[shkkmo]

> you might just find it makes your inductive step impossible to prove, so if you do prove something, you've made a logical error in your inductive step

The inductive step should be proven completely independently of proving a base case. Indeed, if the inductive step is proven correctly you see that it is limited in scope to n>1.

You can then use any base case you can prove where n>1. Let's say you pick a base case of one trillion. Easy enough to show thay every set of one trillion horses is the same color (since no such sets can exist). You can then easily use induction to show that every set larger than one trillion horses is also the same color!

So really, both base and induction were wrong in different ways but if the induction had been proven correctly, the inapplicable base case would have been clear.