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

 Oct 25, 2019
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If there are n people, you would count the number of handshakes as nC2.

nC2= \(\frac{n(n-1)}{2\cdot1}\)

If there were 10 people, there would be (10*9)/2=45 handshakes. Thats not enough, so lets try a bigger number. 12 people: (12*11)/2=66 handshakes so there were 12 people.

 Oct 25, 2019

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