Question

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

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