Math CentralQuandaries & Queries


Question from Chris, a student:

Twenty people have gathered at a party. Find the number of handshakes when each person shakes hands with everyone else at the party.

Hi Chris,

When I looked around the room and saw 19 other people I realized that I had shaken hands 19 times. The same is true for all 20 people in the room, each of them had shaken hands 19 times. Thus it looks like there were 19 × 20 handshakes. But I counted my handshake with Sue and she counted her handshake with me. Each handshake was counted twice so there are only half as many handshakes as I first thought.


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