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    OlympiadEasyCombinatorics7–9

    At a meeting every two people shook hands exactly once, and there were 6666 handshakes in total. How many people were at the meeting?

    Numa reunião, cada duas pessoas apertaram a mão exatamente uma vez, num total de 6666 apertos de mão. Quantas pessoas estavam na reunião?

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    Solution

    Step 1 of 3

    1. 1.With nn people there are n(n−1)2\frac{n(n-1)}{2} handshakes, because each of the nn people shakes n−1n-1 hands and every handshake is counted twice.