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Well, if you like the large number of setups, here's another idea you may find amusing: Googol Chess. In Googol Chess, each square points to a particular non-adjacent square randomly chosen during the setup. A piece has the additional power to leap to the square pointed to by its current square, if that destination square is empty. There are at least (64-9)^64=55^64 > 2.1 x 10^111 possible setups on a standard chessboard.
I want make an overview about crossovers between chess and sudoku.
1-player
- Chess Sudoku (The digits 1-8 and a chess piece in each row, column, and region. Each piece should attack the numbers 1-8 exactly once. (proposal, discussion and examples)
- Slightly Modified Chess Sudoku (The digits 1-8 and a chess piece in each row, column, and region. Each piece can attack the numbers 1-8 exactly once.)
- White Knight Sudoku (each row, column and box contains the digits 1-8, a white chess knight, no white knight attacks one other knight) (example)
- Black Knight Sudoku (each row, column and box contains the digits 1-8 and a black chess knight, every knight attacks at least one other) (example)
- Black and White Knight Sudoku (each row, column and box contains the digits 1-7, a black chess knight and a white chess knight, every black knight attacks at least one other black knight, no white knight attacks one other white knight) (example)
- Knight and Queen Sudoku (each row, column and box contains the digits 1-8 and a white chess knight or a white queen (one per puzzle), no chess piece attacks one other) (example)
- White Queen Sudoku (each row, column and box contains the digits 1-8, and a white chess queen, no white queen attacks one other queen)
- Anti-Knight Sudoku (each row, column and box contains the digits 1-9, no digit is knight-move connected with the same digit) (example)
- Anti-Knight Sudoku X (each row, column, box and both main diagonals contain the digits 1-9, no digit is knight-move connected with the same digit) (example)
- Sudoku with chess piece pattern (example)
2-player
Hints to other chess sudoku crossover are welcome.
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One idea: Each pawn can be one of nine different pawn types:
For the pieces, any of the pieces, except the king, can have any of the 15 combinations of rook, knight, bishop, and camel movements. The king exists in three forms: Can move as a ferz, can move as a wazir, and can move as a FIDE chess king. For an 8 * 8 board, this results in 512,578,125 possible setups; combine this with the pawns above and our 8x8 board now has 22,064,807,537,578,125 possible opening setups. The corresponding 8x10/10x10 board has 402,131,117,372,361,328,125 possible opening setups. Now we're starting to get what looks like a variant template with a decent number of possible starting setups. :)
As a practical matter, this template for the pieces probably usually results in arrays where white has a considerable advantage because there is so much force on the board, but this is a thought experiment, not a practical Chess variant design.
This might work a little better: Make the atoms Betza's crab (leaps from e4 to d6, f6, c3, and g3), a fers, a wazir, and a camel. But that probably makes most setups too weak. Perhaps if we add a randomizing factor with these weak atoms whick randomly strengthens one of the atoms (makes the ferz atom a bishop atom, a wazir a rook, a crab a knight, and a camel a camel + dabbah). This causes each piece to have one of 32 possible forms; for an 8x8 board this results in a grand total of 4,437,222,213,480,873,984 possible setups; for a 10x8 or 10x10 board, this results in 368,040,959,274,957,611,728,896 possible setups.