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

This is another very common question that you may find in employment test.

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

lets generalise this problem and say  there are n persons

1st person shakes hand with everyone else: n-1 times(obviously he will not shake hand with himself.)

2nd person shakes hand with everyone else(not with 1st as its already done): n-2 times

3rd person shakes hands with remaining persons: n-3 times

So total handshakes will be = (n-1) + (n-2) + (n-3) +…… 0;

= (n-1)*(n-1+1)/2 = (n-1)*n/2 = 66 (using sum of n consecutive natural numbers formula)

= n^2 -n = 132

=(n-12)(n+11) = 0;

= n = 12 OR n =-11

-11 is ruled out so the answer is 12 persons.

Reference Guru