I am thinking of a number between 1 and 9. You can ask me

You can't ask me any open questions, I will only answer “Yes” or “No”! However, if for some reason I cannot answer it, I will tell you “I don't know”.¹

What two questions should you ask me to find the number I'm thinking of?

**two yes/no questions**and I will answer them truthfully.You can't ask me any open questions, I will only answer “Yes” or “No”! However, if for some reason I cannot answer it, I will tell you “I don't know”.¹

What two questions should you ask me to find the number I'm thinking of?

¹ Let's pretend I'm a genius and that the

*difficulty*of your question does not stop me from answering it. Also, me not knowing the answer is not the same as making me deal with an*invalid*answer! So having me divide by zero will do you no good. That's just cheating out of a valid yes/no question. Encoding the numbers as yes/no/don't know? Same story!Solution

This puzzle is a whole lot easier to solve if you break it up. First, aim to solve a reduced version: I'm thinking of a number between 1 and 3, and you can ask **one**question.

That's still no picnic! Somehow, you'll have to make sure that each number (1, 2 and 3) has an accompanying answer

*Yes*,

*No*or

*Don't know*(in some order). What kind of question could accomplish this?

There's more than one solution, but a particularly good question would be:

- I too am thinking of a number. It is either 1½ or 2½. Is your number higher than my number?

So now it's time to scale upwards. If one question can find a number between 1 and 3, then an additional question can find a number between 1 and 9 (3 × 3: three groups of three). But the second question depends on the answer to the first.

Now the two questions you should ask me, are clear:

- If I was thinking of either the number 3½ or 6½, would that number be higher than yours?

__Yes:__If I was thinking of either the number 1½ or 2½, would that number be higher than yours?__Don't know:__If I was thinking of either the number 4½ or 5½, would that number be higher than yours?__No:__If I was thinking of either the number 7½ or 8½, would that number be higher than yours?

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