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9eB1 comments on Open Thread March 31 - April 7 2014 - Less Wrong
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Either this problem is not completely stated, there are important things left out, or the answers are gibberish. In any case, I have no idea what is going on even after reading the answers. I can collude with prisoners ahead of time but I can't communicate with them. This presumably means I can't smile or wink or grab or stare meaningfully or longingly at them. I can't tell them what my guess is.
So I find myself in a room full of people, some with red hats and some with black hats, in what is essentially a still picture, for all intents and purposes equivalent to freezing the room full of other people with their red and black hats and I can then examine this fixed scene. How does this even conceivably impact what I would guess the color is of the hat on my head?
Fix!
There are important things left out. Specifically, this is a math problem and putting it in terms of prisoners or humans is intended to be ignored. You should of course just know that when someone is a human in a math puzzle, what they really mean is a hypercomputer or oracle that can return correct answers for uncomputable algorithms. Here's another example:
There is a prisoner in a cell, the same as the prisoners in the question above. Each day the warden hands him an infinitely complex algorithm, and he is released if and only if he can correctly tell the warden whether it halts or not. On what day is he released?
Gur svefg qnl.