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 sup

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.