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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Chuck Norris sleeps with a pillow under his gun.
Because the other two people wore black hats?
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[b]Saif wrote: [/b]
Because the other two people wore black hats?
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It would not take ten miunutes to figure that out...
[b]Saif wrote: [/b]
Because the other two people wore black hats?
[/QUOTE]
It would not take ten miunutes to figure that out...
*edit* - unlike Barbara said below, I was not on the right track, I was considering 3 black hats and 2 red ones.
they guessed
its only a 50/50 chance they'd get it wrong,this time they got it right
its only a 50/50 chance they'd get it wrong,this time they got it right
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.
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.
That's my guess here.
You did not read the clue properly:) Each student could see the colour of the other two students' hats.
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.
???
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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[b]magicalfreddiemercury wrote: [/b]
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.
???
[/QUOTE] I don't think so...that's not much different from my shorter answer but still, nice explanation.
[b]magicalfreddiemercury wrote: [/b]
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.
???
[/QUOTE] I don't think so...that's not much different from my shorter answer but still, nice explanation.
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[b]Saif wrote: [/b]
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[b]magicalfreddiemercury wrote: [/b]
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.
???
[/QUOTE] I don't think so...that's not much different from my shorter answer but still, nice explanation.
[/QUOTE]
Ah, but in my scenario, the other two wore RED hats, not black.
[b]Saif wrote: [/b]
[QUOTE]
[b]magicalfreddiemercury wrote: [/b]
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.
???
[/QUOTE] I don't think so...that's not much different from my shorter answer but still, nice explanation.
[/QUOTE]
Ah, but in my scenario, the other two wore RED hats, not black.
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.
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.
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.
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.
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...
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...