Problem for fun: Three kids stand in a straight line facing forward, and are told to not look anywhere but straight ahead (this means the last kid can see the 2 kids in front of him, the middle kid can see the front kid, and the front kid cant see anyone). A teacher has a bag full of 2 red hats and 3 black hats, and randomly places hats on the three kids, making sure they cant see the color of their own hat. These kids are pretty bright, so the teacher tells them if they can logically figure out what color their hat is, to immediately say it.

Question

Problem for fun: Three kids stand in a straight line facing forward, and are told to not look anywhere but straight ahead (this means the last kid can see the 2 kids in front of him, the middle kid can see the front kid, and the front kid cant see anyone).  A teacher has a bag full of 2 red hats and 3 black hats, and randomly places hats on the three kids, making sure they cant see the color of their own hat.  These kids are pretty bright, so the teacher tells them if they can logically figure out what color their hat is, to immediately say it.

anonymous · Answer

About 10 mins goes by, and the first kid correctly guesses the color of their hat.  What color is it, and why? please prove all your statements

myininaya · Answer

is the first kid=front kid?

anonymous · Answer

yes, my bad >.<

myininaya · Answer

can the kids behind him just tell him what the color of his hat is?

anonymous · Answer

nope <.< that would be too easy!

myininaya · Answer

i think the color of his hat to be more likely black than red since there are more black hats than red, but i dont see how i can know for sure what color of any of their hats are

myininaya · Answer

how can the front kid know any thing about his hat color he cant see the other boys/kids

anonymous · Answer

Think of how the last kid would react if he saw certain combinations.

myininaya · Answer

so have the two kids behind the front kid already said what the color of their hat is?

anonymous · Answer

no, the front kid was the first person to say something. there was silence for 10 mins

myininaya · Answer

oh yeah lol

anonymous · Answer

If the last kid saw 2 read hats in front of him, what would his reaction be?

anonymous · Answer

lol read, red >.>

myininaya · Answer

then his hat would be black but how would the front kid know this

myininaya · Answer

it should be more likely that the first kid who speaks would be the kid who is behind the other kids

anonymous · Answer

the silence.  Because the last kid didnt say anything immediatly, the other two kids now know, there are not 2 red hats on the front 2 children.

myininaya · Answer

oh that makes sense

anonymous · Answer

Now think of how the middle kid would react to that knowledge....im gonna grab a bit to eat lol, i'll be back tonight, this problem is very entertaining (at least to me anywhos) :)

myininaya · Answer

ok i will bb too
and i will think about this

anonymous · Answer

Psssh, only took me five minutes. :-P

*spoilers*

His hat is black.

Number from front to back 1,2,3.
If child 3 had seen 1 and 2 wearing red hats, he would say without hesitation that he was wearing a black hat.

Child 2, knowing that since that child 3 didn't say he had a black hat, that logically either both he and child 1 were both wearing black hats, or one red and one black.

Child 1, giving child 2 enough time to figure that out, deduced that since child 2 couldn't state with certainty what color hat he was wearing, which would mean he must be wearing a black hat because if he was wearing a red one, child 2 would have known that he was wearing a black hat himself.