bonanova Posted June 30, 2012 Report Share Posted June 30, 2012 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? Quote Link to comment Share on other sites More sharing options...
0 EventHorizon Posted June 30, 2012 Report Share Posted June 30, 2012 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. 2 Quote Link to comment Share on other sites More sharing options...
0 bushindo Posted June 30, 2012 Report Share Posted June 30, 2012 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 ? 1 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted June 30, 2012 Author Report Share Posted June 30, 2012 Yeah, both of those questions work. Nice! Are there others? If Jaimie's response is taken as a clue, for example. Quote Link to comment Share on other sites More sharing options...
0 jim Posted June 30, 2012 Report Share Posted June 30, 2012 As of June 30, 2012 is a child born in 2010 at least x yearts old? Quote Link to comment Share on other sites More sharing options...
0 EventHorizon Posted June 30, 2012 Report Share Posted June 30, 2012 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? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted June 30, 2012 Author Report Share Posted June 30, 2012 Subtracting 2 and taking the square root. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted July 1, 2012 Author Report Share Posted July 1, 2012 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! Quote Link to comment Share on other sites More sharing options...
0 bushindo Posted July 1, 2012 Report Share Posted July 1, 2012 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. Quote Link to comment Share on other sites More sharing options...
Question
bonanova
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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