At a party, 55 handshakes took place as everyone shook hands with everyone else in attendance. How many people were at the party?
Math - Reiny, Sunday, November 7, 2010 at 10:11am
For n people the number of handshakes would be
n!/(2!(n-2)!) = 55 , where n is a positive integer.
n(n-1)/2 = 55
n(n-1) = 110
n^2 - n - 110 = 0
(n-11)(n+10) = 0
n = 11