The Problem of the Prisoners
  /\        |     /\          /\          /\
 /  \       |    //\\        /  \        //\\
 O        |     O         O         O

 A              B         C         D

Some stipulations:
1. Prisoner A can only look right.
2. Prisoners B, C, and D can only look left.
3. There is a wall between Prisoners A and B, through which no one can see.
4. Prisoners A and B can see only the wall.
5. Prisoner C can only see Prisoner B.
6. Prisoner D can see Prisoners B and C.
7. None of the prisoners can see their own cap color.

These prisoners are given a deal. One of them must name the color of their own cap correctly, or else they will be put to death. They know that two caps are black and two caps are white. The prisoners are not allowed to speak to each other. The first words out of any of their mouths have to be the color of their cap.

Who saves the day for these prisoners? How does he know he's right? Remember, no guessing from the prisoners, as their lives are on the line.

Solution to the Problem of the Prisoners:

Obviously, Prisoners A and B are going to be unable to give an answer, as they can see no caps. Dead end.

Prisoner D can see both Prisoners B and C, right? Well, he can only see that their caps are different. That does not tell him what color his cap is, though. Seemingly another dead end.

The answer lies in Prisoner C. He can see that Prisoner B's cap is black. He notices that Prisoner D says nothing. He must realize that Prisoner D sees that both Prisoners B and C have different colored caps and thus is unable to give an answer immediately. Knowing that his own cap is differently colored than Prisoner B's, Prisoner C can confidently say, "My cap is white."

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