All horses are the same color

Summary

All horses are the same color is a paradox that arises from a flawed use of mathematical induction to prove the statement All horses are the same color. There is no actual contradiction, as these arguments have a crucial flaw that makes them incorrect. This example was originally raised by George Pólya in a 1954 book in different terms: "Are any $n$ numbers equal?" or "Any $n$ girls have eyes of the same color", as an exercise in mathematical induction. It has also been restated as "All cows have the same color".