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A famous proof that all horses are the same colour hides a flaw in its induction step

the gist

All horses are the same colour is a paradox that appears to prove something obviously false using a tidy piece of logic. The argument uses mathematical induction, a method that shows a statement holds for every number by checking a base case and a step from one case to the next. Here the step quietly breaks down in the one case where the two overlapping groups of horses do not share any member, so the chain of reasoning fails. The puzzle was first raised by George Polya in 1954 in a version about girls' eye colour, and it was later restated with horses and cows. A 1961 satirical article by Joel E. Cohen used the same structure to prove that Alexander the Great did not exist.

so what

It is a clear lesson in why every step of an induction proof must hold, and it shows how easily a convincing argument can conceal a single broken link.

fun fact

George Polya, who first posed a version of the puzzle, was a major figure in the study of problem solving.

more on this

Adapted from Wikipedia, the free encyclopedia · CC BY-SA 4.0