Sam Trenholme wrote on Wed, Sep 20, 2006 02:58 PM UTC:
OK, I've looked at the list and can sorta see why you had 12118 setups when I had 9820 setups. First of all, I consider mirror image setups to be identical, so I have removed them by requiring the queen to be left of the king (from white's side of the board) in all of my setups. This reduces the number of possible setups from 252,000 to 126,000. I note that you consider a setup and its mirror different--which it can be given certain castling rules.
I modified your list of crc setups to only show the ones where the queen is the the left of the king. For some reason, your list of 12118 setups has 6056 setups with the queen to the left of the king, and 6062 setups with the Queen to the right of the king.
Once I did this, I noted that there are some 3764 possible opening setups, where all the pawns are guarded, the king is to the left of the queen, and where there are no bishops together, that are not on your list of possible setups. I have put this list here:
I modified your list of crc setups to only show the ones where the queen is the the left of the king. For some reason, your list of 12118 setups has 6056 setups with the queen to the left of the king, and 6062 setups with the Queen to the right of the king.
Once I did this, I noted that there are some 3764 possible opening setups, where all the pawns are guarded, the king is to the left of the queen, and where there are no bishops together, that are not on your list of possible setups. I have put this list here:
http://www.samiam.org/chessvariants/crc-why-not.txt
This list uses 'M' for the rook + knight piece and 'A' for the knight + bishop piece.
- Sam
Edit: Fixed 'queen' and 'king' wording.