A blind man, and two others

[Snoggums]

Three men, one of them is blind. They walk into a pitch black room full of hats. All of the hats are black, but two are red. Not able to see which hat they are picking, each man chooses a random hat and puts it on. They then walk outside of the room and into the light. Guy 1 looks at the two other men.

"I cannot see my hat, nor do I know what color it is. But I know what colours yours are." Guy 1 one says as he looks at the other two men.

Guy 2 says the exact same thing.

The blind man gets an epiphany.

"I cannot see anything, but I know what color my hat is. As well as both of yours!" He says grinning.

 

What color of hat is the blind man wearing, and how does he know?

[Mr Skeptic]

Since the two guys mention colors, they must be seeing two colors of hat. This would mean that both sighted people have the same color hat, and the blind man has a different color. Since it is highly unlikely that the only two red hats got chosen, the blind man can be fairly certain that he has one of the red hats, and the other two have black hats.

[theCPE]

This seems like a severely edited version of an original puzzle.

 

It has bits of lacking info as well as some added language (colors as opposed to guy one simply saying he doesn't know).

 

And there is NO way that the blind man can know the colors of guy1 and guy2 hats. Unless the OP was making the colors addition intentionally to change the original problem. In which case guy2 would ALWAYS know his hat.....so eh.

 

However, blind man has epiphany and knows his hat has to be BLACK.

 

If his hat were red then guy 2 would KNOW his hat's color. Why?

 

If guy 1 doesn't know than he sees black and black or black and red. If when guy 2 looks and sees red on the top of blind man he would KNOW his was black and could not be red. Thus blind man obviously has a black hat.

 

He can't know the colors of the other two for sure because there is no distinguishable difference between the following four scenarios.

 

Guy 1 red Guy 2 red blind black

Guy 1 red guy 2 black blind black

Guy 1 black guy 2 black blind black

Guy 1 black guy2 red blind black

[MrMongoose]

Wait.. do they know that all the hats are black apart from two which are red?

[YT2095]

the answer is derived from what ISN`T said between them.

 

it`s quite simple really.

[JohnF]

It must be to do with guy1 and guy2 saying they know what colours the others are wearing.

 

The only way that guy1 and guy2 can see more than one colour, but not know the colour of their own hat, is if the blind man is wearing a black hat and the other two are wearing red hats.

 

Though the OP only asked "What color of hat is the blind man wearing, and how does he know?" rather than "What colour are they all wearing".

[Animal]

 

The only way that guy1 and guy2 can see more than one colour, but not know the colour of their own hat, is if the blind man is wearing a black hat and the other two are wearing red hats.

 

Unless the blind man is wearing a red hat and the other two are wearing black hats. They still see two colors and one red hat is missing so there's a chance they could be wearing it.

 

..I'm stumped.

[Softix]

Wow i Have No idea

1 Red Blind and 1 Black Can See

[igosaur]

The blind man is wearing a black hat and the other two red.

 

I'm assuming that because both sighted men say "I can tell what colours you are wearing" rather then colour (singular) that they are both looking at different coloured hats.

 

And if both the sighted men see different coloured hats then it must be the blind man who is wearing black.

 

Of course it could be the other way around with the blind man wearing red and the others both wearing black and given that the room is full of black hats I'd say this option had a much higher probability.

[vortex]

The blind man is wearing a black hat and the other two red.

 

I'm assuming that because both sighted men say "I can tell what colours you are wearing" rather then colour (singular) that they are both looking at different coloured hats.

 

And if both the sighted men see different coloured hats then it must be the blind man who is wearing black.

 

Of course it could be the other way around with the blind man wearing red and the others both wearing black and given that the room is full of black hats I'd say this option had a much higher probability.

 

However, since man 1 says that he can see the "colours" of the hats, man 2 would be able to see the color of the blind man's hat and therefore know the color of his own since the word color was plural in the first man's statement. Unless, of course, they are unaware of the colors of the hats represented in the black room.

 

If you are going to use the word "colours" as evidence, then you must consider that it would also affect the knowledge of man 2. Since there are only two different possible colors, the second man should be able to figure out his own hat color. Or are we assuming that only the blind man picks up on the "colours" hint? In this case the blind man could be wearing either color.

[igosaur]

I'm not too proud to ask for a clue. Preferably a nice big one

[Phi for All]

I'm not too proud to ask for a clue. Preferably a nice big one

You'll have to ask YT then, since the OP hasn't been here since before Christmas.

[YT2095]

it`s actually a Flawed variation of the 3 guys buried in the sand in a line where the guy at the front sees nothing the guy in the middle sees the back of the front guys head and the guy at the very back can see the back of Both their heads, 1 has a white hat the other have a black hat.

how do they know when asked Who has the white hat, when only the guy wearing the white hat can answer?

 

well it`s simple logic, if the guy at the back says nothing that means he can see one of the 2 wearing the white hat, so now it`s between the middle and the front guy, if the guy in the Middle says nothing it means the guy in the front has the white hat.

 

from the data given, the thing he can say with Any certainty is that he has a different color than the other 2 guys.

