Hand-Shake Puzzle

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

Solution:

This is a simple permutation/combination question.

If there are n people in the party. Then, number of ways in which you can select two out of n people is

 = n(n-1) /2

Note: If order is important (i.e AB is different from BA), then the number of ways will be n(n-1). But, in our question, order is not important - For two people there will only be 1 handshake irrespective of whether A shook hand with B or the other way round.

From the question:  n(n-1)/2 = 66

=> n = 12.

Hence, there were 12 people in the party.

Enjoy the party :)