On my favorite puzzle site, there’s a new (at least to them and me) kind of Chess problem: Solitaire Chess. The rules are straightforward:
- Pieces move as standard chess pieces.
- You can perform only capture moves.
- You are allowed to capture the king.
- The goal is to end up with one single piece on the board.
The choice of puzzles start with four pieces which I’m assuming are the easiest puzzles. Then they increase up to 11 pieces. There are also special size puzzles for the daily and weekly special, but the monthly special hasn’t been made free yet.
I’m not having any issues with 4 piece, 5 piece, and 6 piece puzzles. The problem begins with the 7 piece puzzles and runs all the way to the 11 piece puzzles. I’m getting the feeling that the kinks haven’t been worked out yet. By that, I mean maybe there’s no solution.
For example, I’m trying to do this 7 piece puzzle (Puzzle ID: 7,485,757), initial position as follows:
c4: Bishop, c5: Knight, c6: King
d6: Rook
e3: Pawn, e6: Knight
f3: Pawn
My first glance tells me, “Nah, that’s not possible”. After all, the rules require every move to be a capture move. Am I correct that this particular setup is not solvable?
I quite like these puzzles, at least the ones I’m able to solve. 
Since there’s no issue on piece color other than for the pawn movement, I tink it’d be cool to make one that’s slightly different than the all white pieces puzzles on that site. What say we try to make a puzzle with both black and white pieces, running all the way up from to 32 pieces (of course a 2-piece puzzle is trivially easy), allowing only one Bishop for each player to be on a white square and one Bishop for each player to be on a black square? The pawns for black would move down the board and the pawns for white would move up the board. Since each move must be a capture move, the puzzle must be solved in exactly 31 moves. Of course, it would be great for the puzzle to have only one solution, but how would we determine that?
And why not expand the choice of piece and board to other forms of Chess, such as Chinese, Japanese, and Korean Chess? For Chinese and Korean Chess, the generals (kings) and ministers (queens) would have to remain in the marked fortress. The basic rules still apply: every move must be a capture move, even allowing for capturing the general/king. For Japanese Chess, I think there must be a modification to those rules given the short range of most pieces and the drop rule.
What say the Teeming Millions?