If one is given a puzzle to solve one will usually, if it proves to be difficult, ask the owner whether it can be done. Such a question should have a quite definite answer, yes or no, at any rate provided the rules describing what you are allowed to do are perfectly clear. Of course the owner of the puzzle may not know the answer. One might equally ask, ‘How can one tell whether a puzzle is solvable?’, but this cannot be answered so straightforwardly. The fact of the matter is that there is no systematic method of testing puzzles to see whether they are solvable or not. If by this one meant merely that nobody had ever yet found a test which
could be applied to any puzzle, there would be nothing at all remarkable in the statement. It would have been a great achievement to have invented such a test, so we can hardly be surprised that it has never been done. But it is not merely that the test has never been found. It has been proved that no such test ever can
be found.
And yet we try on.
