A logic question

[Starshine]

This is a question that is posed to my current philosophy class. I wonder what x10 members think.

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[FONT=&quot]Three geniuses stand in a file (one behind the other). Each can see only to the front, so the rear person can see the middle and the front, the middle person can see the front, and the genius in the front cannot see anyone.
[FONT=&quot]
[FONT=&quot]You have five hats. Two are white, and three are red. You blindfold the three geniuses, who are utterly truthful, and put a hat – at random – on the head of each. Then you hide the other two hats and remove the blindfolds.
[FONT=&quot]
[FONT=&quot]You then ask each genius to name the color of his hat (which he cannot see).
[FONT=&quot]
[FONT=&quot]The rear one says "I don't know." The middle on says, "I don't know." Then the front one says, "I know."[/FONT]
[FONT=&quot][/FONT]
[FONT=&quot]WHAT COLOR IS THE FRONT GENIUS' HAT??????[/FONT]
[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT]

 

[balaji2u]

this is way far from my thinking lolzz.
i give up even before read out fully..
Edit:
this is way far from my thinking lolzz.
i give up even before read out fully..

 

[azntechguy]

Damn, this one after pulling hair trying to solve Biochem questions (will fail tomorrow's exam anyhow).

From a probability viewpoint, I'd say the front guy's hat is more likely to be red than white.

From a cynical viewpoint, I'd say that the front guy isn't as utterly truthful as you may imagine. He looked at the corners and saw a white reflection; so it must be white.

From an ironic twist viewpoint, the front guy is blind (even prior to blindfolding) and his other senses has taken over in his prediction. My lord, it feels heavy. Must be two hats stacked on my head.

 

[Starshine]

Damn, this one after pulling hair trying to solve Biochem questions (will fail tomorrow's exam anyhow).

From a probability viewpoint, I'd say the front guy's hat is more likely to be red than white.

From a cynical viewpoint, I'd say that the front guy isn't as utterly truthful as you may imagine. He looked at the corners and saw a white reflection; so it must be white.

From an ironic twist viewpoint, the front guy is blind (even prior to blindfolding) and his other senses has taken over in his prediction. My lord, it feels heavy. Must be two hats stacked on my head.

Yikes. Sorry to hear about the biochem quiz. I've bombed a few recent quizzes myself. Luckily, the final paper pulled me through.

Interesting theories on this. If its okay, I may toss your cynical and ironic twists in to my assignment ... just to see what the professor thinks. ( My class name is informal logic. )

 

[Sharky]

Wow, that's horrible:

Red.

Because there are only 2 white hats, at least one of the hats is red. The 3rd genius sees that one is wearing a red hat and one is wearing a white hat (if he saw two whites he'd know his hat was red). Alternatively, that both the first and second geniuses are wearing a red hat, leading to the same conclusion. He says "I don't know".

If the 2nd genius sees that the front genius is wearing a white hat, he would know that his hat is red. He also says "I don't know" therefore the front genius is wearing a red hat.

So that's how he knows.


I believe this is correct. Please feel free to prove me wrong. :naughty:

 

[azntechguy]

Yikes. Sorry to hear about the biochem quiz. I've bombed a few recent quizzes myself. Luckily, the final paper pulled me through.

Interesting theories on this. If its okay, I may toss your cynical and ironic twists in to my assignment ... just to see what the professor thinks. ( My class name is informal logic. )

It's all right with me. Anything I post online that doesn't have a restriction request statement in it is fair game.

But in all honesty, it actually wasn't meant to be taken seriously. Just a little offbeat humor there.

Wow, that's horrible:

Red.

Because there are only 2 white hats, at least one of the hats is red. The 3rd genius sees that one is wearing a red hat and one is wearing a white hat (if he saw two whites he'd know his hat was red). Alternatively, that both the first and second geniuses are wearing a red hat, leading to the same conclusion. He says "I don't know".

If the 2nd genius sees that the front genius is wearing a white hat, he would know that his hat is red. He also says "I don't know" therefore the front genius is wearing a red hat.

So that's how he knows.


I believe this is correct. Please feel free to prove me wrong. :naughty:

Well... If the third guy is wearing a see-through blindfolds (Colorless plastic wrap around his eyes or must be very thin, porous piece of fabric), I think you're on the right trail! :biggrin:

 

[Jake]

Easily has to be red... just like sharky said

 

[seanooi1]

this is confusing, but i would have to say red as well

 

[Smith6612]

It would have to be red as well.

 

[xxll_martin_llxx]

Why has it 'easily got to be red'?

 

[networker]

Surely the odds are on it being a red hat.It would make sense statistics wise.

 

[Starshine]

For those that were kind enough to post an answer, I have gotten the response from my professor and will post it below :


THREE GENIUS SOLUTION



Starting from the back, genius (#3), if he sees two white hats, then he knows there are no more white hats, and his must be red. But he doesn't know what his hat color is, so he either sees 2 red hats, which would leave a third red and two whites for him, or a red and a white, which would leave a white and 2 reds for him. So we know he does not see two white hats.



If the second genius, the one in the middle, (#2), sees a white hat on #1, then he knows that his own is red, since if it was white, then #3 would have known that his was red. If he sees a red hat, then his hat could be either white or red, and he wouldn't know which. Since he doesn't know what color hat he has on, he must see a red hat.



Therefore, genius #1, in the front, is wearing a red hat. Being a genius, he is able to deduce this.




Here is another explanation:



For the sake of explanation, let's call these guys Moe, Larry, and Curly. Moe is in the back, Larry is in the middle, and Curly is up front.



Curly figures it out because he knows that Moe and Larry are geniuses who don't lie. If Moe (in the back) doesn't know what his own hat is, then the only thing you can gather from that statement is that he doesn't see 2 white hats in front of him. If Moe did see 2 white hats, then he'd know that his own was red, and he'd say so. But Moe doesn't say so, so he could be seeing 2 reds, a red and a white, or a white and a red, but NOT 2 whites.



Larry, being a genius, and knowing that Moe is a genius who doesn't lie, already can tell from the Moe's statement that Moe doesn't know what hat is on his own head and that therefore Larry and Curly are NOT BOTH wearing white hats. Knowing that, if Larry looks ahead and sees a white hat on Curly, then he would KNOW that he must be wearing a red hat. But Larry says he doesn't know what color hat he has on. And Larry's a genius who doesn't lie. So therefore, Larry must NOT be looking at a white hat. He must be looking at a red hat on Curly's head.



Curly, being a genius, and knowing that Moe and Larry are geniuses who don't lie, has this all figured out now, and he knows that he's got to have that red hat on.



Notice that it really doesn't matter WHAT hat Moe or Larry have on.

 

[ShadowmasterX]

lol just because 1 person said RED and you wanna copy her.. .

PEER PRESSURE

that was the real test, and you all failed... except sharky and all the others before her

 

[Twinkie]

That is one heck of a puzzle, got my mind working again. If I didn't found out today, I would not sleep tonight.

 

[Sharky]

You're all such cowardly fools! But it did take me a while to think about that.....