The two lions

cog on 2004-07-19T07:54:49

I was once told that the human brain works in the background... and the proof to that was that sometimes you would be thinking of someone's name and not remembering, then stop thinking about it, and later on you'd remember, with no particular reason!

The question is: how does this work, and how long can the brain keep up with this stuff?

A couple of years ago I was given a problem I didn't solve by then... amazingly, yesterday morning, while still in bed, the answer simply ocurred to me :-| Was my brain still working on it, or was it merely coincidence? :-) I'm inclined to the second option :-)

The problem:

You have two doors, the right one and the wrong one. Your objective is to discover which is the right door. Outside the doors there are two lions. One of the lions always tells the truth, while the other always lies. You are allowed just one question, to one of the lions, without ever knowing whether he's the one telling the truth or not. What will your question be? :-)

I'll leave you with the problem for a while :-) If no answers show up, I'll post it myself :-)

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Solution

davorg on 2004-07-19T09:17:07

You ask either one of the lions which door the _other_ lion would say is the right door. The answer you get is guaranteed to be the wrong door so you choose the other one.

It's a very old and well-known puzzle.

3 Person Variation

Limbic Region on 2004-07-19T13:23:08

The one you stated is a well known version. While I was in Germany on business, I found a variation

There are 3 people - 1 always lies, 1 always tells the truth, and one randomly lies tells truth

You can ask two questions this time - both to the same person or to different people - still only two paths/doors though

The questions can't be compound (if this and this) - must be yes/no type questions - and can't create paradoxes

Now I stayed up all night and came up with a solution - submitted it to the author - was told it was correct and promptly forgot about it until now - I can't remember my solution ATM

If you like this sort of puzzle

VSarkiss on 2004-07-19T14:36:12

Sometimes these are called knights-and-knaves puzzles (knights always tell the truth, knaves always lie). If you like them, you should really read some of Raymond Smullyan's books. He's come up with tons and tons of interesting variations.

My favorite puzzle book of his is "What Is the Name of This Book?", although I haven't read some of his newer ones.