There were 20 at a round table at dinner, each of whom shook hands with the person on his or her immediate right and left.At the end of dinner, each person got up and shook hands with everybody except the people who sat to his or her immediate right or left at dinner.Find the number of handshakes that took place after dinner.

Answer 1

Every person shakes hands with 19 people, so at first sight there are 20×19=380 handshakes. But by every handshake two people are involved. So 380 is the result of double-counting. There are 190 handshakes.

Answer 2

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