1. The problem statement, all variables and given/known data Suppose that if there are at least 2 people in a room and each person in the room shakes hands with everyone else, but not with himself. Show that the number of handshakes is (n^2-n)/2. Make sure to show P(1), P(k) and prove P(k+1) 2. Relevant equations 3. The attempt at a solution Well, I don't have too much yet, but here it is: Let P(n) be 1 + 2 + 3 + ... + (n - 1) = (n^2-n)/2. Now, I think I'm going the right direction but when I try to show P(1) I find it doesn't work, because (1^2-1)/2 = 0/2 = 0. I'm missing something, but I don't know what it is. Thanks for any suggestions.