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by fnord123 1656 days ago
Why is the base case 3? H(1) contains one colour of horse. H(2) when removing one horse contains one colour of horse.

The problem afaics is that there is a supposition that we are talking about sets of horses with the same colour. So if you "suppose for all sets of n horses, every horse in the set has the same color" then you can prove that horses in that set have the same colour. If P then P.