Non-PRO Da Inglese a Italiano Altro Generale/Conversazioni/Auguri/Lettere

Non capisco il senso di questa frase.

The Horse paradox was devised by Hungarian mathematician George Polya as an example of how mathematical and logical principles can be misapplied if you are not rigorous. Say there is a group of 5 horses. If you can prove that any group of 4 horses are the same colour, then, because you can break your set of 5 into subsets of 4 covering all possible combinations, the set of 5 has to be the same colour.
You can then use the same logical induction to say that you can prove groups of 4 are monochrome from sets of 3; groups of 3 from 2; and, finally, groups of 2 from 1. One horse is itself inevitably the same colour as itself, so all groups of horses are provably the same colour.
What's the flaw?