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Topic: The Muppets(R) Who's Who (Read 1481 times) |
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James Fingas
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The Muppets(R) Who's Who
« on: Sep 17th, 2003, 9:38am » |
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In a pizza shop, you see some of the Muppets(R): Miss Piggy, Pepe the King Prawn, and The Swedish Chef. Being a puzzle hermit, you do not know which is which.
All you know is that Miss Piggy will answer questions alternately with "Yes" and "No", Pepe the King Prawn will answer questions alternately with the truth and with a lie, and the Swedish Chef, due to his limited command of English, will answer questions randomly "Yes" or "No", except for every third question, to which he will answer "Bork!".
You want to ask the Muppets(R) whether you should order the pepperoni pizza or the deluxe. What is the minimum number of yes/no questions you require to get an answer?
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Re: The Muppets(R) Who's Who
« Reply #1 on: Sep 17th, 2003, 10:33am » |
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My guess is that it will take 3 to 5 questions.
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Mike_V
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Re: The Muppets(R) Who's Who
« Reply #2 on: Sep 17th, 2003, 5:25pm » |
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Question: Are we assuming Pepe is omnicent? That is, if you ask Pepe if the Swedish chef would answer "yes" to a question, could Pepe answer or be forced to say, "I don't know"? (Assuming that it isn't time for a Bork yet.)
Or, better yet. If you ask Pepe, "Will you answer 'yes' to the next question I ask you?" Can he answer? If yes, that's sort of odd, no? (Try then asking "Did you answer 'yes' to the last question I asked you?") And if not, you can then identify Pepe with 3 questions (that first one to each muppet). Piggy and chef will answer yes or no arbitrarly, but Pepe can't answer.
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| « Last Edit: Sep 17th, 2003, 6:05pm by Mike_V » |
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Mike_V
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Re: The Muppets(R) Who's Who
« Reply #3 on: Sep 17th, 2003, 6:29pm » |
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The best I can do for now is best case 3 questions, worst case 7 questions. Without asking any questions that Pepe might not know the answer to, anyway.
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| « Last Edit: Sep 18th, 2003, 7:03am by Mike_V » |
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Icarus
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Re: The Muppets(R) Who's Who
« Reply #4 on: Sep 17th, 2003, 7:54pm » |
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On general principles, I believe one question ought to do it, but it's gonna be one lulu of a question!
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Mike_V
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Re: The Muppets(R) Who's Who
« Reply #5 on: Sep 18th, 2003, 7:00am » |
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I can't imagine you could do this in one question, unless you assume to be lucky and happen to ask Pepe. You get no information when you ask one of the other two a question other than possibly information about who you're talking to.
The typical meta/multi-question in one question won't do, because if you ask Piggy or the chef, they answer yes or no essentially without hearing your question.
For that matter, you can essentially prove you need at least 3 questions.
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| « Last Edit: Sep 18th, 2003, 7:02am by Mike_V » |
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James Fingas
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Re: The Muppets(R) Who's Who
« Reply #6 on: Sep 18th, 2003, 7:15am » |
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on Sep 17th, 2003, 7:54pm, Icarus wrote:| On general principles, I believe one question ought to do it, but it's gonna be one lulu of a question! |
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Please, I want to hear this question!
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Re: The Muppets(R) Who's Who
« Reply #7 on: Sep 18th, 2003, 8:22am » |
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Well, since the question didn't specifically say you can only address a question to a single person you could say,
"I ask all three of you to answer 3 times whether you would say yes if I were to ask you if deluxe is better than pepperoni."
Or you only need to ask one question. But you need to ask it 3 to 5 times.
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Icarus
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Re: The Muppets(R) Who's Who
« Reply #8 on: Sep 18th, 2003, 4:38pm » |
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Sorry - I wasn't paying close enough attention. I was just going off the idea that you only wanted 1 bit of information, so you need only 1 question. But looking closer - I see that since only one of the muppets can supply that bit of information, you will need at least two more questions to determine which one it is. And since one of the respondents gives information at the incredibly slow rate of 1 bit per three questions, more questions are almost a certainty.
Question - how is it that you know all this about their answering abilities, but have no clue as to what they look like? Strangely intimate knowledge for someone so very ill-informed! 
Even worse: If you can't figure out which is "Miss Piggy", which is "Pepe the King Prawn", and which is "the Swedish Chef" just from the names and what they look like, I sincerely doubt that you possess sufficient intellectual capacity to figure it out from any number of yes-no questions! 
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I wonder: Which is larger
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Mike_V
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Re: The Muppets(R) Who's Who
« Reply #9 on: Sep 18th, 2003, 5:20pm » |
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I would suppose you have to determine who's who first and foremost.
:The best way I see to do that is to:
Ask question A,
Then any question (ie what should you order, in case you're talking to Pepe),
And then question ~A (the opposite of question A)
all to the same person.
That way, the answer to the third question positively IDs who you're talking to. If the answer is Bork! it's the chef, if the answer is the same as the answer to the first question, it must be Piggy, cause if you're asking Pepe, he'll answer either falsely both 1st and 3rd or truthfully for both, so he'll have to answer differently.:
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Icarus
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Re: The Muppets(R) Who's Who
« Reply #10 on: Sep 18th, 2003, 5:35pm » |
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The problem with that approach is that it could take you up to 7 questions:
"Are you Pepe?" "yes"
"Should I order the pepperoni?" "yes"
"Are you someone other than Pepe?" "Bork!"
