Just like the classic 4 prisoners hats riddle, here we have 6 prisoners buried to their necks in the ground. They can only look straight ahead so that A only sees B, C, D, E while B sees C, D, E, and so on and F is completely hidden from view. The warden gives them each hats and tells them that there are 3 red hats and 3 white hats. The warden also tells them that he has cut out one prisoner's tongue (in this case C) so that he cannot speak at all (the mute knows that he is mute). All prisoners are executed if they make any noise other than to clearly announce their own hat color. If a prisoner answers correctly, all prisoners will be set free. If incorrectly they will all be executed.
One prisoner will be able to say his own hat color with certainty. Which one?
To clear up some confusion:
1) No prisoner knows who the mute is except the mute himself.
2) The picture is how the story actually went down.
3) The lateral thinking tag was added just because the solution takes some time-dimensional thinking.
Answer
It will be
B.
Both A and B can see, what C sees, and that's why they both know that
C knows his hat colour: If C had a white hat, then both A and B would be able to trivially announce their hats. Neither did, and they cannot both be mute, so C must know that his hat isn't white. Because C isn't announcing his colour, both A and B know that C must be the mute.
From there, the problem reverts to the earlier one:
B knows that A isn't the mute (because C is), and also that A isn't seeing three white hats (because A has't announced his hat), so B can decuce that his hat is red.
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