It seems like this problem is dependent upon what is a reasonable a priori distribution for N.
Oh wait, the answer is much simpler than that. Turns out this is the easiest bonanova puzzle I have ever seen =)
LOL
That may be the first and only time I use LOL in this forum.
I'm not that clever. Really.
But I love it. It's a better puzzle than the one I intended.
Honorable mention.
.