annie needs help with her homework

[knowbody0]

i have no idea how to answer this:

the colored hat problem

the wise teacher offered the 3 nosiest students a deal. he showed them he had two red hats and three blue hats. here's the deal:
the three students would close their eyes, and while their eyes were closed, the teacher would put a hat on each of their heads (and hide the other two hats)
then one at a time, the students would open their eyes, look at the other two students' heads and try to guess which color hat was on their own head.
any student that guessed correctly would have no homework the rest of the semester. but any students that guessed wrong would not only have to do their own homework, but they would have to help grade everyone else's work.
the students drew numbers to see who would guess first. then they closed their eyes and the wise teacher put a hat on each one's head. Irwin, who was to go first opened his eyes, looked at the others' heads and said he didn't really want to play. he couldn't tell for sure and he didn't want to guess in case he was wrong. Next, Gladys opened her eyes and looked at the others' heads. she also thought about the fact that Irwin had said he couldn't tell. Then she said she didn't want to risk it either. she couldn't tell for sure.
Bertha was third. She just stood there with her eyes still closed tightly and a big grin on her face. "I know what color hat I have on" she said.
and she gave the right answer.
your problem is to figure out what color hat Bertha had on and how she knew for sure. Remember, Bertha didn't even look.

[MidwestMomma]

1. i suck at logic problems

But I'll give it a kick :)

[knowbody0]

2. thanks,

i usually rock at them. none of her school budies can get it either

[DawgHouse]

3. Is this the same?

http://mathforum.org/library/drmath/view/61834.html

[knowbody0]

5. DawgHouse - you really rock

thanks!

[DawgHouse]

6. Glad to help. I read the link but still don't get it.

It sorta made my head hurt :)

[AlCzervik]

4. i found this on google, there are other links as well

if you look up "the colored hat problem" I don't know if the answer is there for sure but it may help.
http://groups.google.com/group/rec.puzzles/browse_thread/thread/af9fc43ade9566de/a2e47e0aafb619d2%23a2e47e0aafb619d2?sa=X&oi=groupsr&start=0&num=3

[knowbody0]

7. thanks chimpsrsmarter

annie sends ya a big hugh hug

[AlCzervik]

11. big hug back your way too, i have an 11 year old and i get stumped

more often then not on her homework.

[khashka]

8. Since it's three blue and two red....

The answer is blue.

Right?

Khash.

[knowbody0]

10. i have no fucking idea

my head hurts

[khashka]

12. It has to be

just think it through.

And yeah, my head hurts too and what demon inspired this post?

Khash.

[knowbody0]

14. "just think it through"

smart ass!
8th grade teacher i have not met yet.
thanks Khash

[mainegreen]

9. Evil

I just spent 20 minutes solving that.
And someone else posted the answer!
I hate you!

;)

[DawgHouse]

13. I just searched the internets and there it was!

I googled: "math problems that parents can't possibly figure out". :)

[knowbody0]

15. i feel sofa king wee tod did

[mainegreen]

16. Definitly evil problem.

I went down the wrong path at first. Even created this in notepad:


    B    
  /  \  
B---B

    B       R         R
  /  \    /  \      /  \
R---R  R---B  B---R

    B        R        B
  /  \     /  \     /  \
B---R  B---B  R---B

[knowbody0]

17. thanks mainegreen

my scratch looks just like that.

[C_eh_N_eh_D_eh]

18. I got it! (Spoiler)

If Gladys and Bertha had both been wearing red hats, Irwin would have known he was wearing blue. Since he couldn't be sure, that must not have been the case.

Gladys realizes this, so she knows that she and Bertha can't both be wearing red. So, if Bertha's hat is red, hers must be blue. But again, what Gladys sees doesn't give her enough information.

Therefore, Bertha must be wearing a blue hat.

:P

[knowbody0]

19. that's what i get as well

logic prevails! but my brain itches. thanks!