There are four prisoners on the death row.
All four prisoners will be freed, if at least one of them correctly guesses the color of the hat on his head.
All four prisoners A, B, C, and D can only look forward with the wall in between them.
They are only given this information: there are two black hats and two white hats.
However, if they get the answer wrong, everyone will be executed.
There is only one chance to answer it correctly.
Of course, you can’t see through the wall.
Can the four prisoners be freed?
If so, which prisoner can guess the right answer? And how?
C: “If B and I(C) had the same color hat, D would have said the answer, but D couldn’t answer, so obviously my hat color (different from B’s white) is black!”
Proceed to Conclusion:
- A and B will never know the answer. In other words, C and D are the only ones that have a chance to get the right answer.
- Let’s think about it in D’s shoes.
There is prior information that there are two black and two white hats, and in front of me you can see one black and one white hat.
The color of my hat will be black or white. (Can’t say the answer as there are risks)
- Let’s think about it in C’s shoes.
There is prior information on 2 black and 2 white hats, and a white hat is visible in front of me.
If my hat was also white, D would be able to answer that his hat color was black.
But if my hat was black, D wouldn’t be able to match the color of his hat.
D can’t say the right answer because my hat is black.