Help with logic problem?

Question

There are 3 children, A, B, and C. The teacher says they will get one chance to get an A for the semester without having to do any more homework. All they have to do is to answer one of his math problems right.
The problem is that he has 5 hats, 3 red and 2 blue. The children are told to stand in line with their eyes blindfolded. The teacher puts one hat on each of their heads and then discards the remaining 2 hats so they cannot be seen. Then the first child is told he can look at the other two children and, judging by the color of their hats, he can guess the color of the hat he wears. He can either guess or pass. (The children will only guess if they are 100% positive they are correct.)
The guess and pass process is carried through with the rest of the children. Student A passes, Student B passes, and then without even opening his eyes Student C guesses correctly what hat is on his head. Explain how he knows without even looking.

Basically, what I've gotten is:
If Student A saw two blue hats, then he would’ve been sure that he had a red hat. Student B knew that Student A passed because he either saw two red hats or one red hat and one blue hat. If both Student A and Student C had blue hats, Student B would have been sure he had a red hat.

But it seems to me that A, B, and C can all have red hats or A and B can have red hats while Student C has a blue one. I can't knock either possibility off.

Answer 1

The first part is right:
"If Student A saw two blue hats, then he would’ve been sure that he had a red hat. Student B knew that Student A passed because he either saw two red hats or one red hat and one blue hat. " So now it's B's turn, and he knows that if C has a blue hat, and A has a red hat, his own hat must be red. (If it were blue, A would have known his own hat color) If C has a red hat and A has a red hat, B's hat could still be red or blue. (Same if C has a red hat and A has a blue hat.) He passes, and this means C's hat is red. So C knows his own hat color without looking. That was confusing....but I think it works.

Answer 2

In the scenario that all 3 students are wearing red hat, student

A will pass because he/she saw 2 red hats but couldn't

confirm if his/her hat is blue. And with that knowledge, student

B will only have to confirm that student A is not wearing a blue

hat and he

can be 100% positive that his hat is red and make a guess.

Therefore, 3 red hat wouldn't be possible and that leaves you

with the answer.

Answer 3

If you find those explanations confusing, try this one:

The only way A could guess is if she saw two blue hats. She didn't guess, so B knows that his hat and C's are not both blue.

When B looked, if he'd seen a blue hat on C, he would have known his hat was red - again, because he knows that his and C's hats are not both blue. He passed, so he must've seen a red hat on C. That was all C needed to know.

Answer 4

neither A nor B could have seen two blues.

A could have seen anything else. B+R or R+R.

for B, then if C was blue, then obviously B could not be blue because A did not see two blue hats, therefore C could not be blue otherwise B would be wearing red.

Then C knows their hat is red.