 

if we ignore the 2 red and x amount of other black hats, boil it down to 2 each, 2 red 2 black. since only 3 can be worn leaving only combinations! R.R,B or B,B,R.

up until This point the question is almost the same (swap red for white).

 

the only thing the blind guy knows with any certainty is that he`s the Odd one out (in hat color).

 

 

but I think the OP kinda suffered with Heather Mills syndrome!, as in the More he added the less he was Right.

he should have stuck to the Original puzzle without embelishment.

[vortex]

YT is right about this puzzle being flawed. This variation of the original riddle is impossible with the information given.

[D H]

The OP's version is deeply flawed in the use of the word "colours". The second sighted person knows the color of his own hat by virtue of the first sighted person reporting that he sees two colours. The second sighted person's hat must the opposite of the color of the blind man's hat. Since both sighted people can see the color of the blind person's hat, the second sighted person cannot say the same thing the first sighted person did. This fixes the problem:

 

Three men, one of them blind, walk into a pitch black room full of hats. The men know that two of the hats are red and the rest are black. Each man puts on a hat and walks out of the room. The first sighted person looks at the hats worn by the other two and says "I don't know the color of the hat on my head." The second sighted person then looks at the hats worn by the other two, thinks a bit, and says "I don't know the color of the hat on my head, either." After hearing this, the blind man says "Well I do know the color of the hat on my head." What is it?

[Mr Skeptic]

The OP's version is deeply flawed in the use of the word "colours". The second sighted person knows the color of his own hat by virtue of the first sighted person reporting that he sees two colours. The second sighted person's hat must the opposite of the color of the blind man's hat. Since both sighted people can see the color of the blind person's hat, the second sighted person cannot say the same thing the first sighted person did. This fixes the problem:

 

Three men, one of them blind, walk into a pitch black room full of hats. The men know that two of the hats are red and the rest are black. Each man puts on a hat and walks out of the room. The first sighted person looks at the hats worn by the other two and says "I don't know the color of the hat on my head." The second sighted person then looks at the hats worn by the other two, thinks a bit, and says "I don't know the color of the hat on my head, either." After hearing this, the blind man says "Well I do know the color of the hat on my head." What is it?

 

All you can tell from that is that the blind man and a sighted man cannot both have a red hat. They could all have a black hat, one of them could have a red hat and the other two black, or both sighted people could have red hats and the blind one a black hat. In any case, there is no way the blind person could tell what color hat he has.

 

Did you intend to limit so that there was only 3 hats in the closet, or some other limit?

[YT2095]

we can dismiss the probability part entirely and assume 2 red and 2 black. there is Nothing to be gained from thinking any further about this.

 

although How about, a Darkroom? where 99.999 times outa 10 a Red light is used, black stays that way and red does too, so maybe they Can see???

 

(I`m just messin` with ya )

[D H]

All you can tell from that is that the blind man and a sighted man cannot both have a red hat. They could all have a black hat, one of them could have a red hat and the other two black, or both sighted people could have red hats and the blind one a black hat. In any case, there is no way the blind person could tell what color hat he has.

 

Did you intend to limit so that there was only 3 hats in the closet, or some other limit?

 

No. The only limit is that there are at least three hats (otherwise everyone couldn't come out with a hat) and that exactly two of them are red. Whether there is only one black hat or 10,000 of them is irrelevant.

 

The first sighted person said he does not know what color his own hat is. From this, we and the other two people can infer that he sees at least one black hat (i.e., he does not see two red hats). The second sighted person also says he does not know what color his hat is. He, too must see at least one black hat.

 

The second person can also use the information that the first person does not see two red hats. Since the first man saw at least one black hat, the second person on seeing the blind man wearing a red hat would know his on hat was black. That the second person says he does not know the color of his own hat means that the blind person's hat is black.

 

Another way to look at this is to look at all the combinations of hat colors. In the list below, the sequence of hat colors indicates, in order, the colors of the first sighted man's hat, the second sighted man's hat, and the blind man's hat. There are eight arrangements of hat colors:

• BBB: Neither sighted man can deduce the color of his own hat.
  
• BBR: The second sighted man can deduce he has a black hat.
  
• BRB: Neither sighted man can deduce the color of his own hat.
  
• BRR: The first sighted man can deduce he has a black hat.
  
• RBB: Neither sighted man can deduce the color of his own hat.
  
• RBR: The second sighted man can deduce he has a black hat.
  
• RRB: Neither sighted man can deduce the color of his own hat.
  
• RRR: There are only two red hats. This is not a viable possibility.

There are four possible cases in which neither sighted man can deduce the color of his own hat. These four cases have one thing in common: The blind man is wearing a black hat.

[Mr Skeptic]

Ah! All 3 people are intelligent.

[genuresilience]

I think this is the answer.

Guy 1: red-black

Guy 2: red-black

Blind : black

The biggest hints are that, according to the wording of the question, each hat is black, but two of them are red. (At first I thought each two of the hats were just red.) Second of all, the blind man says "I know which color my hat is." If he is right, he can't possibly have one of the multi-colored hats. The others must have the red-black hats.

Edited June 15, 2008 by genuresilience