(12 votes, average: 3.67 out of 5)
At a party, four people played a game. Three of them sat one behind the other, so that Abe saw Bill and Cal, and Bill only saw Cal, who sat in front and saw nobody else.
Dave had 5 hats which he showed to his three friends. Three of the hats were blue and two were red.
Now Dave placed a hat on the head of each of his three friends, putting aside the remaining two hats.
Then he asked Abe what color his hat was.
Abe said he couldn’t tell.
Bill was asked the color of his own hat, but he didn’t know for certain either.
Cal, though he couldn’t see any hat at all, gave the right answer when asked what color his hat was.
Do you know what color Cal’s hat was and how he reasoned to find out the correct answer?
Color of Cal’s hat?
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Cal <= Bill <= Abe
Abe couldn’t tell means, Cal and Bill both were not having red hats, it could be either RB/BR or BB.
Now Bill also was not certain of his hat color, it means Cal was wearing Blue color hat, as if it was Red, there was only one possibility for Bill’s hat.
So realizing this, Cal immediately told that he was wearing a Blue Color Hat.
Abe couldn’t tell means, Cal and Bill both were not having red hats, it could be either RB/BR or BB.
Now Bill also was not certain of his hat color, it means Cal was wearing Blue color hat, as if it was Red, there was only one possibility for Bill’s hat.
So realizing this, Cal immediately told that he was wearing a Blue Color Hat.
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If B and C have RED Hat then Automatically A will be Blue and he will guess it. but A says he do not know then B and C are Not both RED
1- B= Blue and C = Blue
2- B= Red and C= Blue
3- B= Blue and C = Red
then B says He can not be SURE this mean that C for sure is not RED because if C is red then B would Guess that he is BLUE as B did not confirm then it is for sure that C is BLUE