[thylacine]

N=2 here is same as N=2 in `An interesting proposition' and both are `envelope switching', I guess. For bigger N these problems differ.

I was not sure what you were saying in your post. This stuff seems interesting and fairly deep. It's fun to think about but I've got other things I should be doing. But I'm curious to know what is known about these kinds of things. Your other post saying `the standard answer is...' suggested to me that this was a well explored topic. But when I start thinking about W's possible probability distributions of N-tuples of numbers, and P's possible responses (in either version of these problems), I realise this could be deep stuff.