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Induction based on n=1 works sometimes, but not always. That was my point.
I'm not sure what you mean. I thought I stated it each time I was assuming n=1 and n=2.
In the induction step, we reason "The first horse is the same colour as the horses in the middle, and the horses in the middle have the same colour as the last horse. Therefore, all n+1 horses must be of the same colour". This reasoning only works if n > 1, because if n = 1, then there are no "horses in the middle", and so "the first horse is the same colour as the horses in the middle" is not true.