At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?	Pick:
A) 12  B) 15  C) 17  D) 19  E) 11
In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.   Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.   This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.   Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
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At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?