If I have a checkers board (8x8) and 16 black pieces , 16 white ones (this isn't the usual checkers).
Assume that these pieces can be placed anywhere on the board.
How can I calculate the number of ways the board can be laid out?
(it's trivial to say that each position may be a white piece , black piece or empty, but I have an upper bound on the number of checker pieces).
Considering the upper bound (ie 16 or less black/white piece) how does the number of ways change?
Now, assume that pieces can upgrade to kings. Needless to say, when you gain a king, you lose a normal piece, which preserves the the max 16 pieces rule.
How can I calculate the number of ways the board can be laid out considering the kings?