"There are two variants I'd particularly like to see made.
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."
I thought that sounded quite cool, so I spent a bit of time hacking. Here is the first (to my knowledge) ever Chess Sudoku:
I'm working on producing better ones. This one has a major flaw, which becomes apparent as you start solving it.
Can attacks pass through other pieces? If so, then presumably this has strong implications about the pieces. --AC
This does sound extremely cool :-). However, perhaps like Alex, I'm puzzled as to how it works - my first thought was that attacks would pass through other pieces, but this means a castle will always be attacking 16 different squares - so 8 of those would have to be chess pieces, which seems like rather a lot. A bishop might attack only 8 if it were in a corner. Pawns aren't unusable whether attacks can go through other pieces or not, as they attack only two squares. If attacks can't pass through squares then queens are indistinguishable from kings. Hmmm, maybe attacks should pass through squares with numbers on, but not other chess pieces? What rule have you used in the above? --AL
Given the way the bishops are positioned, I think it's that lines of attack are blocked only by chess pieces. I'd visualise it as a (huge) chessboard with numbers written on it. --Vitenka
The rules as stated rule out AL's suggestion re rooks (because then you'd have >1 chess pieces in a row/col). Rooks, queens and pawns cannot exist, and the other pieces can only exist in subsets of the board. Bishops don't have to be in a corner; they can be on an edge, as indeed they are above. --Rachael, whose lunch break ended too soon to solve it, grr
(PeterTaylor) I'm working on the basis that attacks can pass through numbers and that pieces may not attack other pieces. This does indeed have strong implications about the pieces: it constrains it to Kings, Knights and Bishops. Bishops can only be placed on the edge, and are the only pieces which can be placed on the edge. The only pieces which can be placed at a separation of one square from the edge are Kings. Therefore there must be at least 3 Bishops and at least 2 Kings.
It seems to me that if the pieces are viewed as being on the "same side", then they neither attack each other nor can pass through each other. This could probably permit a variant where bishops can be blocked by other pieces and thus be off the edges (rooks and queens still fall foul of the one-per-row restriction). However, it's arguable whether it adds enough to the game to be worth the complexity. --AC
(PeterTaylor) Now that I've run a brute-force checker over it, I can confirm my hunch that it doesn't add anything at all to the game: namely there are no more legal complete boards with these rules than with the non-attack non-protect rules.
Yay, solved it! :) I didn't spot the flaw, though. Unless you mean the flzzrgel - is that considered a flaw? --Rachael
(PeterTaylor) I've just finished counting the distinct solutions. ("Distinct": partition all solutions into equivalence classes such that A == B if A is a rotation of B; A == B if A is a reflection of B; and A == B if A can be derived from B by permuting [1-8]). It's rather small, which doesn't surprise me. I'm about to check whether any solutions avoid the flaw of the puzzle above.
It turns out that there are only 4 distinct solutions which totally avoid the flaw, and they pair up as distinct-but-very-similar, so I'm only going to produce two more puzzles. Here's the first.
And the second:
PS Thanks to Alex for the suggestion to use the Go markup.
(BenReiniger?) Qb nal bs gur flzzrgevp chmmyrf pbagnva xavtugf? V jnag xavtugf!