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Complexity of Large Variants. Some comments about the complexity of large chess/checkers variants.[All Comments] [Add Comment or Rating]
Sam Trenholme wrote on Sat, Jul 14, 2007 07:28 AM UTC:
Looks like you're right. I will draw it out:

  • First, we place the bishops. There are 2025 ways of arranging the bishops.
  • Next, we place the knights. For each arrangement of bishops, there are 1820 ways to put the knights on the board.
  • Next, we place the rooks. For each arrangement of bishops and knights, there are 495 ways to place the rooks.
  • Next, we place the Archbishops. For each arrangement of the minor pieces, there are 28 arrangements for the archbishops.
  • Next, we place the Marshalls. For each arrangements of all of the above pieces, there are 15 Marshall setups.
  • Next, we place the Queens. For all of the above setups, there are 6 ways to have the queens on the board.
  • Next we place the king. There are two places he can go. However, this is balanced by the fact we remove all mirror images.
2025 * 1820 * 495 * 28 * 15 * 6 = 4,597,292,700,000

Sorry it took so long to verify your number. This is the first time I have had a computer with an arbitrary precision calculator and net access at the same time in a while (Let's hear it for Ubuntu live CDs).

Edit: Yes, 64-bit computer owners, the above number can easily be calculated using 64-bit integers. I'm still in the 32-bit stone age. Do they even make 64-bit laptops that weigh less than 6 pounds?