Metapuzzle is a term coined by Raymond Smullyan to describe puzzles that are about puzzles. In a metapuzzle, you are given a puzzle to solve but not given sufficient data to solve it. You are also told that someone else was able to solve the puzzle under certain circumstances and/or knowing certain information (which is often not precisely specified). Knowing that someone else was able to solve the puzzle allows you to solve the puzzle.
Here are some examples of metapuzzles:
"Are you John?" the judge asked the first twin.
"Yes, I am," was the reply.
"Are you John?" the judge asked the second twin.
The second twin then answered, and the judge then knew which one was John.
Was John the first twin or the second?
First, A stated either that C was the liar or that C was the spy, but we are not told which. B then stated which one of the three A was (truth-teller, liar, or spy), but we are not told what he said. C then stated which of the three B was, but we are not told what he said either. The judge then determined who the guilty party was and convicted him.
The case was described to a logician as above. He looked at the problem, but found that there was not enough information for him to determine who the spy was. The logician was then told what A said, and he determined the spy's identity. Who was the spy?
For solutions, see the answers page.
If you enjoyed the second puzzle, see also Lie Detection Puzzles.