Four criminals are caught and are to be punished. The judge allowed them to be freed if they solve a puzzle. If they do not, they will be hung. They agreed.
The 4 criminals are lined up on some steps (as shown in the picture). They are all facing in the same direction. A wall separates the fourth man from the other three.
- So to summarize:
- Man 1 can see the Man 2 and 3.
- Man 2 can see man 3.
- Man 3 can see none of the others.
- Man 4 can see none of the others.
The criminals are wearing hats. They are told that there are two white hats and two black hats. The men initially don’t know what color hat they are wearing. They are told to shout out the color of the hat that they are wearing as soon as they know for certain what color it is.
Rules:
- They are not allowed to turn or move.
- They are not allowed to talk to each other.
- They are not allowed to take their hats off.
Who is the first person to shout out and why?
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2 calls out that he is wearing a White hat. Why is he 100% certain of the color of his hat?
After a while, 2 comes to the realization that he must answer.
This is because 4 can’t answer, and neither can 1 or 3.
1 can see 2 and 3, but can’t determine his own hat color. 3 can’t see anyone and also can’t determine his own hat color. 4 is in the same situation as 3, where he can’t see anyone and can’t determine his own hat color.
Since 1,3 and 4 are silent, that leaves 2. 2 knows he is wearing a White hat because if 1 saw that both 2 and 3 were wearing Black hats, then he would have answered. But since 1 is silent, 2 knows that he must be wearing a black hat as he can see that 3 is wearing a white hat.