|
|
Post by jean on Dec 7, 2011 9:06:30 GMT
I got this from another board. They're on page 4 now and nobody's (quite) got it. Can you do better?
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 the other two have blue faces, 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?
|
|
|
|
Post by trubble on Dec 7, 2011 15:15:24 GMT
From what you've posed, I really can't see that they have been given any new information whatsoever.
Unless... unless it is a bit of a trick question in that it ascribes to the three people some convoluted thought process that lets them suddenly work it out from the vistor's statement.
Do you know the answer? Do you find it difficult to see?
I don't know the answer but I just can't believe the visitor's comment can make any difference.
|
|
|
|
Post by trubble on Dec 7, 2011 15:16:49 GMT
And what is more, I have a funny feeling that I know this puzzle and was frustrated by the answer before.
|
|
|
|
Post by jean on Dec 7, 2011 16:38:10 GMT
|
|
|
|
Post by jean on Dec 7, 2011 16:40:32 GMT
And then someone PM'd me this:
So no one has jumped on the first night - they all wake up on the second day and still no one knows enough to jump.
Each of them still has two possibilities - that he is blue, like the other two, or that he is red.
What would happen on the second night if I was red? And if it hasn't happened, what do I know on the third day that I didn't know before?
|
|
|
|
Post by Weyland on Dec 7, 2011 17:35:46 GMT
And then someone PM'd me this: So no one has jumped on the first night - they all wake up on the second day and still no one knows enough to jump.
Each of them still has two possibilities - that he is blue, like the other two, or that he is red.
What would happen on the second night if I was red? And if it hasn't happened, what do I know on the third day that I didn't know before?: Doesn't matter whether I'm red or blue, at no stage does anyone see fewer* than one blue. ________________ * Chortle. |
|
|
|
Post by jean on Dec 7, 2011 18:16:10 GMT
There's no such thing as fewer than one, so they couldn't see it, even if it were there.
|
|
|
|
Post by rjpageuk on Dec 7, 2011 18:49:02 GMT
I put my answer in a spoiler, as I think I might have heard a similar problem before but not 100% sure  The three days thing is key about this. I am pretty sure I have this right, but it is hard to explain. Here are the combos of possible face colours (order not important): | Combo Number | Person A | Person B | Person C | | 1) | R | R | R | | 2) | R | R | B | | 3) | R | B | B | | 4) | B | B | B |
Combo 1) is out based on the visitors comment that at least one person has a blue face. Now based on this fact if anyone could see two other red faces they would know their face is blue and therefore would kill themselves on the first night (Combo 2). No one kills themselves on the first night so combo 2 is now ruled out. Now in the second day everyone knows that combo 2 is not possible, therefore if anyone could see a red face and a blue face they would know that their face must also be blue as it is not possible for it to be red and for there to be two red faces. (Combo 3). No one kills themselves on the second night so combo 3 is now ruled out. Therefore on the third day everyone knows the only possible combo is combo 4 and therefore they all kill themselves. (I think thats right, it makes sense - right?) EDIT: It does seem like the visitor has given them no info they didnt already have i.e. they already all knew at least one of the others had a blue face from looking at them but what the visitor does is give the entire group some info on their own face which they didnt have before and this causes everything to unravel. |
|
|
|
Post by Weyland on Dec 7, 2011 19:01:51 GMT
There's no such thing as fewer than one, so they couldn't see it, even if it were there. Chortle. |
|
|
|
Post by rjpageuk on Dec 7, 2011 19:13:14 GMT
|
|
|
|
Post by trubble on Dec 8, 2011 0:28:38 GMT
Perhaps! That annoyed me too!  But I seem to recall red and blue faces. I've cheated and looked at your spoilers, by the way. I can resist anything but temptation. Your logic is, as always, perfect; but it means that the question is slightly flawed. This is what I mean by frustration. I am too tired to talk properly. I will come back tomorrow evening and argue it with you. You can put me straight then.  |
|
|
|
Post by Weyland on Dec 8, 2011 1:17:12 GMT
Thank you, Rob. I'd probably never have got there. Seems to me it boils down to these two statements:
1. There is at least one blue face.
2. If anyone could see two red faces they would know their face is blue and therefore would kill themselves on the first night.
And the rest follows. I like it. Thanks to you as well, Jean. |
|
|
|
Post by jean on Dec 8, 2011 10:22:45 GMT
I've glanced at Rob's solution, but I am not going to look properly or try to follow it until I've at least tried to answer the question put to me above, which I haven't been able to, yet.
On the other board, the thread instigator said
If it's any comfort, Jean, I think that a period of complete bemusement is a necessary condition of being able to solve the puzzle. If you haven't been through that then you probably haven't solved it. So it's a good thing.
I'm not sure if I've been bemused for long enough yet.
|
|
|
|
Post by Weyland on Dec 8, 2011 10:32:51 GMT
I've glanced at Rob's solution, but I am not going to look properly or try to follow it until I've at least tried to answer the question put to me above, which I haven't been able to, yet. On the other board, the thread instigator said If it's any comfort, Jean, I think that a period of complete bemusement is a necessary condition of being able to solve the puzzle. If you haven't been through that then you probably haven't solved it. So it's a good thing.I'm not sure if I've been bemused for long enough yet. I've been through bemused and come out the other side. Now I'm bemused again. |
|
|
|
Post by trubble on Dec 9, 2011 15:33:45 GMT
I put my answer in a spoiler, 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?? |
|
|
|
Post by trubble on Dec 9, 2011 15:41:44 GMT
EDIT: It does seem like the visitor has given them no info they didnt already have i.e. they already all knew at least one of the others had a blue face from looking at them but what the visitor does is give the entire group some info on their own face which they didnt have before and this causes everything to unravel. I think that the 'new information' the visitor gives is nothing to do with what person A knows about person A's own face but rather it's information on what other people know. Person A knows that B and C know a fact. Before the vistor's statement, Person A was left to speculate on what they knew.
However, again there is this flaw that had any of the three had any brains they could have deduced what the the other 2 knew already.
|
|
|
|
Post by trubble on Dec 9, 2011 15:42:41 GMT
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). |
|
|
|
Post by rjpageuk on Dec 9, 2011 16:34:03 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. 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. Also, you are correct that the visitor gives information which they now know everyone knows which is information on their own face in a certain scenario (combo 2), and therefore unravels the whole process. If everyone knows everyone else knows combo2 is impossiboe then yes everything unravels, the issue is that before the visitors comment no one knew what combos the other people thought were impossible (as if they have a red face then the other people would only be able to rule out combo1 and combo4). |
|
|
|
Post by Weyland on Dec 9, 2011 16:42:32 GMT
I put my answer in a spoiler, 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. |
|
|
|
Post by trubble on Dec 9, 2011 22:18:21 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. |
|
A.P.P.S
S C 
. I really dont think there is a flaw in the question.