# Are all "Who did it?" puzzles the same?

I recently came across this puzzle here and several others not on Stack Exchange, which seem to follow a common pattern I call "Who did it?" for now.

"Who did it?" does not refer to any puzzle regarding who the culprit was, but rather to a specific format:

• Several people (A, B, C, D, etc.) are accused of something.
• All but one person blames someone else. (A blames B, B blames C, etc.)
• One person (X) does not blame someone else, but rather says "I didn't do it."
• Everyone except one person lies

The outcome always seems to be the case that the person who does not accuse, but rather just denies any involvement is the culprit. Is this always the case? Or are the puzzles I have come across just exceptions?

And if indeed every "Who did it?" puzzle is solved by just pointing at the person who denies any involvement, should these puzzles still be asked - given that they are then just duplicates of each other with different names and a different number of people?

• Good observation, though. Seems like it cannot be generalized. Commented Nov 27, 2017 at 18:11
• @MeaCulpaNay It seems to be true under the constraint that every person involved may only make one accusation or one defense. Though as Deusovi♦ pointed out, this does not hold true if one were to make multiple accusations, such as "A claims either B or D did it" Commented Nov 27, 2017 at 18:14

No, they are not all the same. Consider this:

• A says B did it
• A says D did it
• B says C did it
• C says that C didn't do it
• D says C did it

If everyone's lying except one person (and there is one culprit) then the culprit here is not C but A.

However, if you allow each person to make one statement, then the only way to have a unique solution is to have the denier be the culprit. But I don't think this is a problem.

This category (liars and truthtellers puzzles where all but one person lies, exactly one person denies that they did it, the others all accuse someone else, and everyone makes exactly one statement) is absurdly specific. If we get another one that is the same but with names changed, then it should be closed as a duplicate. I don't see any reason to worry about it for now, though.