This is an interesting puzzle which was passed to me by a friend some time ago. I do know the answer, but will refrain from self-answering on this to see where it goes.
I'm thinking of a number: 1, 2, or 3. You may ask me one question, which I will answer to the best of my ability. I may not, however, tell you my number or any codified version of my number. I can only answer yes, no, maybe, I don't know, etc.
How do you tell the number I'm thinking of?
Answer
Would it work if I ask:
"I'm thinking of a number: either 0 or 1. Is the sum of our numbers greater than 2?" I could figure out the answer if that's a question I'm allowed to ask.
If your number is 3, then you would say "yes" because no matter what you add, it would be true.
If your number is 2, you would say "I don't know". If my number was 0, then the answer would be no, but if my number is 1 the answer is yes. So you don't know.
If your number is 1, then you would respond "no". No matter what number you add, the number will never be greater than 2.
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