A circus has 13 performing elephants. In the finale of their act, one at a time, each elephant steps out of the group, and the remaining 12 balance each other on an enormous see-saw, with six elephants on each side.
The question is, what are the weights of the elephants? Obviously, one solution is that all the elephants weigh the same. So the real question is, is that the only possibility, or is there another solution in which at least two elephants have different weights?
(From the description of the problem, it might seem that the elephants could adjust for small differences in weight by moving a little back and forth on the seesaw. We don't mean to allow this. The two sets of elephants must always have exactly the same weight.)
I give up, show me the solution.