with n people, how many handshakes will there be if every will shake hands with everyone else.

    n people will shake hands with (n-1) other people. Since we are counting twice for each handshake, the number of handshakes is n (n-1) / 2.

    For n=5, the number of matches is 5 (5-1) / 2=10.

    This is also the number of diagonals in an n-sided convex polygon.
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