At a party, everyone shook hands with everyone else. There were 66 handshakes. How many people were at the party? Explain.

Question

Mathematics

Cesar Monroe

12 April, 14:40

At a party, everyone shook hands with everyone else. There were 66 handshakes. How many people were at the party? Explain.

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Answers (1)

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Amiya Odonnell · Answer 1

N-the number of people

The first person shake n-1 hands, the second n-2 ... the last person shake one hand

1+2+3 + ... + n-1=n * (n-1) / 2=66

⇒ n * (n-1) = 66*2=132=12*11

⇒ n=12 people was at the party