[wisty]

No, the induction step works for n>=3. The induction step fails for n=2.

For n=2, you can't prove h1 is the same colour as h2, because you don't have a h3 to compare it to.

[diffeomorphism]

tomayto tomahto

We are talking about the exact same case. The induction step is n-> n+1 and works perfectly well for n+1=3 horses.