If seven people meet each other and each shakes hands only once, how many handshakes will there have been?

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If seven people meet each other and each shakes hands only once with each of the others, how many handshakes will there have been?

posted May 6, 2015

2 Solutions

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The first of the 7 people will shake hands with 6 others. Only 6 because no person is going to shake hands with themselves. The second person also shakes hands with 6 people, but you have already counted one of those handshakes, namely the one with the first person. Therefore, the second person shakes hands with only 5 NEW people. Then the third person adds 4 new handshakes, etc., down to the 2nd to the last person who adds 1 new handshake. The last person has no one new, so all of the last person's handshakes are already counted. In summary:

6+5+4+3+2+1=21

solution May 6, 2015
+1 vote

7*6/2=21 handshakes

solution May 7, 2015

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