Mid-Week Brain Teaser

King Damager

King Damager

King Damager

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So I was doing this in a lecture the other day. I wonder how many of you can solve this.

I'll request you put your possible solution/answer in spoilers.

I'll reveal the answer at some point in the next couple of days, if no one gets it or, if someone gets the correct answer.

Puzzle is as follow:
For fun, one fine summer day, a schoolteacher puts hats on the heads of each of the children in class. Some hats are black; some (seven) are red. The children can all see each other’s hats, but not their own. They are clever, obedient children, and they do not talk.
The teacher then asks each child in turn whether her hat is red, explaining: “If you do not know then you should say so, for if you guess incorrectly then I shall keep you in long detention. But if you do know, and tell me correctly, then while the rest of us recite Latin verbs you may go out and play in the sunshine.”
Each child, when asked, reluctantly admits that she does not know the whether her own hat is red.

In another class of similar children, the teacher repeats the game. This time she remarks, during her explanation: “At least one hat is red.” This time, after six children with red hats, and a few with black hats, have all admitted that they do not know whether their hats are red, the next child correctly asserts that her own hat is red and the remainder (correctly also) that their hats are not red.

How do the children in the second class discover the answer?
Click to expand...

This is a relatively simple Game Theory issue for those interested, and shouldn't be too challenging (I'd be surprised if someone doesn't get it) :)

kd
 
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We don't know how many kids are in the class. So if by the time everyone in the second class has said 'they don't know', there are only two children left (you said 'remainder', so presumably, more than one), it is a 50/50 chance that her hat is red. If she correctly gusses that it is right, and the next child know that there is at least one red, then the next child might believe that only one is red (given their presumed age) and deduce that their hat is unlikely to be red
 
I think you missed out the bit where they can only see the hat of the kid standing directly in front of them and no one else's... ;)
 
Skeeter said:
Are the kids aware there are seven red hats?
Click to expand...

No

doofer said:
I think you missed out the bit where they can only see the hat of the kid standing directly in front of them and no one else's... ;)
Click to expand...

This would complicate it further potentially, and break the current solution.

utajoker said:
they tell each other?

it does not state that they do not talk.
Click to expand...

Right at the beginning it does. 'They are clever, obedient children, and they do not talk'

kd
 
I think I have it.

the last red hat wearer to guess "I don't know" can see 5 other red hats, including 'the girl' so don't know what colour they are wearing. at this point, If 'the girl' had a black hat, the last guesser would have known that theirs was the final 7th red had, but they don't because they can see 'the girl's' red hat

from this point;

'the girl' can see 6 red hats and then only black ones. the last black hat wearers know they have black once all 7 red are confirmed
 
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mame said:
I think I have it.

the last red hat wear to guess "I don't know" can see 6 other red hats, including 'the girl' so don't know what colour they are wearing. at this point, If 'the girl' had a black hat, the last guesser would have known that theirs was red, but they don't because they can see 'the girl's' red hat

from this point;

'the girl' can see 6 red hats and then only black ones. the last black hat wearers know they have black once all 7 red are confirmed
Click to expand...

But the kids don't know there's 7 ...
 
Basher said:
But the kids don't know there's 7 ...
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"at least one hat is red". the final guesser must be able to see at least one red (un-guessed) hat to not know that theirs is red. 'the girl' can see no red unguessed hats when she says that hers is red

actually, i still don't think thats right

it's something to do with the final "I don't know"
 
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The more I think about this, the more I think one rule or condition has been missed from it.
 
I've thought it over and over and I just don't think it's possible unless they know that there's 7 red hats or they cheat such as the other class telling them (which isn't really a puzzle) If they do know there is 7 red hats then it's quite simple
 
Mirror.
Are the children in the second class also told that there are seven hats? The brackets around the word seven in the first paragraph doesn't make it clear (to me) if they are aware that there are seven.

Assuming the second group knows that there are seven the the girl counts all of the other hats which she can see and therefore how many of each colour?

How many hats per child : p
 
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