This puzzle has been attributed to the Hungarian mathematician George Pólya. It’s a cheeky “proof” by mathematical induction that all horses are of the same colour. (The proof does not say which colour.)

To prove that all horses are of the same colour, we prove something stronger, namely, that in

How does one prove this?

Well, suppose that, in any possible group of

Then it’s not hard to see that the same must be true of any possible group of

Clearly this can only happen if all

So if the supposition is true of any group of

Moreover, if

Q.E.D.

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