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

Question

theraggedydoctor · Answer

66 handshakes. One person has two hands.. What do you think?

aravindg · Answer

OMG That classic question!

aravindg · Answer

First could you find number of combinations considering that each handshake requires 2 persons?

beautifulmystery. · Answer

12

 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.

aravindg · Answer

So you understood the answer?

beautifulmystery. · Answer

yes lol