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Post by jean on Dec 9, 2011 22:23:03 GMT
I've looked now. Re: your second post, you said that if they had any brains they could deduce what the others can see but they cant. They dont know if the others can see one blue and one red face or just two blue faces as they dont know the colour of their own face. But it must be possible for A to conclude that either B or C could possibly have enough information at the end of the first day to make them jump. And I can't see that they could. George is going to post his answer on the other board tomorrow, and I'll post it here. He says he's got it down to fourteen pages...
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Post by trubble on Dec 9, 2011 22:23:59 GMT
I'm discussing your answer in the spoiler. So far so good. Excellent work. A+ No, Combo 1 is ruled out based on what each can see. Combo two is also ruled out based on what each can see. They can each see 2 blue faces so only combos 3 and 4 were ever possible. And now it unravels. Now, I think that your answer is very likely to be the "correct" answer. That's why I say the question is flawed rather than your answer. I think the question is set up to produce your answer but that the question has forgotten itself. I might be wrong, of course! What do you think of my response? Yours is the wrong answer, isn't it?? That's exactly why I said I was bemused again. When I reread my grovelling post in the cold light of day I realised that I was talking shyte. Perhaps if the meddler had said "at least two of you are blue"? But I suppose that would be too easy to bother with. Perhaps a bit easy, yeah ;D I really think, though, that Rob has the answer right and the question is wrong.
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Post by trubble on Dec 9, 2011 22:27:26 GMT
Jean, don't forget to tell 14-page-George that the question is wrong. Remember: oh! I've found the flaw in the question! It should propose that each person can see the other two faces and that one face is blue and the other red (not two blue faces).
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Post by Weyland on Dec 9, 2011 22:31:59 GMT
I think we can just give up with the spoilers at this point? I dont think there are that many people reading this topic . I really dont think there is a flaw in the question. Ok in response to your first question. It is true that combo1 and combo2 can be ruled out by what each individual can see. The problem is they dont know what other people can see and therefore cannot start the deduction process that people will start killing themselves without the extra piece of information the visitor gave to them. Therefore while they can rule out combo 1 and combo 2 individually they can go no further than this without knowing what combos the others have ruled out so can never be sure if their face is red or blue. Ok, this seems logical but isn't. Weyland and I both thought this was correct but now we think not (right Wey?). Here's why: Combo1) R R R Each person (X, Y, and Z) can see 2 blue faces. So each person can see that the answer cannot be red, red, red. X does not know that Y can see 2 blue faces, but X knows that Y can see AT LEAST ONE blue face because even if X has a red face Z does not. The visitor says there's 'at least one blue face'. This is not new information.2) R R B Same as above. X can see blue + blue, therefore X knows that Y can see blue + another undetermined colour (either red or blue). X would be a certified moron if he believed that Y could see two red faces. Right? The vistor says there's 'at least one blue face'. This is not new information.Now seemingly the vistor's remark has made X Y and Z realise it but now we can see that the remark was not necessary and did not provide new information. Combos 3 and 4 [ 3) R B B, 4) B B B ] remain completely unknowable even with the vistor's remark. The only thing in your proposed solution that gives them any knowledge is (as someone remarked to jean originally) the reaction after the first night. But there should be no reaction. Ergo, no new information on the second or third night. Ergo no jumping. Yes indeed, Trubs. Well put. Just one thing . . . if you're not right I'll definitely have to jump.
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Post by trubble on Dec 9, 2011 22:33:34 GMT
Me too.
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Post by jean on Dec 9, 2011 22:41:02 GMT
Jean, don't forget to tell 14-page-George that the question is wrong. Remember: oh! I've found the flaw in the question! It should propose that each person can see the other two faces and that one face is blue and the other red (not two blue faces).But if the rest of the problem was as stated, that would just be a lie! (It did occur to me that there might be some significance in the phrasing of the visitor's statement I can say that... because anyone can say anything, but it doesn't have to be true.) (Sorry - I missed your #18 because I was writing mine. I'm going to have to go back and deal with it now.)
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Post by Weyland on Dec 9, 2011 22:42:59 GMT
At no time can any of the three not know that the other two are blue. That's more than "at least one".
Surely a 14-letter analysis is more likely than 14 pages?
