I have been trying from the beginning of this long thread to help poor gnu overcome the difficulty he's been having in understanding this problem. It is not helpful when, having stated the rules of the game absolutely correctly and then asking for confirmation that he has indeed understood the problem correctly, gnu is then told by you that no, he had not stated the rules correctly.

JotSC, let me tell you that I find your last post insulting -- you think I don't get it, do you? I'm a Ph.D. mathematician whose research was largely in mathematical logic. I suggest that you refer back to the various posts on the subject, paying particular attention to yours and mine.