Riddle: What Colour is your Hat?

[Cal_21]

"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?

 

[samoth]

"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?

"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]

"And person B couldn't have seen the green hat on person C's head."
Doesn't this only work if they're seated in a LINE where person b cannot see person C?

 

[samoth]

"And person B couldn't have seen the green hat on person C's head."
Doesn't this only work if they're seated in a LINE where person b cannot see person C?

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]

In this scenario, one person would see 2 green hats, and the other two would see 1 green and 1 yellow. You stated earlier that they can all see the color of the other two hats. How can one deduct from this information the color of their own hat?

 

[samoth]

In this scenario, one person would see 2 green hats, and the other two would see 1 green and 1 yellow. You stated earlier that they can all see the color of the other two hats. How can one deduct from this information the color of their own hat?

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?

 

[Cal_21]

I'll admit I skimmed over that part too quickly. Nice riddle.

 

[Mavafanculo]

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