Handshake Puzzle

Handshake Puzzle

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

Solution:
If there are n people,

the first person will shake hand with n-1 persons,
the second with n-2,
the third with n-3,
and
the (n-1)th person with n-(n-1)=1 person means the last person.

Hence, total handshakes are (n-1)+(n-2)+(n-3)+….+3+2+1
Which can be equated using n(n-1)/2=66
Hence, n=12

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