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

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