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Yes or No? I really don't know!

Question

I just thought of a positive integer less than 4

said Alex to his friends Davie and Jaimie last

night at Morty's while idly tossing darts in the

back corner of the room.

It was a slow night, and Alex loved to keep things

interesting, as best he could. Now if I were to

give you two questions of the standard Yes/No

variety, I have no doubt that even you two geniuses

could deduce what my number is. So, I'll raise

the challenge a bit, and buy the next round of

beer, if you can tell me my number - with absolute

certainty - after asking me a single Yes/No question.

Davie didn't even bother to stroke his beard.

Can't be done, pure and simple. A waste of time,

If you ask me, agreed Jaimie. Neither of them

noticed the twinkle in Alex's eye as he continued

to reel them in. All right, I'll turn it around. You

pick the number and I'll ask the question. And if

you can't answer it, you'll have to say so. But it

will cost you to play. If I get it right, with certainty,

you buy. If I get it wrong, I'll buy. Either of you

up to that?

Jaimie Just walked away, muttering something

quietly about complexity. This time Davey did

stroke his beard and after a minute said, OK,

you're on.

Who bought the next round?

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Davey.

How about the question "If I pick my own number that is a positive integer less than 3, will it be greater than or equal to your number?"

Answer of no: His number is 3. My number can be 1 or 2, neither of which are greater than or equal to 3.

Answer of yes: His number is 1. My number can be 1 or 2, both of which are greater than or equal to 1.

Answer of maybe/could be/i don't know/i cannot answer: His number is 2. If my number is 1, the answer is no, but if my number is 2, the answer is yes... so it could potentially be either since he doesn't know my number.

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I just thought of a positive integer less than 4

said Alex to his friends Davie and Jaimie last

night at Morty's while idly tossing darts in the

back corner of the room.

It was a slow night, and Alex loved to keep things

interesting, as best he could. Now if I were to

give you two questions of the standard Yes/No

variety, I have no doubt that even you two geniuses

could deduce what my number is. So, I'll raise

the challenge a bit, and buy the next round of

beer, if you can tell me my number - with absolute

certainty - after asking me a single Yes/No question.

Davie didn't even bother to stroke his beard.

Can't be done, pure and simple. A waste of time,

If you ask me, agreed Jaimie. Neither of them

noticed the twinkle in Alex's eye as he continued

to reel them in. All right, I'll turn it around. You

pick the number and I'll ask the question. And if

you can't answer it, you'll have to say so. But it

will cost you to play. If I get it right, with certainty,

you buy. If I get it wrong, I'll buy. Either of you

up to that?

Jaimie Just walked away, muttering something

quietly about complexity. This time Davey did

stroke his beard and after a minute said, OK,

you're on.

Who bought the next round?

Here's one approach

Let x be the positive integer less than 4. Is ( [ -1/(x - 3 ) * 2 ] modulo 2 ) > .5 ?

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Yeah, both of those questions work. Nice!

Are there others? If Jaimie's response is taken as a clue, for example.

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As of June 30, 2012 is a child born in 2010 at least x yearts old?

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Yeah, both of those questions work. Nice!

Are there others? If Jaimie's response is taken as a clue, for example.

If I ask a question for which a yes makes me guess 2 and a no makes me guess 1, which response will let me guess your number?

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Subtracting 2 and taking the square root.

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As of June 30, 2012 is a child born in 2010 at least x yearts old?

Hi jim, welcome to the Den.

Sorry I didn't see your post earlier.

Yes, that question would do it.

I had in mind the idea inthe previous post,

and now three others have been given.

Nice!

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Hi jim, welcome to the Den.

Sorry I didn't see your post earlier.

Yes, that question would do it.

I had in mind the idea inthe previous post,

and now three others have been given.

Nice!

Thought I had a nice question based on Fermat's last theorem, but turned out I was mistaken. Nice solutions, bonanova, Eventhorizon, and jim.

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