What Colour is your Hat?

stripes

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.

This one took me about 15 minutes to figure out using a lot of "outside the box" thinking.

light_bulb

because he could see two students hats, they both raised their hands so he knew his hat was green, there for all three hats were green.

stripes

Not exactly. Think about it, if only two hats were green, then all three would STILL raise their hands. There are three people, person A, person B, and person C. Person A and Person B are both wearing green hats, while person C is wearing a yellow one. Person A would raise his hand seeing Person B's hat, person B would raise his hand seeing person A's hat. Finally person C would see both person A and person B's hat.

One hint, the fact that all three are very intellegent is important to the answer.

No one will be able to answer this one :)

stripes

Gosh I'm so tempted to post the answer, but light bulb, you ARE on the right track.

light_bulb

all you have to do is look at what direction 2 of the students are looking when they raise their hands so you don't raise your hand until you stand up which confused the other two students because they didn't know why you weren't raising you hand.

or

two of the student raised their hand when looking in only one direction while the student who stood up looked in both directions before raising his hand and standing up.

stripes

Because this information is not presented in the question, the direction in which they looked is negligible in this situation.

light_bulb

saw his reflection somewhere? took the hat off and looked at it?

light_bulb

asked the other two students if he had a green hat?

light_bulb

everyone asked each other what color the hat was and the student who stood up told one of the others his hat was yellow, while he is being told his hat is green the winner stood up. :P

light_bulb

the room was lit with a blacklight, and the yellow would be glowing.

stripes

He he he, sorry light bulb, it's not quite that easy, although when I was figuring it out before, I had WISHED it was. Anyways, I'm afraid I cannot give anymore hints or information until at least a few more people have looked at it and tried it. You were on the right track though.

light_bulb

they were small beanies and only visible from the back so the stand up student made the finger motion to turn in a circle after he did one turn with a thumbs up from one of the other students. now if the student on the left turned counter-clockwise and the student on the right turned clockwise he would have been the first to see the colors.

light_bulb

the stand up student stepped out for a sec to go to the bathroom, mirror.


ok i'm done.

stripes

You've got one creative mind light bulb, hence your name :D
(and no, I intend that as being an insult or anything, you're answers were very amusing lol)

light_bulb

thanks, i try :P

Rogerio

Lets call them A, B & C, where C is the student who answered the question.

Suppose C is yellow.
If B was yellow, then A wouldnt see any green hat.
But A saw a green hat. So B would have to be green.
But B didnt answered anything, that is, B doesnt know his color.
So, C cant be yellow, and all of them are green.

stripes

Yes Rogerio, that is correct. Looks like my question isn't as hard as I thought, he he.

My answer below:
Given all of the information, we know that there are two green hats. Like Rogerio said, suppose C (ours) is yellow, and the other two, B and A, are green. A and B raise their hands, as do I. Now, if we (remember, "we" are in person C's head), if we go into the mind of person B, he would see a green hat (person A) and a yellow hat (person C [which is what we are]). At this point, he knows there are TWO green hats somewhere and he sees one yellow, and one green. He therefore, should assume that his is green, but he doesn't say anything, because in fact, he DOESN'T see a yellow hat on Person C (us), he sees two green hats! This means that we CANNOT assume that Person C (our) hat is yellow, it isn't possible!