One more riddle

theintellectual · Site Regular Joined: 26 Oct 2006 Posts: 55

What person is 100% certain of their hat color and why?

....A...!.W.!.....B..........C..........D
.Black!..A.!...Black....White...White
...-->.!..L.!.....<--......<--.......<--
.........!.L..!..................................

Facts:[/u]
-All four people know that between them there are 2 white hats and 2 black hats.
-People can't see the color of their own hats
-Can't see through the wall
-can't turn around

The people have 10 minutes for one of them to yell out the color of the hat they are wearing. They can't talk to each other and if they answer wrong then they all die. (Like Saw) After 9 minutes one of the peole yell out with 100% certanty the color of their hat.

Hope the visual helped. Razz

[u][/u]

Unclever title · Posted: Thu Dec 07, 2006 1:37 am Post subject:

The arrows are the direction the people are facing I gather, does this mean that the people cannot look around to see the person behind them, as I assume.

If this is indeed the case, then Person C has a dramatic advantage,

B, as with with A, sees only the wall, therefore they know their hat could be either white or black, as they have no further information they know four possibilities of two colors, 2 white, 2 black, thus making their perception of the odds be 50/50 for either color.

D also perceives a 50/50 chance as he sees a white and a black hat in front of him thus, leaving two possibilities, 1 white, 1 black.

C's advantage comes from the fact that he sees only one hat in front of him, black. From that info alone, he knows that there are three possibilities left, one of which is black, and two of which are white. this initially gives him a better chance of 66/33. (2/3 to 1/3) But he has a further advantage, no one has said anything yet, meaning that the others are still uncertain and unwilling to take the risk of calling out a color, meaning that the person behind him, with more information, is also uncertain, "This can only mean one thing," thinks C, "If he saw two black hats in front of him he would immediately call out that his hat is white as there are no other possibilities, but he didn't which means that he must see two different colors, which means my hat is not black..."

So C calls out "White!" and he, and maybe the others as well, is saved (I assume). The maniac behind this may very well have done this just to give them some small sliver of hope too watch them squirm before they die... If he were truly a jackass, he'd give person C, a tie-die hat and person D would know that they are all screwed.

theintellectual · Site Regular Joined: 26 Oct 2006 Posts: 55

Very good. You got it.

Riddleman · Site Admin Joined: 18 May 2005 Posts: 595

hmmm...not making much sense to me

theintellectual · Site Regular Joined: 26 Oct 2006 Posts: 55

Riddleman, is it the way Unclever title answered it, or the way the riddle is said?

Riddleman · Site Admin Joined: 18 May 2005 Posts: 595

both...but it sounds good reading it...im not that smart compared to unclever and you

theintellectual · Site Regular Joined: 26 Oct 2006 Posts: 55

Ok I'll try to explain it.
C can only see B' and is therefore only 50% sure of the color of his hat. Don't forget that it is C that calls out. Now D, who can only see B and C, sees a black hat and a white hat, so he too is 50% sure of the color of his hat so he doesn't say anything. Now this makes C think "if i see a black hat, and D sees a white and a black hat, then my hat must be white!"
I hope that helped.

Unclever title · Posted: Mon Jan 08, 2007 3:30 am Post subject:

Yeah, that explanation was a bit long winded, however, just to let you know it took me longer than ten minutes for me to figure it out so I'd be just as dead as the next person.