I think a better explanation would be that the induction step missed an edge case: To claim that H/h1 and H/h2 are the same color, we need the two sets to overl

I think a better explanation would be that the induction step missed an edge case: To claim that H/h1 and H/h2 are the same color, we need the two sets to overlap by at least one horse. This actually works perfectly for all but n=2...