Homework----Deductive Reasonsing???

Question

Find the color of the hat for the front genius?

3 geniuses stand in a file (one behind the other).Each can see only to the front, so the rear person can see the middle and the front,the middle person can see the front, and the genius in the front cannot see anyone.

You have 5 hats. 2 are white, and 3 are red. You blindfold the 3 geniuses, who are utterly truthful, and put a hat-at random-on the head of each. Then you hide the other 2 hats, and remove the blindfolds.

You then ask each genius to name the color of his hat(which they cannot see).

The rear one says "i don't know". The middle says, 'I don't know". Then the front one says, "I know".

What color is teh front genius hat????

You do not have to tell me the answer, but can you please explain what I need to do to get the answer, or if you give me the answer, explain to me how you got it.

Please I need help badly.

Answer 1

Okay if the third genius says he does not know, it is because the two in front of him are not wearing two white hats. If they were wearing two white hats (then #3 would have to be wearing red because the two white would have been used up.) So you know now that at least one person (out of genius 1 and 2) is wearing a red hat. Now genius 2 knows that he is either wearing a white hat or a red hat based on the fact that genius 3 didn't know. But genius 2 can see genius 1. If genius 1 was wearing white, than genius two would know that he is wearing red (because as we said earlier both cannot be white). But genius 2 says he does not know because genius 1 is wearing red. If genius 1 is wearing red, genius 2 could be wearing another red or a white-In both cases genius 3 doesn't know what he himself is wearing. So genius 1 is wearing red.

Answer 2

The only way the front genius can know is if he sees 2 white hats. That would mean his hat is red.

If any of the other genuises has a red hat, then there is a chance he has a white hat and he wouldn't know.