Solving The Alleged “Hardest Logic Puzzle In The World”

cuong set out to solve this puzzle:

“Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are ‘da’ and ‘ja’, in some order. You do not know which word means which.”

Here’s a few clarifications about the puzzle.

1. It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).

2. What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)

3. Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.

4. Random will answer ‘da’ or ‘ja’ when asked any yes-no question.

Your Solution?  Click here to see how cuong did it.

About Daniel Fincke

Dr. Daniel Fincke  has his PhD in philosophy from Fordham University and spent 11 years teaching in college classrooms. He wrote his dissertation on Ethics and the philosophy of Friedrich Nietzsche. On Camels With Hammers, the careful philosophy blog he writes for a popular audience, Dan argues for atheism and develops a humanistic ethical theory he calls “Empowerment Ethics”. Dan also teaches affordable, non-matriculated, video-conferencing philosophy classes on ethics, Nietzsche, historical philosophy, and philosophy for atheists that anyone around the world can sign up for. (You can learn more about Dan’s online classes here.) Dan is an APPA  (American Philosophical Practitioners Association) certified philosophical counselor who offers philosophical advice services to help people work through the philosophical aspects of their practical problems or to work out their views on philosophical issues. (You can read examples of Dan’s advice here.) Through his blogging, his online teaching, and his philosophical advice services each, Dan specializes in helping people who have recently left a religious tradition work out their constructive answers to questions of ethics, metaphysics, the meaning of life, etc. as part of their process of radical worldview change.

  • The Vicar

    Does Random always answer the question with a response which is true or false, or does he merely choose “da” or “ja” at random? There is a distinct difference, as illustrated by the following question:

    “If, instead of this question, I had asked you [yes-or-no question X] and you answered exactly as truthfully as you answer this question, would you have replied in the affirmative?”

    As long as the response is taking care to be really true or really false, the response will be identical to a true answer to X. (That is, a truth-teller will truly give the true answer they would have given, while a liar will lie about the lie they would have given, thus reverting to the truth.) But if the actual answer is random selection, then the answer can be false.

    Obviously, if Random always either tells the truth or tells lies, as opposed to merely speaking at random, this method would allow you to establish whether “da” or “ja” was “yes”. Although given the structure of the puzzle, I suspect that the solution does not involve knowing this.