Solve Hard Logic: Who Knows Their Hat Color?

• sjsustudent2004
In summary, in this scenario with 4 people, where two are wearing red hats and two are wearing blue hats, the person behind the wall is the only one who knows exactly which color hat they are wearing. This is because they are not limited by the restrictions of only being able to see one other person and can take off their own hat to see its color. The others in the line can only see one other person and may not be able to determine their own hat color based on the silence of the person in front of them.
sjsustudent2004
Suppose there are 4 people, two of which are wearing red hats, and two of which are wearing blue hats. one person is behind a wall, and the other three are standing in a uniform line, only able to see the person directly in front of them. Which person knows exactly which color hat he's wearing, and why?

My initial response is the one behind the wall since there seem to be no restrictions as to if he can see the others in the line, or even his own hat for that matter.

Does each person himself know what hat he is wearing...or is that what you're asking? It's just not clear.

If you're asking which person knows what hat he himself is wearing...maybe the one behind the wall b/c he can take it off of his head and look at it without anyone knowing.

infinitetime said:
Does each person himself know what hat he is wearing...or is that what you're asking? It's just not clear.

that is what he is asking, yes. which one will get to know what colour his hat is.

I would answer this one, but I've come to it many times, and I know the answer. Just a hint for everybody: you have to think in why he is the only one that knows his hat, and what does the fact that no other one knows which hat he is wearing means and impplies.

If they can see their own hat, then everyone knows what color hat they are wearing.

If they can't see their own hat, then no one can see more than one hat, and some can't even see that. So none of them knows what color hat they are wearing.

no: each of the three in a row can see the other two people and thus, their hats.

I'm not saying more because I want to see what is the answer of each, and how s/he got it.

This is actually an easier problem than the normal one (with three people: each whashing the other two's hats) because altohught there are more people, it has easier solution.

So, do we have people like this:

x x x | x

Where x is a person, and | is a wall? Also, would the left most person only be able to see the second person, and the second person only be able to see the third person? Would the third person (the one just to the left of the wall) and the fourth person (just to the right of the wall) not be able to see anyone? Given this, I don't see how it's possible for anyone to know which hat they have, unless they are allowed to communicate somehow.

the above question isn't descriptive enough

are they standing x-> x-> x-> | x-> OR x-> x-> x->x->| the question above doesn't say that they are separated by teh wall.

<<<GUILLE>>> said:
no: each of the three in a row can see the other two people and thus, their hats.

I'm not saying more because I want to see what is the answer of each, and how s/he got it.

This is actually an easier problem than the normal one (with three people: each whashing the other two's hats) because altohught there are more people, it has easier solution.
sjsustudent2004 said:
Suppose there are 4 people, two of which are wearing red hats, and two of which are wearing blue hats. one person is behind a wall, and the other three are standing in a uniform line, only able to see the person directly in front of them. Which person knows exactly which color hat he's wearing, and why?
Each person in the line can only see one of the other two people, except for the first in the line, who can't see anybody.

It has to be some kind of trick question. The person behind the wall has 1-way glass for example so he can see all the people in the line.

What if the two people in front of the person are wearing a blue and a red hat; then he would not know if he was wearing a blue or a red hat himself.

infinitetime said:
What if the two people in front of the person are wearing a blue and a red hat; then he would not know if he was wearing a blue or a red hat himself.

If the third person could see both hats in front, and saw one red and one blue hat, then as you say, they wouldn't know what color their own hat was. The person in the middle would 'hear' the silence of the third person and realize that their own hat was a different color from the first person's hat. Since they can see the first person's hat, they know the color of their own hat.

This is idle speculation. According to the wording of the puzzle, no one can see two other people. I continue to believe my solution is correct.

However, that phrase "behind a wall" bothers me. Can the person behind the wall see any hats?

The phrase: "only able to see the person directly in front of them". bothers me too. Can anybody see any hats?

Oops.

Actually, I was confusing this hat problem with a different one. There is no obligation or incentive for anyone in the puzzle to say anything so the person in the middle would have no way of interpreting the silence of the third person.

If I understand it correctly that three persons are standing one behind another, the second person(or third) can tell which hat he is wearing. If the hat colors of first and second persons are same then the third person(so the third person) can easily tell which hat he is wearing. If the third person can't say what color hat he is wearing(because he is looking at two different colored hats) then second person's hat color is other first person's hat color.

Jimmy,

It seems we both are right(actually I posted before reading your post).

