Author 

YourValentine
registered July 27th 2001
Deity: 7615 posts

Three top math students with equally great achievements were subjected to the following task: They were shown 5 hats. Three of them were red, two were black. The students were given a hat to wear each and while they could see the hats the two other students wore they could not see their own and not the two spares. The task was to find out which colour their own hat was without any help and without talking or signing to each other. After ten minutes one of them said: "I wear a red hat". And it was true. How could she know?
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john bodega
Deity: 12705 posts

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Saif
Royalty: 1109 posts

Because the other two people wore black hats?
"only way to really know what the hell we are doing on this earth is through sacred plants and mushrooms."  Treasure Moment

YourValentine
registered July 27th 2001
Deity: 7615 posts

Saif wrote: Because the other two people wore black hats? It would not take ten miunutes to figure that out...
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Raf
Stop this noise!
Deity: 8274 posts

*edit*  unlike Barbara said below, I was not on the right track, I was considering 3 black hats and 2 red ones.
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JoxerTheDeityPirate
Deity: 6272 posts

they guessed its only a 50/50 chance they'd get it wrong,this time they got it right
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YourValentine
registered July 27th 2001
Deity: 7615 posts

It's not a guess, it is a logical thought process. I think Raf is on the right track. Remember they are all very intelligent.
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inuliger
Deity: 13057 posts

I'm going to go out on a limb here and guess that, because there are THREE of them, and THREE red hats, they probably thought, with two of the hats being spares after all, and two of them being black, that they in some way would "trick" themselves into stupidly guessing they were wearing black. That's my guess here.

YourValentine
registered July 27th 2001
Deity: 7615 posts

You did not read the clue properly:) Each student could see the colour of the other two students' hats.
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magicalfreddiemercury
Deity: 2695 posts

No doubt this sounds clearer in my mind than on the page but here goes... The other two students had already guessed that they were wearing black hats. That meant they each saw a red hat on the other two students and, so, probability suggested to each of them that they would be wearing black hats. However, the third student saw each of the others with red hats and realized that they saw she was wearing a red hat as well. ???
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Saif
Royalty: 1109 posts

magicalfreddiemercury wrote: No doubt this sounds clearer in my mind than on the page but here goes... The other two students had already guessed that they were wearing black hats. That meant they each saw a red hat on the other two students and, so, probability suggested to each of them that they would be wearing black hats. However, the third student saw each of the others with red hats and realized that they saw she was wearing a red hat as well. ??? I don't think so...that's not much different from my shorter answer but still, nice explanation.
"only way to really know what the hell we are doing on this earth is through sacred plants and mushrooms."  Treasure Moment


magicalfreddiemercury
Deity: 2695 posts

Saif wrote: magicalfreddiemercury wrote: No doubt this sounds clearer in my mind than on the page but here goes... The other two students had already guessed that they were wearing black hats. That meant they each saw a red hat on the other two students and, so, probability suggested to each of them that they would be wearing black hats. However, the third student saw each of the others with red hats and realized that they saw she was wearing a red hat as well. ??? I don't think so...that's not much different from my shorter answer but still, nice explanation. Ah, but in my scenario, the other two wore RED hats, not black.
"The others don't like my interviews. And frankly, I don't care much for theirs." ~ Freddie Mercury

pow wow
Bohemian: 423 posts

Student 1 sees a red on Student 2 and black hat on Student 3. He/She doesnt know what his colour is except if 2 & 3 are black. Student 1 keeps quiet. Student 2 sees red on Student 1 and black on Student 3. He/She doesnt know what his colour is except if 1 & 3 are black. Student 2 keeps quiet. Student 3 understands that Student 2 and 1 are seeing the same and knows that since there are 2 black hats they have to be worn by Students 1 and 2. Student 3 knows they are wearing RED.
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YourValentine
registered July 27th 2001
Deity: 7615 posts

My head is spinning..:) Magicalfreddie has the result right but the explanation is incomplete. pow wow has this mistake: "Student 1 sees a red on Student 2 and black hat on Student 3. ... ... Student 3 knows they are wearing RED." It's easier to solve when you look at it from the perspective of the student who had the solution first.
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Saif
Royalty: 1109 posts

Let me try again: The third student DEFINITELY wears red(given). The first student looks at the second and third ones. He sees the second one wearing black and the third one red. He can't come to a conclusion. The second student looks at the first and third ones. He sees the first one wearing red and the third one red as well. He can't deduct the colour of his own hat either. The third student looks at the first student and the second student. He sees that the first one has a red hat and the second one a black one. He sees that both of them are silent. He realizes that the first student could easily have deduced that he himself was wearing a red hat had his(third student's) hat been black since there were two black hats in total and the second student was wearing one already. So the third student realized that he must be wearing a red hat... Does it make sense? I don't know if I'm right...
"only way to really know what the hell we are doing on this earth is through sacred plants and mushrooms."  Treasure Moment

Saif
Royalty: 1109 posts

"only way to really know what the hell we are doing on this earth is through sacred plants and mushrooms."  Treasure Moment

YourValentine
registered July 27th 2001
Deity: 7615 posts

Here is the solution: Just imagine to be the student who has the solution first: You see the other two students  which are the possibilities? 1. both wear a black hat In this case you know you must wear a red hat and you say it immediately. 2. one of them wears a red hat, the second one wears a black hat. Now you can wear either black or red but if you wear a black hat the guy with the red hat would say "red" immediately because he would see two black hats and would know immediately. When he does not say "I wear a red hat" you know that he does not see 2 black hats and you wear a red hat. This cannot take 10 minutes because the other two are very intelligent and if they do not say anything, you know right away that you wear a red hat. 3. both wear red hats. Now you can again wear a black or red hat but if you wear a black hat, the other two see a black and a red hat each and are in the situation Nr. 2. They would guess pretty soon that they wear red because the other one is silent. Since none of the two says he wears red, it's obvious that you all wear red hats and the first who has thought this to the end wins.
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