Old GL Puzzle Solution

[Zealot]

http://www.greylabyrinth.com/Puzzles/puzzle051.htm

Excerpt from the solution:
Let's simplify the paradox a bit- we don't need a whole week to cause a problem, two days will work just as well. If the judge tells the prisoner he is to be hanged either tomorrow or the next day, and he won't know until the day of the execution, we have a problem. After tomorrow, the prisoner will know the day, which violates the rule. So it must tomorrow. But if it must be tomorrow, then the prisoner knows the day. Which violates the rule. Must make the prisonner's head spin.

Which is fortunate for the judge, because it is this paradox he has constructed which makes the judge's sentence valid. He has created a logical system which traps the prisoner from being able to know the truth.

This even works if the judge had said: "You will be hanged tomorrow and you will not know that will be hanged tomorrow." Think about it- from the prisonner's perspective he cannot know that sentence to be true. If he could, it would be false.
[/excerpt]

My head hurts. Would anyone care to explain that last paragraph? I think that I understood it the first time I read this solution, but now I can't seem to remember why...

[Chuck]

If the prisoner does reach the conclusion that he'll be hanged tomorrow then the judge must be lying. If the judge is lying then the prisoner might not be hanged tomorrow. Since the prisoner can't be sure he'll be hanged tomorrow the judge is telling the truth, but the prisoner can't know that until he's hanged. Or something like that. Maybe.

[Zealot]

Thank you Chuck, I think that is exactly it.

[Neo]

*breaks Hy's rule* maybe the judge could pass sentance and hang the prisoner immediatly after?

[Zealot]

Then the judge would have lied and the sentence would be void.