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    OlympiadMediumCombinatorics7–9

    At a party each of the 1010 guests shook hands with exactly 33 of the others. How many handshakes took place?

    Numa festa, cada um dos 1010 convidados apertou a mão a exatamente 33 dos outros. Quantos apertos de mão houve?

    Answer options

    Solution

    Step 1 of 3

    1. 1.Count the ends of the handshakes: each guest supplies 33 of them, giving 10×3=3010 \times 3 = 30 ends.