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Topic: NEW PROBLEM: THE PUZZLE FORUM (Read 9674 times) |
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Jonathan_the_Red
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Re: NEW PROBLEM: THE PUZZLE FORUM
« Reply #50 on: Sep 27th, 2002, 10:53am » |
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Tim, I like your answer, but that might violate causality just a wee bit too much  Here's mine:
Resolve at the beginning to ask one and only one question of each puzzler. That way causality is not violated: the Pathopuzzler and Jaded Senior Puzzler will lie, while the Meta-Newbie will tell the truth. A set of questions that works is:
A: Is B the Pathopuzzler?
B: Is C the Jaded Senior Puzzler?
C: Is A the Meta-Newbie?
JPM : N Y N
JMP : Y N Y
PMJ : Y Y Y
PJM : Y Y N
MPJ : Y N N
MJP : N N N
edit apparently, Tim's solution is what was intended... oh well
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| « Last Edit: Sep 27th, 2002, 11:05am by Jonathan_the_Red » |
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James Fingas
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Re: NEW PROBLEM: THE PUZZLE FORUM
« Reply #51 on: Sep 27th, 2002, 10:54am » |
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Tim,
Your answer may seem minimal, but right-minded individuals like Eric and I will only be convinced by a proof. And make it a good one!
The puzzle started off with the realization that the rules for the puzzlers are largely arbitrary, but I found the final solution interesting ... I hope it wasn't too blindingly obvious!
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| « Last Edit: Sep 27th, 2002, 11:48am by James Fingas » |
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Eric Yeh
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Re: NEW PROBLEM: THE PUZZLE FORUM
« Reply #52 on: Sep 27th, 2002, 2:09pm » |
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VERY VERY amusing James!!!!! I am esp won over by the use of my quote near the end!!  Tx! (The question itself, though quick, is interesting, too! )
Best,
Eric
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"It is better to have puzzled and failed than never to have puzzled at all."
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TimMann
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Re: NEW PROBLEM: THE PUZZLE FORUM
« Reply #53 on: Sep 27th, 2002, 10:26pm » |
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I'm sure you're just kidding about demanding a proof, but I'll write one out anyway.
If we take the U's statements as axiomatic, then no matter what questions you ask of whom during a discussion, the JSP always answers exactly one question wrong. Perhaps the JSP has psychic powers that force you to ask one of your questions of him no matter what you had planned -- or perhaps his powers are even more far-reaching -- but all this belongs to the realm of physical or psychical speculation, not mathematical proof. We are merely given that the JSP always gives one wrong answer in every discussion.
Therefore, if we ask "A, is B the PP?" and end the discussion, the answer we receive must come from the JSP, and it must be wrong. Therefore Y->JMP, and N->JPM.
Let me close by observing that my solution is minimal for A, but most likely not for U. As we read, "Master Joda, I do not have your Uberpuzzler powers!" Undoubtedly Joda could sense the location of the JSP using no questions at all, but merely by sensing the disturbance he caused in the Farce.... Um, I mean the Force.
Here's a followup question (really).
Can the apprentice solve the puzzle in exactly N questions for any given N?
(edited: I know the answer to this followup now.)
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| « Last Edit: Sep 27th, 2002, 11:13pm by TimMann » |
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TimMann
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Re: NEW PROBLEM: THE PUZZLE FORUM
« Reply #54 on: Sep 27th, 2002, 10:36pm » |
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p.s. Seriously, it wasn't quite blindingly obvious. Somehow, even though I realized right away that if you ask only one question, the JSP has to be the one who answers, it took me a few more minutes of thought in the shower afterward to realize that you could then use the information in his known-wrong answer to finish the puzzle. D'oh.
Oh, here's another followup. Suppose the apprentice walks into the room, shakes hands with the first puzzler he sees, and absentmindedly says, "Good morning! Did you sleep well last night?" Counting this as one of the questions, how many questions will it take the apprentice to identify who is who?
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Eric Yeh
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Re: NEW PROBLEM: THE PUZZLE FORUM
« Reply #55 on: Sep 29th, 2002, 11:52am » |
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on Sep 27th, 2002, 10:26pm, TimMann wrote:| Can the apprentice solve the puzzle in exactly N questions for any given N? |
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Yes.
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Eric Yeh
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Re: NEW PROBLEM: THE PUZZLE FORUM
« Reply #56 on: Sep 29th, 2002, 11:54am » |
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on Sep 27th, 2002, 10:36pm, TimMann wrote:Suppose the apprentice walks into the room, shakes hands with the first puzzler he sees, and absentmindedly says, "Good morning! Did you sleep well last night?" Counting this as one of the questions, how many questions will it take the apprentice to identify who is who?
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Two.
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| « Last Edit: Sep 29th, 2002, 11:54am by Eric Yeh » |
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TimMann
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Re: NEW PROBLEM: THE PUZZLE FORUM
« Reply #57 on: Sep 29th, 2002, 2:24pm » |
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Eric, I agree with your answer to the first followup I asked. Partial spoiler: For n>2, you just ask the first puzzler the question from the 1-question solution over and over, and believe the answer that he gives more than once. For n=2 you need a custom solution, but it's easy to find.
On the second one, though, I don't see how you can do it in so few questions, unless perhaps you're limiting the JSP's powers by some assumption about causality. I.e., are you assuming that if the apprentice asks the JSP two questions, the JSP has to be wrong on the first because he doesn't know for sure that the apprentice will ask another question? I haven't been assuming that. I've been assuming the puzzlers know the apprentice's strategy ahead of time, then choose who is who and when each one will answer wrong, in a way that's sufficient to meet the conditions stated by Joda, but no more.
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| « Last Edit: Sep 29th, 2002, 2:26pm by TimMann » |
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Eric Yeh
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Re: NEW PROBLEM: THE PUZZLE FORUM
« Reply #58 on: Sep 29th, 2002, 9:45pm » |
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Nope, I am making no such assumptions.  The rules I have followed are the same as the ones you listed.
Best,
Eric
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TimMann
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Re: NEW PROBLEM: THE PUZZLE FORUM
« Reply #59 on: Sep 29th, 2002, 10:05pm » |
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Oh, I see: Address the same guy again and say, "Did you sleep well last night XOR is this guy on your right the PP?"
I bow to the Uberpuzzler!
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| « Last Edit: Sep 29th, 2002, 10:09pm by TimMann » |
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Eric Yeh
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Re: NEW PROBLEM: THE PUZZLE FORUM
« Reply #60 on: Sep 30th, 2002, 7:25am » |
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Precisely. Nice puzzles by the way!
Best,
Eric
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James Fingas
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Re: NEW PROBLEM: THE PUZZLE FORUM
« Reply #61 on: Sep 30th, 2002, 12:17pm » |
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Tim,
When I said we needed a proof, I didn't mean a proof that the solution works ... that should be self-evident!
I meant a proof that it's an optimal solution.
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