Besides working on Prometheus, I like to distract myself from time to time trying to solve riddles and logic puzzles procured by philosophers. Raymond Smullyan, a prominent logician, has a number of logic puzzles available online for people to solve. I’m proud to say that I solved a fair number of them but there’s this one particular puzzle by Smullyan that’s been coined by many philosophers to be “The hardest logic puzzle ever.” I found this early on in September 2008 and I’ve contemplated and quarreled with myself trying to solve this puzzle. Here’s how it goes:
“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.
So after five months of on-and-off work on the problem, I think I’ve finally solved it. But it wouldn’t be fun just to tell you my answer and how I solved it. In all honestly, I’m more interested IF YOU can solve it and, if so, how quickly.
I’m positive there’s someone out there who can solve it faster than I. If you think you have an answer to the puzzle, feel free to post in the comments section your solution. At the release of the next issue, I’ll put up my solution to the puzzle and compare it to the solution given by philosopher George Boolos.
Is there a prize? Of course, you win the honor of solving the hardest logic puzzle ever with your own wit! I encourage everyone to join in on the fun and definitely look forward to your solutions.
NOTE: I know there are solutions online but, please, don’t ruin the fun for yourself and everyone else by looking up the answer. You can do it by yourself. Trust your own abilities!
[ UPDATE: You can find my solution and other solutions to the puzzle here. ]
Cuong Q. Nguyen
Cover image: “introspection” by ~final-testament