Like I said, it really isn't that hard to find a usable solution. The upper limit of all board positions will be insignificantly greater than the number of all possible board positions, and with that in mind it is a long-winded combinatorics problem. I don't think you'll find anybody wiling to sit down and grind out the numbers though... I remember reading that the number of possible games of chess is greater than the number of all the grains of sand in the world.
That's a lot, and those numbers aren't easy to calculate, even with 3ghz P4 beasts.