tag:blogger.com,1999:blog-5730391.post7433344630225832915..comments2024-02-22T06:43:27.705-08:00Comments on Blaine's Puzzle Blog: NPR Sunday Puzzle (Aug 9): Would you like cream and sugar with that?Blainehttp://www.blogger.com/profile/06379274325110866036noreply@blogger.comBlogger55125tag:blogger.com,1999:blog-5730391.post-27747133711628180772009-08-15T18:17:28.629-07:002009-08-15T18:17:28.629-07:00By the way, the waitress' name was not Suze, b...By the way, the waitress' name was not Suze, but Ivy (geddit ! - lighten up people..)DaveJhttps://www.blogger.com/profile/10386638780058713432noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-41052912255072796592009-08-15T15:39:04.790-07:002009-08-15T15:39:04.790-07:00Very simple. Number 5 does not want coffee, so sh...Very simple. Number 5 does not want coffee, so she knows that the answer to the waitress's question is "no". All the rest of the logicians, although thirsty for coffee, also know that the only logical answer is "no", that they don't ALL want coffee!<br /><br />So the puzzle is defective. A waitress-logician would never have fallen into such a trap by asking the wrong question! If she had asked it, and gotten a sequence of 5 "no" answers, she would have been smart enough to follow it up with a roll-call vote to identify any thirsty individual.<br /><br />That is why I consider the puzzle defective.dumpsterdiveladhttps://www.blogger.com/profile/05296636733423295606noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-19574680172357300522009-08-15T08:08:44.173-07:002009-08-15T08:08:44.173-07:00Well ... I have BEEN that consummate server: tale...Well ... I have BEEN that consummate server: talented and skillful at it – and, more importantly to you the customer, to you my manager ... ... I loved doing it ---- Louise Sawyer – style in one of the busiest, long – distance hauling, interstate truckstops within the very midst of middle America. ... And, further, because I was so good at it 40+ – of – my – Woodstock years ago, very well could, if job situations came about again in this economic era such that I needed to, I could very well step right in and perform for a solvent living food - servicing serving ... again ... today.<br /><br />When a truckstop server IF I had, at the first, asked logician #5 with her no answer, THEN what I wanna know from folks here in BlaineNation is: how is it that the minds can be read of logicians’ #4, #3, #2 and #1 – to know ... now ... what then after #5’s no answer, their subsequent responses are to have become? <br /><br />Someone states "they all would have answered no." This is known ... now ... how exactly? Further stated is, “yada, yada, yada ... she would have been fired” cuz “what kind of consummate logician yada, yada?” “defective puzzle” and so forth.<br /><br />Again, I ask: How is it that minds can be read re logicians’ #4, #3, #2 and #1?<br /><br />Mr Shortz’s Sunday, 09 August 2009 puzzle challenge is not defective.Blue of Central Iowahttps://www.blogger.com/profile/07390169381894607875noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-76744364406046863282009-08-14T15:26:03.388-07:002009-08-14T15:26:03.388-07:00If that waitress had asked around the table in the...If that waitress had asked around the table in the reverse order, beginning with the 5th logician, they all would have answered, "no". <br /><br /> She would have brought NO coffee to their table. Four of the logicians would have been thirsty. They would have complained to the manager, and the waitress would have been fired! What kind of "consummate logician" is that? As I have commented, this puzzle was defective!dumpsterdiveladhttps://www.blogger.com/profile/05296636733423295606noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-39330895924524471522009-08-13T18:45:04.093-07:002009-08-13T18:45:04.093-07:00My thoughts exactly, Patdugg. Glad to see your po...My thoughts exactly, Patdugg. Glad to see your post.Natashahttps://www.blogger.com/profile/14139505187498448200noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-36057247621729485432009-08-13T13:19:51.506-07:002009-08-13T13:19:51.506-07:00Re: Beret puzzle
