At a party, there were 105 handshakes. If each person shook hands exactly once with every other person, how many people were at the party?

Answer 1

for n people there will be C(n,2) handshakes

C(n,2) = 105
n!/(2!(n-2)!) = 105
n(n-1)/2 = 105
n^2 - n - 210 = 0
(n-15(n+14) = 0
n = 15 or n=-14, but n > 0

so there were 15 people

Answer 2

Good