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Old 07-07-2010, 08:44 AM   #9
LazyScot
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Spoiler:

On the first night, if either can see 11, 12 or 13, they can report the answer as 13

On the second night, if either is seeing 0, 1 or 2, they can report the answer as 10, since if the other person could see 11, 12, or 13 they would have already answered.

At this point each must be seeing between 3 and 10 towns.

On the third night, if either is seeing 8, 9 or 10 towns, they can report the answer as 13.

At this point each must be seeing between 3 and 7 towns.

On the fourth night, if either is seeing 3, 4 or 5 towns, they can report the answer as 10 (since there is no way that the other can be seeing 10, 9 or 8 towns to make 13 towns as they would have already answered).

At this point, each must be seeing between 6 and 7 towns.

So if they are still there on the fifth night, either can answer it as being 13 towns.

I'm sure this could be expressed mathematically....

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