Please Scroll Down to See Forums Below A professor wished to figure out who was the smartest of his graduate students. He brought them into his office, blindfolded them, covered all the mirrors in the room, and sat them in chairs facing one another. He told them that he would put either a yellow or a green hat on their heads, but then placed, on all three students, a small green hat (representing Creativity from De Bono's Six Thinking Hat Colors) and no yellow ones! He then told them to remove their blindfolds and to look at one another, but not their own heads. He asked "raise your hand if you see a green hat" to which all three raised a hand. Next, he said "stand up if you know the color of the hat on your head." After a lengthy pause, only one student stood up and correctly stated the color of all three hats was green. How was this known? Outline your logic.
Riddle: What Colour is your Hat?
- Thread starter samoth
- Start date
Basic_wonder
New member
Seems like this question is making the rounds and I cant seem to find an answer ....
My guess is that one of the graduate students had glasses so that the one kid that did answer was able to see the reflection of his own hat within the glasses ....
My guess is that one of the graduate students had glasses so that the one kid that did answer was able to see the reflection of his own hat within the glasses ....
Mavafanculo
New member
one of the other students looked at only the answering students head before raising his hand - so he knew his was green, and could see the other 2 green
Mavafanculo
New member
to clarify:samoth said:
the answering student could see the other two were green.
the answering student noticed that one of the other students looked ONLY at the answering students hat before raising his hand.
so the answering student knew his own hat was green and therefore all 3 green.
jerkbox said:
I tried to follow it too, but I got lost in the third or fourth sentence. I have on a black Red Wings hat though.
S
Spartacus
Guest
pasty
I would know the answer to this if one of the hats had been yellow. Then it would have been a matter of the one student realizing that the hesitation of the other two meant both saw a yellow and a green hat, meaning his would have to be yellow. But with all three green I am lost.
samoth said:Now, take the given in the OP that the students are intelligent grad students. Now rework your above post into the answer to the riddle!
uuuuummmmm
The student realizes the professor isn't going to ask a question that only one of them can get right?
That doesn't feel correct at all. I hate riddles. lol
T
the_clockwork
Guest
he saw the brim of the hat w/ his vision
Solution:
Imagine it this way:
Let's pretend we're person C. We see that A and B each have green hats. So there's two possibilities. Either our hat is green, or yellow. First, let's suppose that our hat WAS yellow. What would happen?
Well, if that were the case, person A would see a green and a yellow hat. He'd see a green hat on person B's head, and a yellow hat on person C's head. So in this case, person A could make a simple deduction. He would know that person B saw a green hat. And person B couldn't have seen the green hat on person C's head. Person B HAD to have seen the green hat on Person A's head. Therefore, person A would know that his own hat was green! So person A would stand up pretty quickly and say "I *know* I have a green hat!"
But that didn't happen! Person A *didn't* make this conclusion. So obviously, since it DIDN'T happen, our hat (that is, person C's hat) is NOT yellow, because if it were, Person A (or person B for that matter) would be able to make a conclusion right away, and they didn't. Therefore, the hat on person C's head is green!
(Now here's where Nef left off)
More specifically, if all the hats are green, *nobody* can logically prove the color of their own hat if all they know is that each other person saw a green hat. Hence, everyone will sit around and say nothing. But that's the ONLY case where nobody can determine anything. For any OTHER combination of hat colors, at least one person can logically deduce the color of their own hat. Three green hats is the only way an impasse can be reached. So because we know that to be true, we actually *can* determine the color of our own hat, because if nobody is able to conclude anything, then we can conclude something!
(See? lol)
Of course, this relies on the intelligence of the other two people as well. If they're both 4-year old kids, they might have known enough to acknowledge that they saw a green hat, but not be smart enough to deduce their own hat color simply by the other people's actions. But for the sake of the problem, we're assuming that the other people are reasonably smart.
Imagine it this way:
Let's pretend we're person C. We see that A and B each have green hats. So there's two possibilities. Either our hat is green, or yellow. First, let's suppose that our hat WAS yellow. What would happen?
Well, if that were the case, person A would see a green and a yellow hat. He'd see a green hat on person B's head, and a yellow hat on person C's head. So in this case, person A could make a simple deduction. He would know that person B saw a green hat. And person B couldn't have seen the green hat on person C's head. Person B HAD to have seen the green hat on Person A's head. Therefore, person A would know that his own hat was green! So person A would stand up pretty quickly and say "I *know* I have a green hat!"
But that didn't happen! Person A *didn't* make this conclusion. So obviously, since it DIDN'T happen, our hat (that is, person C's hat) is NOT yellow, because if it were, Person A (or person B for that matter) would be able to make a conclusion right away, and they didn't. Therefore, the hat on person C's head is green!
(Now here's where Nef left off)
More specifically, if all the hats are green, *nobody* can logically prove the color of their own hat if all they know is that each other person saw a green hat. Hence, everyone will sit around and say nothing. But that's the ONLY case where nobody can determine anything. For any OTHER combination of hat colors, at least one person can logically deduce the color of their own hat. Three green hats is the only way an impasse can be reached. So because we know that to be true, we actually *can* determine the color of our own hat, because if nobody is able to conclude anything, then we can conclude something!
(See? lol)
Of course, this relies on the intelligence of the other two people as well. If they're both 4-year old kids, they might have known enough to acknowledge that they saw a green hat, but not be smart enough to deduce their own hat color simply by the other people's actions. But for the sake of the problem, we're assuming that the other people are reasonably smart.
if you're person C, you look at A and B and see green hats. They were told to raise their hand if they saw a green hat. B raises his hand because he sees a green hat on A. A raises his hand because he sees a green hat on B.
Which means that if you're C, you still don't know if you're green or yellow.