I understand the answer and logi...Re: Beret puzzle<br /><br />I understand the answer and logic, but an assumption is necessary. Specifically, that one student is more logical than the other two. Or at least a faster thinker. <br /><br />When the puzzle states that one person raises his hand after ten second it implies that this one person was able to come to his conclusion as to what color beret he's wearing uniquely and that he had information unavailable to the others that allowed for his deduction. However, all three had enough information to confidently raise their hands once they saw no one raise their hands after a few seconds. But only one did?<br /><br />The wording is, at least, misleading.patdugg79https://www.blogger.com/profile/02699939367868272276noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-60014717044947234792009-08-13T10:14:09.830-07:002009-08-13T10:14:09.830-07:00Natasha and Dave, here are your 1000 (virtual) dol...Natasha and Dave, here are your 1000 (virtual) dollars. You have to decide how to split the prize.<br /><br />Incidentally, I can't take credit for this puzzle. It came from a post on a blog entitled <a href="http://divisbyzero.com/2009/08/10/infinite-hat-problems/" rel="nofollow">Division By Zero</a> which in turn came from a talk at MathFest.<br /><br />If you liked this puzzle, try out the *infinite* hat problems in the same post. Infinity was too much for my little brain to handle so I stopped at two hats. :-)Blainehttps://www.blogger.com/profile/06379274325110866036noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-8554345771833556102009-08-13T09:57:38.354-07:002009-08-13T09:57:38.354-07:00Great puzzle by the way Blaine - please keep '...Great puzzle by the way Blaine - please keep 'em coming ! I donate my share of the prize to the retired logistics waitress' fund...DaveJhttps://www.blogger.com/profile/10386638780058713432noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-42560286855869574852009-08-13T09:43:54.521-07:002009-08-13T09:43:54.521-07:00Blaine, when can I expect to receive my share?Blaine, when can I expect to receive my share?Natashahttps://www.blogger.com/profile/14139505187498448200noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-39174679351599064252009-08-13T07:55:31.747-07:002009-08-13T07:55:31.747-07:00Lorenzo and DaveJ are correct. The key is *either*...Lorenzo and DaveJ are correct. The key is *either* of them can be right. If they cover both cases (same or different), one of them will be right and they'll win the $1000 prize.Blainehttps://www.blogger.com/profile/06379274325110866036noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-60193002371225786902009-08-13T07:50:49.046-07:002009-08-13T07:50:49.046-07:00The berets are either red or blue, so Natasha and ...The berets are either red or blue, so Natasha and Dave either have the same color or opposite color hats. If one bets the same and the other bets opposite - seems like they would have both cases covered...DaveJhttps://www.blogger.com/profile/10386638780058713432noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-80471061032525830702009-08-13T07:45:25.905-07:002009-08-13T07:45:25.905-07:00Blaine,
Is there any relationship between the two...Blaine,<br /><br />Is there any relationship between the two berets? <br /><br />Or are we starting with a sufficiently large supply of berets so any combination is possible?<br /><br />-- Other BenBenhttps://www.blogger.com/profile/00600537639204656778noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-25378619684728347242009-08-13T02:11:54.732-07:002009-08-13T02:11:54.732-07:00How about if Natasha agrees to say the opposite of...How about if Natasha agrees to say the opposite of Dave's color and Dave agrees to say the same color as Natasha's hat ? <br />Since their hats are either going to be the same color or opposite, I think one of them will be right - yeah ? (or as Mark Knopfler said "two men say they're Jesus, one of them must be wrong...)DaveJhttps://www.blogger.com/profile/10386638780058713432noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-42567966200371595272009-08-12T17:01:02.194-07:002009-08-12T17:01:02.194-07:00DaveJ, feet placement is communication, I believe....DaveJ, feet placement is communication, I believe. Lorenzo I wish I knew the answer you have in mind.Natashahttps://www.blogger.com/profile/14139505187498448200noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-46890328963933062182009-08-12T16:30:06.976-07:002009-08-12T16:30:06.976-07:00Hmm, $1,000 in Blaineworld dollars - wonder what t...Hmm, $1,000 in Blaineworld dollars - wonder what the exchange rate is on Second Life...<br /><br />Unless standing feet apart for red/together for blue doesn't count as "communication" I'm kind of stuck for ideas...DaveJhttps://www.blogger.com/profile/10386638780058713432noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-6151464098464012282009-08-12T10:06:12.302-07:002009-08-12T10:06:12.302-07:00Blaine, very nice puzzle with an elegantly simple ...Blaine, very nice puzzle with an elegantly simple solution (which I won't reveal until others have a chance to try).<br /><br />Dave and Natasha: I have a deal for you. I'll give you the strategy if you each agree to give me half of your winnings.Lorenzohttps://www.blogger.com/profile/08116815111532628378noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-35303076199550765362009-08-12T07:56:13.005-07:002009-08-12T07:56:13.005-07:00Wow, I feel like a celebrity!
