From the Putnam Competition (I believe):

*SupposeĀ # is a binary operation on a set S such that the following properties hold:*

- For all a, b, c in S, (a#b)#c = a#(b#c);
- For all a, b in S, if a#b = b#a then a=b.

Prove that, for all x, y, z in S, we have x#y#z = x#z.