I am thinking of an integer $1,2$ or $3$. You can ask me only a single question to which I can reply "Yes", "No" or "I don't know". I will be completely honest. What will you ask me to figure out what number I am thinking about?

Note: Since there are an infinite number of solutions to this puzzle, I'll select the wittiest one / the one with most upvotes. (Because the one I came up with is kind of overly mathematical and a little too out of the box.)

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    $\begingroup$ The possible duplicate, though very similar, has 4 possible answers ("maybe"), which in essence changes the answers. $\endgroup$ – AvZ Feb 8 '15 at 14:58
  • $\begingroup$ "Maybe" can be changed to "I don't know" in almost all circumstances. Besides, there are enough answers on the other question that don't use "maybe" already. $\endgroup$ – mdc32 Feb 8 '15 at 15:03
  • $\begingroup$ @AvZ I have a feeling this question is gonna be closed, perhaps you should accept my answer, and tag this as open-ended. $\endgroup$ – warspyking Feb 8 '15 at 15:06
  • $\begingroup$ @warspyking Like I have said before, comments like that make me think you answer for the reputation only. $\endgroup$ – mdc32 Feb 8 '15 at 23:41
  • $\begingroup$ @mdc32 My answer was the only understandable one here. Why just leave it unanswered? $\endgroup$ – warspyking Feb 9 '15 at 0:53

I'm going to think of a random number too, 1 or 2. If we multiply our numbers, will the product be greater than or equal to 3?

  • No -> 1
  • Yes -> 3
  • I don't know -> 2
  • $\begingroup$ Nice, this works. Let's see what others think. I am going to acxept this within a day or 2 if there aren't any other better answers. $\endgroup$ – AvZ Feb 8 '15 at 14:55
  • $\begingroup$ @AvZ If there is a better answer I'll just have to get cleverer. $\endgroup$ – warspyking Feb 8 '15 at 14:56
  • $\begingroup$ Is there any particular reason why people downvote "duplicatish" posts. $\endgroup$ – AvZ Feb 8 '15 at 17:44
  • $\begingroup$ @AvZ Yes, because you didn't research enough. $\endgroup$ – warspyking Feb 8 '15 at 19:08

I'm thinking of either 1.5 or 2.5 . Is your number greater than mine?

  • Yes - 3
  • No - 1
  • I don't know - 2

Is either of the following true:

  • Your number is $1$.
  • Your number is $2$, and the Riemann hypothesis is true?

If you say "yes", it's 1, if you say "I don't know", it's $2$, and if you say "no", it's $3$. And, if you say "yes" and I find out your number isn't $1$, I'm gonna want a proof.

(You could replace "Riemann hypothesis" by anything else the answerer would not know. For instance, "Is a random number I just thought of equal to $1$?")

  • $\begingroup$ Glad you asked. Here $\endgroup$ – AvZ Feb 8 '15 at 17:43

Is the reciprocal of 2 minus your number greater than zero?

  • If the number is 1, the answer is YES (as $\frac{1}{2-1}>0$ )
  • If the number is 2, the answer is I DON'T KNOW (as $\frac{1}{2-2}$ is undefined )
  • If the number is 3, the answer is NO (as $\frac{1}{2-3}<0$ )
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    $\begingroup$ You generally consider the form $\frac{1}{0}=+\infty$ which is greater than $0$ $\endgroup$ – AvZ Feb 8 '15 at 14:34
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    $\begingroup$ @AvZ I would consider $\frac{1}{0} = \pm\infty$, but the other answers are better anyway. $\endgroup$ – frodoskywalker Feb 8 '15 at 17:37

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