Dave we need to disc...Wow, I feel like a celebrity!<br />Dave we need to discuss the strategy.Natashahttps://www.blogger.com/profile/14139505187498448200noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-58874723142415720212009-08-12T01:00:44.652-07:002009-08-12T01:00:44.652-07:00TWO BERET PROBLEM:
Natasha and Dave are wearing b...TWO BERET PROBLEM:<br /><br />Natasha and Dave are wearing berets. The berets are either red or blue. They can see each other’s beret, but not their own which they must guess. If <i>either</i> person gets the color right, then they both receive $1000. They cannot communicate with each other in any way after the hats have been placed on their heads and they must both say their guess at exactly the same time. However, they can meet in advance to decide on a strategy. Find a strategy that guarantees a payoff.Blainehttps://www.blogger.com/profile/06379274325110866036noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-36570663317373377242009-08-11T14:09:14.065-07:002009-08-11T14:09:14.065-07:00Other Ben,
Thanks for the beret puzzle, and indee...Other Ben,<br /><br />Thanks for the beret puzzle, and indeed, given the premises, the answer has to be "red." About the other berets, though, I think one of them still needs to be blue, at least if you want the puzzle to be purely logical. The reasoning behind your answer that all berets are red goes beyond the premises, as it invokes assumptions made by student C about the nature of that ten-second period of silence.<br /><br />As you pointed out yourself, the only way to establish logically, for certain, that your own beret is red is if you see one of the other students wearing a beret that is blue. Ten seconds is a pretty good time for anyone to figure that out, don't you think? Another ten seconds, and the other student who was also wearing a red beret might have come up with that result for herself.<br /><br />I see where you are going with student C inferring from what *appears to be* uncertainty on the part of the other students that all berets are red. But again, if you wanted the solution to this puzzle to be determined by logic and by logic only, then you would need for one of the three berets be blue. That way, one more student could infer their beret is red, and the third student could answer that a logical conclusion is impossible based on the visual information available to them.<br /><br />I have a logic-related issue of a different kind with this puzzle: Per your explanation, all of the three students are females, since at some point you refer to each as "she" or "her." The professor, however, is quoted as saying, "Who knows the color of their own hat?" If these are the professor's *exact* words, then there must be at least one male among the three students; otherwise, it wouldn't make sense for the professor to use the gender-neutral "their." So... which one is it, A or B? Or perhaps it is both--since they were both lagging behind the smart one? ;-)Wolfganghttps://www.blogger.com/profile/02700971115994061654noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-88025000221666991732009-08-11T13:47:50.853-07:002009-08-11T13:47:50.853-07:00Shorter explanation:
Only one of two scenarios sup...Shorter explanation:<br />Only one of two scenarios support each student seeing at least one red hat: either 2Red/1Blue or 3Red. <br />If anyone saw a blue hat, they could immediately deduce that their own hat was not blue ('cos then someone would have seen 2 Blues and that is not viable )<br />Thus after 10 seconds, no-one deduces that they don't have a blue hat, therefore the only possibility is 3 reds (anyone of three students could deduce this by the way).DaveJhttps://www.blogger.com/profile/10386638780058713432noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-82003364460554365822009-08-11T13:41:46.187-07:002009-08-11T13:41:46.187-07:00This comment has been removed by the author.DaveJhttps://www.blogger.com/profile/10386638780058713432noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-91257279638108702852009-08-11T12:01:56.751-07:002009-08-11T12:01:56.751-07:00I think you do need assumptions in the beret puzzl...I think you do need assumptions in the beret puzzle. The assumptions being that the students all "know" if it is immediately "knowable" or not and if they know they make it known that they know.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5730391.post-67978774160659501552009-08-11T11:42:33.136-07:002009-08-11T11:42:33.136-07:00The Beret Puzzle, Answered:
