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