Handshake Puzzle

Solution:

If there are n people,

1. The first person will shake hands with an n-1 person,
2. The second with n-2,
3. The third with n-3, and
4. 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