George Polya posed the following problem:
Find where the error is in the following argument, which purports to prove by mathematical induction that all horses are of the same color:
i. If there's only one horse, there's only one color.
ii. Suppose within any set of n horses, there is only one color. Now look at any set of n + 1 horses. Number them: 1, 2, 3, ..., n, n + 1. Consider the sets {1, 2, 3, ..., n} and {2, 3, 4, ..., n + 1}. Each is a set of only n horses, therefore with each there is only one color. But the two sets overlap, so there must be only one color among all n + 1 horses.