Just about everyone is familiar with the riddle about only being able to ask one question of two brothers, 1 who always lies and 1 who always tells the truth, but not knowing which is which. You need to ask a question that doesn't matter which one you ask will lead you down the right road.
Back in 1999 I was in Germany for a couple of months for work. I happened upon a variation on the above riddle that the author claimed he had heard in college and was offering his estate to the first of his heirs who solved it.
The riddle goes something like this:
You have just died and find yourself in vast nothingness. Suddenlyl, 2 roads appear along with 3 faceless men and a booming voice from everywhere says that one of these men always tells the truth, one always lies, and one randomly lies or tells the truth. You may ask two questions to determine which road you will take. One leads to heaven and the other to hell.
You may ask the same man both questions or change but you do not know in advance which man is which. Your questions must not be compound (if this and this) and they must not lead to paradoxes.
What two questions would you ask to get to the locale of your choice? Oh yeah - you hear the responses echoing in your head since they don't have any faces (didn't want you to waste a question on that).
Ok - so I stayed up for quite some time solving this riddle. I emailed the guy, confirmed that it was an acceptable answer though not exactly the one he knew, and promptly forgot it. Now I have a really good memory and yet I couldn't for the life of me remember the solution. I have played with it off and on since then. Last night the answer popped into my head out of nowhere.
I will post the answer if no one has gotten it tomorrow at this time - so don't read SPOILER subject lines if you don't want to know.
Cheers,
L~R
You should definitely pick up a book or two by Raymond Smullyan. He's the absolute king of knights-and-knaves puzzles and variations on them: humans who sometimes lie, vampires who lie when it's daylight but tell the truth otherwise, sane and insane versions of all -- e.g., insane knights always tell the truth, but believe every true proposition to be false -- and many others.
A good place to start would be What is the name of this book? or Riddle of Scheherazade. I liked the former a lot more. It goes from the puzzles to Goedel's incompleteness theorem in a very fun way.
Re:SPOILER
gibbon rib on 2006-06-05T02:29:43
What if you ask the man who randomly lies, and he says "Neither"?Re:SPOILER
Limbic Region on 2006-06-05T13:10:08
I never really felt comfortable with the answer myself. The solution is obvious, find a question that will always lead you to either the truth teller or the liar. Once there, you may simply turn it into the 2 person variation.
The trouble is finding a question that regardless of whom you ask (since you don't know). I welcome you to try to think of a better worded question but the author of the riddle (many years ago) confirmed that this was the answer.
Cheers,
L~R
