[ Help | Earliest Comments | Latest Comments ][ List All Subjects of Discussion | Create New Subject of Discussion ][ List Earliest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]Single Comment Complexity of Large Variants. Some comments about the complexity of large chess/checkers variants.[All Comments] [Add Comment or Rating]Sam Trenholme wrote on 2007-07-14 UTCLooks 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?