The second person who only sees a wall has no information.
The third person knows the second person is wearing a blue hat and knows he also has no information.
The person in the back knows what everybody knows and sees one blue cap and one white cap.
If the third person were wearing a blue cap like the man in front of him is, then the person in the back would immediately know he must be wearing a white cap since there are two of each color. But he isn't, so he doesn't.
By not hearing the person in the back exclaim the color of his cap, the third person knows the color of his cap is different from the person in front of him.
Seems about right.
How does person 3 know person 4 is behind him?
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A show of kindness may not do much help, but a show of cruelty may do much harm.