Which means that if you're C, you still don't know if you're green or yellow.
Mavafanculo
New member
I'm buying a megadeath CD and burning it in protest.
Mavafanculo
New member
stilleto said:
unless you notice that A or B ONLY looked at your hat before raising their hand.
me and stilleto split the prize.
stilleto said:
Take the two possible cases: Case A would be you (or me, denoted person C here) with a yellow hat. Case B would be person C with a green hat. In either case, the OP states that all three raised their hand.
Okay, I see where you're coming from. Try writing it down, it helps. You have to shift your POV. E.g., if A, B = green and C = yellow, then A from A's POV sees green and yellow. Shifting to B, from B's POV, he doesn't know he's green, but he sees yellow on C and then A can deduce that given both see that C=yellow and B raised his hand, A knows that he's green.
samoth said:Take the two possible cases: Case A would be you (or me, denoted person C here) with a yellow hat. Case B would be person C with a green hat. In either case, the OP states that all three raised their hand.
Okay, I see where you're coming from. Try writing it down, it helps. You have to shift your POV. E.g., if A, B = green and C = yellow, then A from A's POV sees green and yellow. Shifting to B, from B's POV, he doesn't know he's green, but he sees yellow on C and then A can deduce that given both see that C=yellow and B raised his hand, A knows that he's green.
this would work if you see a green hat and a yellow hat, but you dont- you see two green ones, which means you can't POSSIBLY know if yours is green or yellow. both of your fellow students could be looking at eachother when they raise their hands to seeing a green hat, and NOT to yours which could just as easily be yellow.
this riddle would ONLY work if someone besides you is wearing a yellow hat.
stilleto said:
"More specifically, if all the hats are green, *nobody* can logically prove the color of their own hat if all they know is that each other person saw a green hat. Hence, everyone will sit around and say nothing. But that's the ONLY case where nobody can determine anything. For any OTHER combination of hat colors, at least one person can logically deduce the color of their own hat. Three green hats is the only way an impasse can be reached. So because we know that to be true, we actually *can* determine the color of our own hat, because if nobody is able to conclude anything, then we can conclude something!"
Cal_21
New member
"For any OTHER combination of hat colors, at least one person can logically deduce the color of their own hat."
Explain the logic behind that. There were no conditions attached regarding the colors of the hats...wouldn't that be necessary in order to derive a meaning from the color hats the other two are wearing?
Explain the logic behind that. There were no conditions attached regarding the colors of the hats...wouldn't that be necessary in order to derive a meaning from the color hats the other two are wearing?
Cal_21 said:
"Imagine it this way:
Let's pretend we're person C. We see that A and B each have green hats. So there's two possibilities. Either our hat is green, or yellow. First, let's suppose that our hat WAS yellow. What would happen?
Well, if that were the case, person A would see a green and a yellow hat. He'd see a green hat on person B's head, and a yellow hat on person C's head. So in this case, person A could make a simple deduction. He would know that person B saw a green hat. And person B couldn't have seen the green hat on person C's head. Person B HAD to have seen the green hat on Person A's head. Therefore, person A would know that his own hat was green! So person A would stand up pretty quickly and say "I *know* I have a green hat!"
(important part here
But that didn't happen! Person A *didn't* make this conclusion. So obviously, since it DIDN'T happen, our hat (that is, person C's hat) is NOT yellow, because if it were, Person A (or person B for that matter) would be able to make a conclusion right away, and they didn't. Therefore, the hat on person C's head is green!"
Cal_21 said:
Person B couldn't have seen the green hat on person C's head because, as the end of the previous paragraph states, "First, let's suppose that our hat WAS yellow. What would happen?"
Try drawing it out -- a triangle with A, B, C, where A, B = green and C = yellow for this hypo. Look at person A: he sees a green hat on B and a yellow hat on C, but can't see his. He knows that, since B raised his hand, that B sees a green hat. Now look at person B: he sees a yellow hat on C and a green hat on B. Person A can make this deduction because 1) A knows that if B raised his hand, he saw a green had, and 2) A knows that C has a yellow hat. If A had a yellow hat, B would see both A and C with yellow hats, and would not have raised his hand.
Cal_21 said:
From this part of the solution:
"Well, if that were the case, person A would see a green and a yellow hat. He'd see a green hat on person B's head, and a yellow hat on person C's head. So in this case, person A could make a simple deduction. He would know that person B saw a green hat. And person B couldn't have seen the green hat on person C's head. Person B HAD to have seen the green hat on Person A's head. Therefore, person A would know that his own hat was green! So person A would stand up pretty quickly and say "I *know* I have a green hat!""
This is the hypo given C = yellow hat. Note the bold part. If C = yellow hat, A knows that B saw the green hat on A (because we already know that C = yellow). So A would have said in the OP that he knew the color of his own hat -- green!
But he didn't. Because C = green. And with A, B, C = green, no one will be able to stand up and say they know the color of their own hat. And becasue no one stands up with the exclaimation, one of these rather intelligent grad students (this is important!) calculates in his head that the only way that no one stands up and states he or she knows the color of his or her hat is if they were all green. Okay?
Mavafanculo
New member
I just spent 2 paragraphs explaining why the solution is wrong and proved it was right instead. lol
this is the key from your solution
This is the hypo given C = yellow hat. ........ If C = yellow hat, A knows that B saw the green hat on A (because we already know that C = yellow). So A would have said in the OP that he knew the color of his own hat -- green!
But he didn't. Because C = green
this is the key from your solution
This is the hypo given C = yellow hat. ........ If C = yellow hat, A knows that B saw the green hat on A (because we already know that C = yellow). So A would have said in the OP that he knew the color of his own hat -- green!
But he didn't. Because C = green
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