According to ancient Greek legend, a poor peasant called Gordius arrived with his wife one day in a public square of the town of Phrygia, riding in an ox cart. As it happens, an oracle had earlier informed the townspeople of Phrygia that their future king would ride into town in a wagon.
Upon seeing poor Gordius, the people made him king. In his gratitude, Gordius dedicated his ox cart to chief god Zeus, tying it with a highly intricate knot -- the so-called Gordian knot.
An oracle, perhaps the same one, foretold that the person who untied the knot would rule all of Asia. The Gordian knot resisted all attempts at untying it until the year 333 B.C., when Alexander the Great arrived.
Alexander had a great ambition to rule Asia, so he didn't fool around trying to solve the problem by untying the knot. Instead, he cut through the knot with a sword. "That's not fair!" many thought, though no one was so unwise as to point that out to Alexander.
Alexander's approach did seem to violate the spirit of the problem. Surely, the challenge was to untie the knot -- to "solve the problem" -- not to cut through it.
Sometimes, though, the correct solution is to re-define the problem.