Socks and Handshakes
S_n = n*(n+1)/2 Well..that is what KF Gauss says!
Consider two scenarios and answer the questions. Scenario 1: there is a box with 24 socks (12 blue and 12 red). You can't see inside. You can reach in and pull out 1 sock at a time. How many times must you reach in and pull out a sock to GUARANTEE you have a matching pair. Scenario 2: You are in a room with 6 other people. If each of you shakes hands with each other one time each, how many handshakes will there be?