"@#$#&%"
"Alright then, YOU! Are YOU Pepe?" "no"
"Should I order the pepperoni?" "yes"
"Are you Miss Piggy" "no"
"#$&@()!&$_@"
"Okay then you must be Pepe: If I ask you as my next question 'should I order the pepperoni', will you say 'no'"?
This approach will work, but I am sure you can better it!
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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Mike_V
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Re: The Muppets(R) Who's Who
« Reply #11 on: Sep 18th, 2003, 6:25pm » |
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Yeah, that was my reasoning too.
I'd still like to know what James would say to my earlier question. That is, how Pepe would answer a question that he doesn't (or can't: see my post above) know the answer to. If he can't answer it or has to answer "I don't know", you could then do this in 4 questions.
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James Fingas
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Re: The Muppets(R) Who's Who
« Reply #12 on: Sep 19th, 2003, 6:40am » |
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If a question cannot be answered according to Pepe's scheme, he answers randomly, and then gets confused as to whether or not his last question was a lie.
Just to make it easy on you...
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James Fingas
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Re: The Muppets(R) Who's Who
« Reply #13 on: Sep 19th, 2003, 6:52am » |
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on Sep 18th, 2003, 4:38pm, Icarus wrote:| Sorry - I wasn't paying close enough attention. I was just going off the idea that you only wanted 1 bit of information, so you need only 1 question. But looking closer - I see that since only one of the muppets can supply that bit of information, you will need at least two more questions to determine which one it is. And since one of the respondents gives information at the incredibly slow rate of 1 bit per three questions, more questions are almost a certainty. |
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I was so hoping to see your single question. Now I'm all disappointed.
Quote:| Question - how is it that you know all this about their answering abilities, but have no clue as to what they look like? Strangely intimate knowledge for someone so very ill-informed! |
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Hmmm ... this calls for some story background. Let's just say that you were in a couple of IRC chats where they discussed the muppets, and also read some Slashdot articles, but you use only the Lynx browser, so you've never seen a GIF or a JPG of them. From these sources of information, you have logically deduced the way in which these three muppet characters would act if asked yes/no questions in a pizzeria.
Quote:| Even worse: If you can't figure out which is "Miss Piggy", which is "Pepe the King Prawn", and which is "the Swedish Chef" just from the names and what they look like, I sincerely doubt that you possess sufficient intellectual capacity to figure it out from any number of yes-no questions! |
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Let's just say that a puzzler may be strongly gifted in certain areas without being quite as gifted in others (e.g. common sense, social skills, ...). ... reading the question ...
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| « Last Edit: Sep 19th, 2003, 6:54am by James Fingas » |
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Re: The Muppets(R) Who's Who
« Reply #14 on: Sep 19th, 2003, 8:51am » |
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My solution is ask all three of them "Will you answer yes if my next question is 'should I order the pepperoni?'" If all three answer the same, you're done. If two answer one way and one the other, ask the odd man out the same question two more times. Either that's Pepe, or you will know Pepe's answer.
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Icarus
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Re: The Muppets(R) Who's Who
« Reply #15 on: Sep 19th, 2003, 3:43pm » |
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on Sep 19th, 2003, 6:52am, James Fingas wrote:| I was so hoping to see your single question. Now I'm all disappointed. |
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"Okay, you three, listen up! I'm going to ask you a question about what's best to eat, see. And I better like the answer I get, or I'm havin' a meal of pork - short AND long, with a little seafood on the side! Got it? So I suggest you think very carefully before you answer the question. And if I hear any 'borks' - lets just say the long pork can be slow-roasted. So now - what's best to order?"
Quote:| Let's just say that a puzzler may be strongly gifted in certain areas without being quite as gifted in others (e.g. common sense, social skills, ...). ... reading the question ... |
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Hah! Reading questions is for wimps!
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"Pi goes on and on and on ...
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I wonder: Which is larger
When their digits are reversed? " - Anonymous
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rmsgrey2
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Re: The Muppets(R) Who's Who
« Reply #16 on: Apr 27th, 2004, 4:38am » |
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I think I can get the answer by asking the same question up to 6 times.
::
Ask "If my next question to you was: 'Should I order the pepperoni pizza?' what would you say?" to muppet A. Unless they Bork, repeat the question. If they repeat their answer, ask a third time. If they give the same answer three times, then they're Pepe. Otherwise, ask muppet B. If they don't Bork, ask again. If the answers match and muppet A Borked, then muppet B is Pepe. If the answers match and muppet A didn't Bork (meaning they gave two different answers) then ask B a third time. If they answer three times the same, then he's Pepe. Otherwise, muppet C is Pepe and you need to ask him the question once to find out his answer.
Once you have Pepe's answer to the question, order pepperoni if he answered no, and deluxe if he answered yes.
Essentially, you repeat a question that Pepe will always give the same answer to to the same muppet until you know whether they are Pepe. Worst case it takes 3 questions to eliminate the Chef (randomly giving the same answer twice) and 2 to eliminate Miss Piggy, requiring a 6th question to get Pepe's answer. Best case it takes 3 questions (either A Borks first time and Pepe is B or Pepe is A)
::
PS
yes, this is me, but I can't stay logged in - the system clock here is currently set to the year 9999 meaning that the login cookie expires about 8000 years before it gets here... Since I don't have admin privileges, I'm stuck.
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