The Problem of the Prisoners
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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.
Problem:
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."