The Three Demons Puzzle

Spent my entire lunch break solving this brainteaser that some sadist e-mailed to me, so I thought I’d share it with you. I’ll post a solution soon.

The Three Demons Puzzle

You have been granted an audience with the three demons of time and space, who know everything about the past, present, and future, and can even read minds: Amos, Baeti, and Corpi. You are allowed to ask them only three questions, but you can direct these three questions at the demons in any configuration: so you could, for example, ask all three questions of one demon, if you wished. Obviously this gives you a great deal of power, and you could use it to learn any secret you desired, but, as always, there is a catch:

  • The demons will only answer questions that can meaningfully be answered with “yes” or “no”.

Still; that’s not so bad. But it gets worse:

  • One of the demons always tells the truth.
  • One of the demons always lies.
  • One of the demons randomly answers “yes” or “no”, regardless of the question asked.
  • You do not know which demon is which.

Starting to get a bit more problematic? There’s more:

  • The demons will only answer in their native tongue, saying “da” and “ja” rather than “yes” and “no”. You do not know which demon syllable (“da” and “ja”) means which answer.

The aim of the puzzle is to determine which demon tells the truth, which one lies, and which one is random.

Special Rules And Tips

Some thoughts to help you get started and to ensure you don’t accidentality cheat:

  • You may only ask “yes or no” type questions. For example, you could ask Amos “Did Baeti say ‘yes’ to the last question I asked of him?” but you could not ask “What answer did Baeti give to the last question I asked of him?” Despite the fact that the latter would be expected to produce the same result as the former, the context is different: all questions must be phrased as “yes or no” type questions.
  • There is no point in repeatedly asking a demon the same question in order to try to determine whether or not he is the one that answers randomly.
  • If you can’t find a solution, try first removing the “you may only ask three questions” restriction. My first solution required that four questions be asked, for example, and I later refined the first two questions into a better single question, once I knew what I needed to determine before asking the next one.

Your Questions

In answer to some of the questions I’ve been asked:

  • Each question is asked to exactly one demon: you can’t ask a question to multiple demons at the same time.
  • The answers given by the random demon are random insofar as it is not possible for any human to determine what an answer would be in advance. However, as the demons themselves are able to see the future, each demon would theoretically know what the next answer that the random demon was going to give. However, I can’t think of a way that could possibly be useful.

Good luck! I’m not sure whether or not this is harder than the blue eyes/green eyes puzzle I posted to my blog last year. You decide.

I’ve published the solution in a separate post.