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Post by trubble on Dec 9, 2011 22:47:11 GMT
At no time can any of the three not know that the other two are blue. That's more than "at least one". Surely a 14-letter analysis is more likely than 14 pages? Yes, at all times, each person knows for certain that there are at least 2 blue faces. The thing that no one knows is that the others know that. I repeat: the question should not state that each has a ble face, the question should state that each person can see one red face and one blue face. The question is wrong. And I'll keep saying that until george concedes. I'll say it till I am blue in the face.
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Post by trubble on Dec 9, 2011 22:51:46 GMT
Jean, don't forget to tell 14-page-George that the question is wrong. Remember: But if the rest of the problem was as stated, that would just be a lie! (It did occur to me that there might be some significance in the phrasing of the visitor's statement I can say that... because anyone can say anything, but it doesn't have to be true.) (Sorry - I missed your #18 because I was writing mine. I'm going to have to go back and deal with it now.) Here's what I mean:- Here is the original puzzle, as copy and pasted (I presume?) by you in the OP, but with one cross out and one small change (in black): It's like this. Three men live on an island where everyone has either a blue face or a red face. As it happens all of them have blue faces. However, while each can see that one has a blue face and the other has a red face, they don't know what colour their own face is. And they have all sworn not to communicate anything to each other, in any way, about the colour of their faces.
There is another rule, which they are all bound by, that if they ever discover beyond doubt what colour their own face is, they have to jump off the cliff at midnight that same day. They live together, if perhaps in a state of some anxiety, for several years until one day a visitor appears on the island. Having been fully briefed on the island rules beforehand he is anxious not to give anything away that they don't know already. So he says nothing about their face colour except, as he's leaving, he says to all of them collectively but to none of them in particular, “I can say that at least one of you has a blue face”.
That night nothing happens. The next night nothing happens. But the following night all three of them jump off the cliff at midnight. Why is that?
There are no tricks about looking in mirrors, or pools of water or going cross-eyed to look at their own noses or anything. It's a purely logical puzzle based on those facts alone. It's really quite difficult to work out so, if you have heard it before and know the answer, or you google it, it would be jolly spiffing of you not to reveal it here. If however you do work it out I will genuflect before you lost in admiration.
I'll give the answer here this time next week (unless anyone pleads with me not to). However, in a sense, that is only the beginning because the really exciting thing IMHO is that even when you know the answer it is still very difficult to see how the visitor's comment could have made any difference. What has he said that gives them information that they didn't have already?EDIT: oh! Bugger me, you can't have each man seeing both a red and a blue face. One has to see two reds or two blues. And bugger me even more, the puzzle doesn't work anyway because they can't all find out at the same time. It's not just that the question is wrong, it's that the question is utterly broken. Utterly.
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Post by trubble on Dec 9, 2011 23:01:47 GMT
Because they are slow thinkers.
Any other answer is pants.
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Post by jean on Dec 10, 2011 0:02:05 GMT
We are still waiting. In the meantime, someone posted this:
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Post by Weyland on Dec 10, 2011 6:42:51 GMT
We are still waiting. In the meantime, someone posted this: That's just the drink talking. The stripy one's already had a skinful of Aldi vodka at home before venturing forth. Seriously, though, where's the logic supposed to be, if any? ~ Golden Oldie Department"We don't serve neutrinos in here." A neutrino walks into a bar. ~ Silver Oldie DepartmentII'll be down the Smoke tomorrow. I may desire refreshment after an arduous bus journey. A magpie walks into a bar. "We don't serve Geordies in here."
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Post by Weyland on Dec 10, 2011 7:38:18 GMT
At no time can any of the three not know that the other two are blue. That's more than "at least one". Surely a 14-letter analysis is more likely than 14 pages? Yes, at all times, each person knows for certain that there are at least 2 blue faces. The thing that no one knows is that the others know that.I repeat: the question should not state that each has a ble face, the question should state that each person can see one red face and one blue face. The question is wrong. And I'll keep saying that until george concedes. I'll say it till I am blue in the face. Wait . . . I mean It doesn't matter that they don't know the others know. They all know that all can see at least one blue face at the beginning, before the incomer tells them the same thing. Nobody jumps. Can't wait to see the 14 pages.
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Post by Weyland on Dec 10, 2011 8:04:06 GMT
Good news, bad news, and bad news: Bad: I'll have to jump. Bad: I've seen the answer, and cannot fault it. (Not that the latter means much at this stage.) It's seven lines. Good: I'm not saying any more than that, except that I still can't see what difference the "extra information" makes. ~ Modification after further thought: Worse: I now see it all. I think. Great puzzle.
