Puzzle - NO SCIENCE!

[Mockery]

In light of the recent controversial topics about planes and balls, I thought people might like something to ponder and/or argue about without the added complication of science. Once someone gets the right answer, I have another one which is quite good, but not as hard


So here's a little something:
(Don't worry, it's still just as confusing if not more so)

Blue Faces
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Suppose, on an island, there are three men. None of these men like this island, they all want to leave. But because of how they have been raised, they may ONLY leave if they have a blue face. In fact, if they have a blue face and know it, they MUST leave before dawn on the next day.

Suppose, in fact, that leaving with a red face (the only other option for these people) is absolutely taboo. Just as taboo is to speak about face colour, or to try to determine your face colour by looking in a puddle, a mirror, or the side of your nose etc.

The ONLY way they can reasonably learn what colour their faces are is by pure reason. Because they know this, they all practice their reasoning, and are impeccable when it comes to logic, decision theory, etc. The three men are sitting in a circle, facing each other. The three men all have blue faces, and of course they don't know this, or they would have left.

On MONDAY, a stranger walks up (you can suppose it is an explorer, come from another island or country, who does not share the taboos of these men), and says to the group "At least one person here has a blue face." He then leaves, saying NOTHING else. On THURSDAY morning, right before dawn, they all get up and leave.

So the question is: What is the logic by which the men deduce that their faces are blue?

It's not as simple as it might seem to some, remember it took 3 days to be sure...

[Jedi]

No wonder they want to leave the island some prick keeps painting all their faces blue.

[mekon]

They all want to leave the Island.

Sitting in the circle the explorer puts misinformation forward that at least one of them has a blue face. By logic each sees the other two men are blue and this applies to each man looking at the other men, but they can't be sure of their own face colour until the day passes and another day and they can each be sure that the other men are also thinking the same or they would have got up and left before dawn the first day. Da Dah!

Is I on the right track?

I'm with Jedi though, fuck the blue face painting ass clown... Damn red faced hater

[Brougham]

^ WHS. they all originally assume that it's them, and so once 3 days are up they all agree that they are all blue.

[xphread]

not quite... its a little more complex than that.
(its not misinformation! its the truth - and they know it!)
They can see the colour of the others.

If you just consider yourself as one of "them". You dont know if you are red or blue.
Instantly you can see since the other two are blue you know each of them see one blue person and you (red or blue). No matter which colour you are - they know there is one blue person so they cant decide if they are blue or red. (they could only know they are blue if they see the other two are red.)

there is a reason it takes 3 days... they are not thinking... they are waiting... and eliminating possibilities.

[Jedi]

I think after three days they really, really want a beer and decide to go to the Windsor.

[Juffy]

They all left because they heard that the OTHER island has a treadmill and two buckets of water, which beats the shit out of sitting in a circle with a blue face.

[XSorXpire]

When they all got up to leave noone said "Why are you coming"?

[sathid]

Well, if it's right before dawn, it is dark. So no-one can see if you are leaving with a red face.

[xphread]

Do I really have to type out the explanation??? bleeaggghhh!

Cmon... Whats the other one?....

[sathid]

I'm not sure how any of them could be sure. The stranger has not told them anything more than they already know. Each of the men KNOWS the other two have blue faces. If they each assume that they themselves have a red face, then they also KNOW that each other man, can at least see one blue face. Since they can each see two men, and any two men can both see the remaining man with a blue face, NONE can assume that any other man see's no blue faces. Unless I am missing something.

[xphread]

I'm not sure how any of them could be sure. The stranger has not told them anything more than they already know. Each of the men KNOWS the other two have blue faces. If they each assume that they themselves have a red face, then they also KNOW that each other man, can at least see one blue face. Since they can each see two men, and any two men can both see the remaining man with a blue face, NONE can assume that any other man see's no blue faces.

correct

Unless I am missing something.

and correct

...see my first post.

[sathid]

So what you are saying is:

Person A see's person B, and person C, and that they both have blue faces.
Person A knows that he may have a red face.
He also knows that person B will also think he may have a red face.

So, person A assumes he has a red face, and imagines the scenario from person B's perspective:

If person B thinks he has a red face, and person A has a red face (as in this assumption), then logically person C will leave.

If person C does not leave, it is because he sees one blue face (which, since person A has a red face, must be person B ).

So if that happens, person B would assume that he has a blue face, and then he himself will leave.

Person A notes that this has not happened, and so he assumes he must also have a blue face, and will leave. They all make these same assumptions, and thus after 3 days, they all leave together. That might be the answer, but I think it is flawed, since these men can only leave if they KNOW they have a blue face. Which they do not. And because the moment they see anyone else leave, these assumptions fall apart.

[xphread]

getting very warm...

[Klink]

No science... (but a bit of math)