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

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Bufjasmineid
At a party, everyone shook hands with everybody else. There were 66 handshakes in total. How many people were at the party?12 people. 
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12 people were at the party.

You can choose 12 people to be one person, and 11 to be a person they are shaking hands with.  However, this allows us to choose person A, then person B, or Person B, then Person A.  We don't want to double-count this case, so we divide by 2.  12*11/2=66, so 12 works.