But the other problem given in the first thread(which was initiated by the forum adminstrator) of this forum is much tedious and can't be solved if all the three persons are of not equal intelligence. For ex. if first person can't think what the second person thinks about the third person.

Quark, it is difficult for me to imagine which part of your answer you consider to be correct. Your solution requires that the third person be able to see two other people. The problem specifically disallows the third person from being able to see more than one other person. I quote:

the other three are standing in a uniform line, only able to see the person directly in front of them.

This puzzle is getting tedious sjsustudent. What is the answer?

Isn't just the guy at the back f the line? Nobody can see if they look, because they're all facing forwards...or have i missed something?

"Pssst...hey, buddy...yeah, you standing behind me. Can you tell me what color hat is on my head?"

Logical analization

sjsustudent2004 said:
Suppose there are 4 people, two of which are wearing red hats, and two of which are wearing blue hats. one person is behind a wall, and the other three are standing in a uniform line, only able to see the person directly in front of them. Which person knows exactly which color hat he's wearing, and why?

Ok there are only a fixed amount of logical outcome's from this...

1."behind a wall" doesn't state that the wall is higher than his field of vision.
2.The " a wall" is not stated to block his vision/or be no transparent.
3. Dosnt state that the wall cannot be a mirror.
4.Dirctly in front of him doesn't state that person in the middle of the uniform line has perif-vision of the two people on each side.
5. i can go on and on about there is a lack of guidline's what is allowed to be done and not, due to lack of pre-set information discribing each thing.
________________
1. 2 people have blue hats=true
2. 2 people have red hats=true
3. there is one wall=true
4. there is one person behind the wall=true
5. there are 4 people in total=true
6. 3 of the 4 people are standing in a uniform line
only able to see directly in front of them=true
7. dose any person knows exactly what color hat they have on=unknown

So from these 6 true's and 1 unknown factor, there are only 4 logical correct outcome's each one having a equal % of being correct due to the lack of information, but one has a higher % of being correct with the flawed information given...
_________

8. the person behind the wall know's because the wall is not in between him and the 3 uniform lined up people, so he can see all three of them and which hat they have on, and therefore he knows which hat he has on. because 1-6 are true and 7 is unknown 8 must be true.. for a person to exactly know which hat he has on..but 8 can only be true if 9 is true
9.(he's behind a wall but he can turn around and other 3 uniform lined up people have there back's turned when the person behind the wall turns around)=true

So the person behind the wall has the highest logical % of being the person to exactly know which hat he has on because 1,2,3,4,5,6,9 are true and 7 is unknown and thats

he know's why because he can turn around and see the three people in uniform line facing the other way but conflict #10 is about there all infront of a wall but not, but are but not... this question is very silly and lack's detail's... i hope this question isn't used in any test in any schools ever...

so in short the set up looks like this
<x...x...
<x...___...
<x.../-----\...

the person behind the wall can see everyone looking the other way the ...'s are the angles he can see and the ----'s would be the place behind the wall that he can't see. kinda ezy question, but it lacks correct details

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quark said:
If I understand it correctly that three persons are standing one behind another, the second person(or third) can tell which hat he is wearing. If the hat colors of first and second persons are same then the third person(so the third person) can easily tell which hat he is wearing. If the third person can't say what color hat he is wearing(because he is looking at two different colored hats) then second person's hat color is other first person's hat color.

The part about they can only see the person direcitly infront of one another, so that mean's the person in the (x).x.x can't see the person in front of the person direcitly in front of him. therefore he would only know 1 person's colored hat, and not 2 out of four, but even if he could see 2 out of four hat's each one could be diffrent color's and therefore he wouldn't exactly know which hat he has on, he would only know there is a 50-50 chance of having a red or blue hat on...so he still wouldn't exactly know :)

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does each know that there are only two blue and two reds? maybe the person infront of the line is looking at the person behind him? all it says is that he is standing in line and is looking at the person in front of him, not their direction at all. or the person at the front of the line is looking into a mirror? maybe the two with blue hats are police and the two with red are arrested and are getting their picture taken. what kind of hats? every time i imagine them standing there, there whering those big huge redneck straw hats(no offense to any who take it). are they all the same types of hats? if there different, one of them could just see it(like the straw hats, or a baseball cap that is placed snuggly in front of his eyes), and who said they couldn't move? couldn't talk? couldn't interact whatsoever?

if each person can see a maximum of 1 other person and cannot see their own hat then none can say. I'm willing to put money on it [virtual money of course]

phlegmy said:
if each person can see a maximum of 1 other person and cannot see their own hat then none can say. I'm willing to put money on it [virtual money of course]

not the 4th person, he wasn't given a limit or a minimum.

