Riddle: What Colour is your Hat?

[stilleto]

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.

 

[nefertiti]

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.

That's it right there. Because no one answered all right away, person C realized they were ALL in a position of not being able to possibly guess. Meaning everyone saw two green hats.

 

[stilleto]

That's it right there. Because no one answered all right away, person C realized they were ALL in a position of not being able to possibly guess. Meaning everyone saw two green hats.

they were only told to stand up if they saw ONE green hat, not two.
so they each saw one green hat, but the person (you) didn't know if any of them were raising their hands to YOURS.

 

[jerkbox]

so, i was right.

well, sorta right

 

[nefertiti]

they were only told to stand up if they saw ONE green hat, not two.
so they each saw one green hat, but the person (you) didn't know if any of them were raising their hands to YOURS.

Yes, but if they ONLY saw one green hat, someone would have known the answer and jumped up quickly. Since they all hesitated, they all had to be in a position where they couldn't logically prove they had either color.

 

[nefertiti]

so, i was right.

well, sorta right

You would have been right if you'd said, since no one assumed his was green, they all had to be green.

 

[jerkbox]

i'd say my answer was closer....but whatever

 

[stilleto]

Yes, but if they ONLY saw one green hat, someone would have known the answer and jumped up quickly. Since they all hesitated, they all had to be in a position where they couldn't logically prove they had either color.

hesitating has nothing to do with it.

 

[samoth]

hesitating has nothing to do with it.

"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!"

 

[stilleto]

"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!"

ok. it hit me. yes. the hesitation does matter.