Well, all I heard back from my bro to whom I sent this puzzle, was that he would try to work on it when he had some time, and a suggestion: i would try to solve the problem for the case of 3 prisoners and then see if it is possible to extend or modify the method for larger numbers.

But but but....With only three prisoners, it's easy, is it not? The three agree among them which one will use the B switch - only one of them - and then the other two use the A switch.

Say I am the prisoner who gets to use the B switch. I go into the room. Both switches are up. I put B down. Okay, this ain't gonna work either, ais it?

Damn! Damn!