I think the problem was misstated, it probably should have read "the other three are standing in a uniform line, only able to see the person or people directly in front of them"

Clearly people cannot see their own hat, since then there would be no problem.

The person behind the wall shouldn't be able to see the others, otherwise it's trivial for him to figure it out.

Just realized this is an old revived thread from the distant past. Is it just me, or has that been happening a lot this weekend?

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is this like the "cat in the box" question? everyone is wearing both a blue hat and a read hat lol

Thanks go to zidiane for reviving this thread.

sjsustudent2004 said:
Suppose there are 4 people, two of which are wearing red hats, and two of which are wearing blue hats.

We're instructed to make a supposition. OK.
one person is behind a wall,

There is one and only one person behind a wall. But relative to you, or the other three hat wearers? (Additionally, I've seen any number of walls having doors and/or windows.)
and the other three are standing in a uniform line,

I think this means a straight line. Some could be facing each other, perhaps. They could be lined-up, standing on the ceiling, I suppose. But I think the best answer is to keep it real, and without additional props like mirrors and talking to each other.

It's of some note that the guy behind the wall is not one included in the uniform line.

only able to see the person directly in front of them.

OK, but this says nothing about seeing the hats of the people in front of them.
Which person knows exactly which color hat he's wearing, and why?

This question implies that one and only one person knows exactly which color hat he's wearing. You're a person too. Do you wear a hat?

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ok assuming the guys are
1-> [wall] <-2 <-3 <-4
and number 4 can see numbers 3 AND 2 then:

a:
number 4 sees that 2,3 are wearing the same color hats and deduces that his hat is a different color, thus he announces. and all is well

OOORRR

b:
number 3, assumes that number 4 isn't totally stupid, and that had number 3 and number 2 been wearing the same color hats he would have said something.
seeing as number 4 has not said anything, he deduces that both he [number 3] and number 2 are wearing different color hats. he then looks at the color of the hat in front and declares that his is a different color
and all is well!

nice

flemy- I'm leaning toward that answer too. As there's always a chance that the question was not posed as intended, you might be right in assuming they are each told how many of each color has there are.

Another answer is "the one who knows which color hat is is wearing is other than the three who do not." Why? "because the other three do not know."

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Delete this thread... the riddle itself is flawed, since it says the people in line can only see the person in front of them. IF it said "persons" then there'd be more info, but still not enough. It is also titled as a logic problem, not a "the wall was transparent!" riddle.
I don't think there's an answer.

Redbelly98 said:
Just realized this is an old revived thread from the distant past. Is it just me, or has that been happening a lot this weekend?
There was a firestorm of necromancy this past weekend.

I'm wondering how and why people dig up these old threads. You have to go the 10th page of thread topics in "Brain Teasers" to get to when this thread was started. Do people searching back that far just not realize how old the thread is, or do they realize it but find it so interesting that it still merits a response?

I'm seeing that the thread was revived in April this year by a one-time poster, so in this more recent revival it was only 2 months old.

1. How do I approach solving the "Solve Hard Logic: Who Knows Their Hat Color?" problem?

To solve this problem, you need to use logical reasoning and deduction. Start by considering all the possible hat color combinations and eliminate those that are impossible based on the given information. Then, use the remaining information to determine the correct hat colors.

2. What is the purpose of the "Solve Hard Logic: Who Knows Their Hat Color?" problem?

The purpose of this problem is to test your ability to think critically and use logical reasoning to solve complex problems. It also helps to develop your problem-solving skills and improve your ability to think creatively.

3. Is there a specific strategy or technique for solving the "Solve Hard Logic: Who Knows Their Hat Color?" problem?

There is no one specific strategy for solving this problem, but some common techniques include creating a table or diagram to organize the given information, using the process of elimination, and making logical deductions based on the given information.

4. Can I use trial and error to solve the "Solve Hard Logic: Who Knows Their Hat Color?" problem?

No, trial and error is not an effective approach for solving this problem. It is important to use logical reasoning and deduction to eliminate incorrect possibilities and arrive at the correct solution.

5. Are there any tips for solving the "Solve Hard Logic: Who Knows Their Hat Color?" problem more efficiently?

Some tips for solving this problem more efficiently include carefully reading and understanding the given information, breaking down the problem into smaller parts, and using a systematic approach to eliminate incorrect possibilities. It can also be helpful to practice similar logic problems to improve your skills.

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