In the county jail, 4 prisoners A, B, C, D are selected and D is blind. The sher
ID: 3195998 • Letter: I
Question
In the county jail, 4 prisoners A, B, C, D are selected and D is blind. The sheriff Anne Oakley puts blindfolds on A, B, and C since D is already blind. Next she selects four hats from seven hats hanging on the hat rack, three of them are red and the other four are white. She places four hats on the prisoner’s heads and hides the remaining three hats. Then she takes the blindfolds off A, B, and C and tells what she has done, including the fact that there were three red hats and four white hats to choose from. Sheriff Oakley then says, “If you can tell me the color of the hat you are wearing, without looking at your own hat, you can go free.” The following things happen:A says that he can’t tell the color of his hat. So the sheriff has him returned to his cell. Then B says that he can’t tell the color of his hat. So he is also returned to his cell. Then C says that he can’t tell the color of his hat. So he is returned to his cell. Then D, the blind prisoner, says that he knows of the color of his hat. He tells the sheriff, and she sets him free. What color was D’ hat, how did D do his reasoning? In the county jail, 4 prisoners A, B, C, D are selected and D is blind. The sheriff Anne Oakley puts blindfolds on A, B, and C since D is already blind. Next she selects four hats from seven hats hanging on the hat rack, three of them are red and the other four are white. She places four hats on the prisoner’s heads and hides the remaining three hats. Then she takes the blindfolds off A, B, and C and tells what she has done, including the fact that there were three red hats and four white hats to choose from. Sheriff Oakley then says, “If you can tell me the color of the hat you are wearing, without looking at your own hat, you can go free.” The following things happen:
A says that he can’t tell the color of his hat. So the sheriff has him returned to his cell. Then B says that he can’t tell the color of his hat. So he is also returned to his cell. Then C says that he can’t tell the color of his hat. So he is returned to his cell. Then D, the blind prisoner, says that he knows of the color of his hat. He tells the sheriff, and she sets him free. What color was D’ hat, how did D do his reasoning? In the county jail, 4 prisoners A, B, C, D are selected and D is blind. The sheriff Anne Oakley puts blindfolds on A, B, and C since D is already blind. Next she selects four hats from seven hats hanging on the hat rack, three of them are red and the other four are white. She places four hats on the prisoner’s heads and hides the remaining three hats. Then she takes the blindfolds off A, B, and C and tells what she has done, including the fact that there were three red hats and four white hats to choose from. Sheriff Oakley then says, “If you can tell me the color of the hat you are wearing, without looking at your own hat, you can go free.” The following things happen:
A says that he can’t tell the color of his hat. So the sheriff has him returned to his cell. Then B says that he can’t tell the color of his hat. So he is also returned to his cell. Then C says that he can’t tell the color of his hat. So he is returned to his cell. Then D, the blind prisoner, says that he knows of the color of his hat. He tells the sheriff, and she sets him free. What color was D’ hat, how did D do his reasoning?
Explanation / Answer
D's hat is WHITE in colour.
REASONING:
D thinks like this:
If I have RED hat on my head...( D is thinking...)
Following cases arise. Those are:
Now, take 1st case: It is not possible because already D has RED hat so other three cannot have red hats simultaniously.
2nd, 3rd, 5th cases: If any two persons among A, B and C wear red hats, then the third person among them can easily tell the colour of his hat as white as he sees 3 RED hats. (Since D also wears RED hat).
4th, 6th and 7th cases: If any two persons among A, B and C wear white hats and other person wears red then definitely one of the white hat person can tell the colour of his hat as white. Because the white hat person thinks as he sees two red hats( D and one among (A,B and C)): If he also wears red, definitely someone( the other white hat person) would tell the colour of his hat. But that is not happend that means he didn't wear red.
8th case: If all three persons A, B and C wear white hats, definitely someone among the three would tell the colour of his hat because that someone thinks like this: If I have red hat, other two can see two red hats one of mine and one of D's. If this is the case one of the other two can tell the colour of their hat as white.
for example: A, B and C wear white hats.
A's perspective: If I wear RED hat, B and C can see two RED hats( A's and D's). If that is the case B thinks that:
As B can see two red hats, if he also wears red hat then C could tell the colour of his hat but he was quite so B can tell his hat colour that is white.
So, in above all cases one of the A, B,and C can tell the colour of their hats. But here, that is not happend. That means, if D wears RED hat someone among A , B and C should tell but the colour of their hat. Since that is not happend D finally concludes his hat colour as WHITE.
A WEARS B WEARS C WEARS 1. RED RED RED 2. RED RED WHITE 3. RED WHITE RED 4. RED WHITE WHITE 5. WHITE RED RED 6. WHITE RED WHITE 7. WHITE WHITE RED 8. WHITE WHITE WHITE