There are three very intelligent men, and each one knows the others are as smart as he. They are shown a box?

Question

that contains three blue and two red caps. The men are positioned in indian file in front and facing a wall. The man closest to the wall we shall call A. The second man standing behind A and also facing the wall we will call B, The third man standing behind B and also facing the wall we will call C. Caps are taken out of the box at random and placed on the heads of the three men. Of course, C can not see the color of his cap but can see the caps on A and B. B cannot see his cap nor C's cap but can see A's cap. Finally, A cannot see neither his nor A's and B's cap. C is asked if he knows the color of his hat and, after thinking for a few moments, answers that he doesn't know. Then the same question is asked of B who, after thinking for a few moments also answers that he doesn't know. Finally, A is asked the same question and, after thinking for a few moments, answers correctly. Now, the question is: What is A's cap color and how did he know?

Ignore the question sign after the word "box" in the second sentence. For whatever reason this site does not allow me to edit the questions!

To Nelson de Blue: You don't have a clue of what is going on, do you?

To Nelson De Bon: You don't have a clue about what this is all about, do you?

To Jinx: You make abxolutely no sense! Read the question again!

Answer 1

He's wearing a blue hat.

C can see A and B, but doesn't know what his hat is. This says that A and B are not both red.

Since C did not know, B knows that his hat or A's hat (or both) is (are) blue. If A had a red hat on, he would know that he had a blue hat himself, and would know the colour of his hat. Since he didn't know, this means A did not have a red hat on and thus had a blue hat.

A did the reasoning that I just did, and knew he had a blue hat.

Answer 2

So C must see that his buddies are wearing a red cap and blue cap (or 2 blue caps). Leaving a red cap and two blue caps (or 2 red caps and a blue cap) that he might be wearing, he doesn't know which. B knows that he and A are either wearing 1) 2 blue caps or 2) a red cap and a blue cap. He looks at A and crap! He can't tell which means that A is wearing a blue cap, leaving a red or blue for B. A also knows this and can figure, safely, that he is wearing a blue cap. Or maybe I'm just pulling this out of my butt.

Answer 3

A knows he has a blue cap.

If both A and B had a red cap, then C would know his cap was blue, but he can't tell, so either A or B or both has a blue cap.

B knows that both he and A cannot have red caps from C's answer. If A's cap was red, then he would know that his was blue. Since he can't answer, A will know he has a blue cap.

Answer 4

I referred to a combination of caps as (A's color, B's color, C's color) abbreviated b = blue and r = red. (example: (b r b) as in A has blue cap, B has red cap, and C has blue cap)

The possible cases are:
(b r b)
if combination was (r r b) C would have known so it is not possible. Therefor A knows his is blue

(b r r)
A knows his is blue

(r b b)
B would have known his is blue this combination is not suitable. B knows that if his was red C would have known the color of his cap so his is not red.

(r b r)
Not possible. B knows

(b b b)
(The hardest one to explain. Hope i make myself clear..) A assumes his is red. in this case C would have not known the color of his cap but at this point B would have figured out that his cap is blue otherwise the combination would have been (r r a) and C would have known. B does not know so A knows his is blue.

(b b r)
A assumes his was red but B would have known his was blue therefor A knows his is not red.

In all possible cases A figures out his is BLUE

Answer 5

A has a blue cap.
Since C didn't know, B knew that either him and A has different colors or both had blue.
B -> "C sees B with blue and A (which B can see). or C sees B with red and A's."

Because of C's answer, we know A and B did not both have Red.
Because of B's answer, we know that A did not have Red since if A had red, B could only have Blue and B did not know his color.

Answer 6

A has a blue cap--he can see that the other two have red ones.

Answer 7

Blue. If C can't tell, then A+B is 1 or 2 blue. If B can't tell, then A+C=1or2 blue. The only way A can thus know is if both B & C have red hats, thus A must have blue.

Answer 8

hi, nice question, pretty simple answer really.
for C to not know what he is wearing combintion must be ONLY (bbb,bbr,brr,brb,rbb,rbr) and NOT (rbb)
now, since C said he doesnt know, B knows now that it its NOT (rbb).
if A had a red hat and B saw this, it would only leave the combination to (rbb) or (rbr) meaning B would know his hat is blue, as b doesnt know what his hat is. i.e b's hat CANT be blue or he would know it was blue
the combination is now (bbb,bbr,brr,brb)
leaving A to only have that hat colour b = BLUE!!!

[plz let me know if i am wrong]
THIS IS PROB THE ANSWER, EXPLAIND IN SIMPLE

Answer 9

BLUE

Answer 10

huh?