Prisoners and hats puzzle
There are 3 person and 5 caps: 2 black caps and 3 white caps. Each person wear one cap. The are standing like below:
Person 3 > Person 2 > Person 1
Person 3 can see Person 2 and Person 1 and can see the color of their caps but doesn't know the color of his own cap.
Person 2 can see Person 1 and can see the color of his cap but doesn't know the color of his own cap.
Person 1 don't even know the color of his own cap.
When asked to Person 3 about the color of his cap, he replied "I don't know".
When asked to Person 2 about the color of his cap, he replied "I don't know".
Now Person 1 is sure about the color of his cap.
What is the color of Person 1's cap and why?
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1 solution
Great variation of this problem, very accessible!
Denote the 3 people as p 3 , p 2 , and p 1 .
When p 3 says she doesn't know her cap's color, all three now share the knowledge that the black hats cannot be on both p 1 and p 2 , or else p 3 would have been able to deduce that her own cap was white.
When p 2 says she doesn't know her cap's color, all three now share the knowledge that p 1 's cap is not black, or else p 2 would have been able to deduce that her own cap was also not black.
Therefore, p 1 knows that her own cap is white.