Four prisoners are blindfolded and arranged as follows: Three of them are lined up one behind the other (i.e. facing the same way), while the last prisoner is placed on the other side of a screen. A hat is then placed on each of their heads. When the blindfolds are removed...
- Prisoner A can see B and C in front of him, but not D.
- Prisoner B can see C, but neither A or D.
- Prisoners C and D can only see the screen.
- None of them is able to see what colour hat they are wearing themselves.
The prison warden then announces his beastly scheme: "Each of you has either a red or a blue hat on your head. There are two hats of each colour. One of you will be able to say -- with 99% certainty -- what colour hat you are wearing. Moreover, you should be able to do so within a minute. Should that person call out the correct answer, you are all free to go. Failing that, you are all to be sentenced to death!"
[Cue: Dramatic music]
Which prisoner calls out the correct answer and how is he able to do so without resorting to a 50/50 guess? (Rest assured, this a puzzle of logic and so there are no petty tricks like whispering to each other, turning around, mirrors, peaking over the screen, etc.)
Solution below the fold!