If I think of a number between 1 and 1,000, guessing it in 10 yes-no questions is easy... so that's not the puzzle!

Guessing it in 10 yes-no questions, that must be all asked in advance, is also relatively easy... so that's not the puzzle either!

How many questions would you need to guess my number, if you had to ask all questions beforehand, and I also could lie once?

(In reply to re: Unexpected solution by Leming)

The one question solution is not nearly so satisfying.  It must rely on a paradox, such as this one, one of my favorite paradoxes.

Basically, I would ask:

Is the following statement true?  If this statement is true, then your number is 1.

In a pure true and false world, the answerer cannot deny that this statement is true.  Since it is true, the number must be 1, regardless of whatever the answerer thought it was.  Ask again, replacing 1 with 2, and perhaps you'll prove that 1=2.

Of course, in reality, the answerer must say "no" because the statement is neither true nor false.

Posted by Tristan on 2005-04-18 23:18:29