All horses have the same color: (George Polya)
Proof: A set of n horses have the same color.
Induction:
Base: Let consider a set of only 1 horse. This is clear that this set has one color since horses can not change their color.
Induction: Assume that any set of n-1 horses as the same color. Let A be a set of n horses, enumerate as 1,…n. Divide A into two set A_1, A_2, where A_1 = 1, 2,…n-1 and A_2 = 2,…n. The color of A_1 and A_2 should be identical, since the horses in the intersection of these two set have only 1 color.
Lesson: Even a huge castle is built from brick.
conmaths 