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Post by jean on Dec 10, 2011 11:12:38 GMT
Well, here is George's explanation. Does it work? I got myself in a right tangle trying to put this down in writing because you have to jump about a bit (a) between different people's perspectives of what the other two might be thinking about what their 'other two' might be thinking, and (b) at the same time keeping tabs on whether you are inside or outside a hypothesis. So, elegance and non-soporificness are not guaranteed. But, taking "I" here to be one of the three (any one of the three) it goes like this:
"At the outset I know (and have always known) that there can at most be one red person (namely me) because I can see that the other two are blue.
Hypothetically then, just suppose I am red. What would happen?
Each of the other two would see one red and one blue. But neither of them would know what colour they themselves were, so each of them would be under the impression that there could be two reds (i.e. me, who under my hypothesis is red, and himself).
But (these other two would each be thinking) if there were two reds then at least one person here would see them both, and because of what the visitor has just said, that person would now know that they themselves were blue. And so they will jump off the cliff tonight.”
First midnight: But no one jumps. So the following morning ...
“Hmm, no one jumped off. Not much difference in behaviour there from the old days before the visitor came. But each of us (and not just me, but I now know it's all three of us) now knows that there can be at most only one red.
But, by my tentative hypothesis above, there is one person who is red, namely me. In which case the other two will now know that they must be blue (which of course I can already see they are). So they will have to jump off the cliff tonight.”
Second midnight: But again no one jumps. So the following morning ...
“Hmm, no one jumped off again. Much like the old days again except I now know that my hypothesis (that I am red) must be wrong.
So I now know that I am blue. Oh bum! That means I'll have to jump off the cliff tonight."
And all three will have gone through exactly the same same reasoning (because they are all in the same position and have the same information available to them). So …
Third midnight: All three jump off the cliff. (And land gently in a huge pile of soft feather pillows and live happily ever after. No blue men were harmed or distressed during the making of this puzzle.)
So what is it exactly that the visitor has added that wasn't there before? All he said was “At least one of you has a blue face”. But that was something they all knew anyway.
Well, the information he unwittingly provided, for each individual, was information about what the other two would think about the others' thoughts if they were in a hypothetical situation which in fact couldn't ever obtain Not only that, but it is a hypothetical situation which they all knew couldn't ever obtain. And each of them knew this even before the visitor appeared on the island.
Which makes it a very strange piece of information indeed. But one which makes all the difference. I hope to goodness I've got that right. It is quite slippery to get hold of and, in my experience, has a disconcerting habit of turning slippery on you again even after you've understood it. I felt the cold chill of doubt clutching at my heart earlier in the week when discussing it with Tommo but together we were able to stumble back to the light again. Mutual support groups will be set up if requested.
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Post by Weyland on Dec 10, 2011 12:17:33 GMT
Well, here is George's explanation. Does it work? I think so. He must have very small pages. Even so, it's much longer than this, which convinced me (the informant being a pizza delivery bloke) . . . On day 0 each guy thinks, "I know there is at most one red (me) because the other two guys are blue. If I am red, then the other two guys would think it is possible for two reds (me and themselves)."
On day 1 each guy thinks, "Since no one is dead, both the other guys now know that there is at most one red. If there were two reds, the lone blue guy would be dead (based on the pizza guy's statement)."
On day 2 each guy thinks, "If I was red, then each of the other two guys would be dead because yesterday they both knew there was at most one red and they could see me. If they could see that I was red AND there was at most one red, they would have known that they were blue. Since they are not dead, we must all be blue."
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Post by trubble on Dec 10, 2011 13:34:59 GMT
Quite true. Bugger.
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Post by Weyland on Dec 10, 2011 13:44:06 GMT
Quite true. Bugger. I would jump now, only I have an appointment on Tuesday with some valued friends. And it's Jean's round. So it'll have to wait.
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Post by trubble on Dec 10, 2011 14:04:29 GMT
We'll jump together, holding hands. Bags you be Thelma.
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Post by rjpageuk on Dec 10, 2011 14:49:03 GMT
I came ready to post an answer to the posts here but now jean has posted up the answer which is the same as what I posted, right? It doesnt matter if they all individually knew that combo2 was impossible from the start, what the visitor told them meant that after the first night they also knew everyone else knew combo2 was impossible and thats what changed and cause the situation to unravel.
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