Three students are ga...The Beret Puzzle, Answered:<br /><br />Three students are gathered in a room. The lights are turned off and a bin is passed around containing six berets, identical except that three of them are red and three are blue. Every student puts on a beret, the bin is closed, and the lights turned on. All three can now see the colors of the other two hats but not their own.<br /><br />"Who can see at least one red hat?", asks the professor. All three students raise their hands.<br /><br />"Who knows the color of their own hat?", asks the professor. About ten seconds pass, at which point one student then raises her hand. <br /><br />What color is her beret and how does she know?<br /><br />ANSWER:<br /><br />Her beret is red. In fact, all three are red. The answer lies in the ten second pause before she raises her hand.<br /><br />We'll call her student C. She sees student A with a red beret and student B also with a red beret. All three students, of course, raise their hand noting that they see a red beret.<br /><br />The professor asks "Who knows the color of their own hat?" and nobody raises a hand. <br /><br />Student C realizes that if she wore a blue beret, then students A and B would know the color of their hats to be red. Why? Because C sees A and B wearing red. <br /><br />C imagines life from A’s perspective. If A had seen B wearing red and C wearing blue, then A had noted B raising her hand that B saw a red hat, then A could have guessed that A’s hat was indeed the red hat that B was seeing when she raised her hand. So if A is logical, then C’s hat cannot be blue. <br /><br />Likewise, if B had seen A wearing red and C wearing blue, then noted A raising her hand that A was seeing a red hat, then B could have guessed that HER hat was the red hat A was seeing.<br /><br />Since nobody raised their hand in those ten seconds, C knew that her hat, like the other two she can see, is red.<br /><br />-- Other BenBenhttps://www.blogger.com/profile/00600537639204656778noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-63292642280708657812009-08-11T10:52:34.819-07:002009-08-11T10:52:34.819-07:00First, I agree with what was said about this week&...First, I agree with what was said about this week's NPR "challenge": I had it figured out by the time WS finished stating the question. Sorry if I sound conceited, but this was so easy as to be prohibitive--I have memories from back in sixth grade when we used to do these kinds of puzzles, at which time they really *were* challenging.<br /><br />I also agree there are two kinks that determine the solution to this puzzle, one on the question side and one on the answer side; the conversation had to go exactly the way it did and only the way it did in order for the solution to be absolutely certain.<br /><br />Liane appropriately commented on WS's puzzle, "Sounds like the beginning of a bad joke." Which takes me to Blaine's "related joke": Unlike WS's puzzle, which only requires logic, this one requires logic plus one piece of knowledge... Again, not to brag, but I do like this Descartes joke! 8-D<br /><br />Finally, about the beret puzzle: you do *not* need any "assumptions" on top of the premises provided. In fact, there is a logically compelling answer for each of the two other students as to what color his or her beret is.<br /><br />Does everyone on this blog have the answer to the beret puzzle by now? -- I don't know. >;@>Wolfganghttps://www.blogger.com/profile/02700971115994061654noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-85778390940571590882009-08-11T09:46:35.482-07:002009-08-11T09:46:35.482-07:00I don't agree with that assumption. The 10 sec...I don't agree with that assumption. The 10 second interval before the deduced answer implies a reasoning process. It's possible that one or both other students had sufficient information but did not reason the answer.Alicehttps://www.blogger.com/profile/00269672967336600394noreply@blogger.com