OK I finally understood your solution. Unfortunally it is not 100% accurate, and is based on an assumption (depending on how the prisoners are chosen, you can either be sure, or be almost sure). It is a good solution, but still not completly mathematically correct. I think it goes to your definition of "practical mathematics", agains my clear notion of "logical mathematics".

As I said before I'm completly sure that it is "logically" impossible, but I'll try to think of a way to improve your solution - even though I'll never get to 100% accuracy, it might lead to an error, even though the chances of getting it right are huge.

I must say it was one of the most intriguing logical problems I've ever seen.

I'll ask this one to some people I know, see if they can come up with a better answer - chances are they won't.