At a voter registration meeting everybody shook hands exactly once with everybody else. How many handshakes took place? (It'll be a formula, not a number, of course.)
Solution
If there were n people at the meeting, each one shook hands n-1 times. Then it would seem that there were n(n-1) handshakes. But if person A shook hands with person B, remember that B also shook hands with A. So the formula n(n-1) is counting each handshake twice. So the formula for n people is n(n-1)/2 handshakes.