Quote:
Originally Posted by GeoffC
But you are missing my point.
In order to progress from evening one to the next they have to know that the answer they have come up with is wrong.
How do they know it is wrong without telling the gaoler ?
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I will give an example. This is definitely in spoiler territory.
Spoiler:
OK, suppose I'm one of the wise men. I'm in my first day in the tower. I can see 2 towns. I cannot know from this whether there are 10 or 13 towns, so I will say nothing to the Gaoler tonight, the first night.
Since I see 2 towns, I know that the other wise man must be seeing either 8 or 11 towns.
Now, if he sees 8 towns, he too cannot tell whether there are 10 or 13 towns, and so he will say nothing to the Gaoler tonight, the first night, and I'll still be in the tower tomorrow morning
But if he sees 11 towns, he will know that there must be 13 towns, he'll tell this to the Gaoler tonight, the first night, and we'll both be free before the morning.
It's the next day. We weren't freed yesterday, so I now know that the other wise man didn't see 11 towns. So he must have seen 8 towns. I can see 2 towns. So there are 10 towns altogether, I'll tell this to the Gaoler tonight, and we'll both be free.
No guesses that are incorrect. But on the second evening I know how many towns there are — not a guess.