Thomas, thanks for your observation. Of course there are at least 2 solutions with the reflection about the main diagonal. The example is wrong and we will see if this is the only mistake they've made.

I guess rule 3 is there combined with rule 4 to make sure one can only achieve one solution isomorphically. An interesting problem is how many pieces do we need in the initial setup to ensure a unique solution.

For example, how many solutions does the following 5-piece setup give?

Smythe Dakota wrote:Can queens, and rooks, move 8 squares (e.g. from r1c1 to r1c9)? In chess, they can move at most 7 squares.

In fairy chess variants on 10x10 boards the queens/rooks can move 10 squares, so I guess the common sense is that they are not distance-limited on larger-sized boards.

Smythe Dakota wrote:There is at least one other way to generate additional solutions, too. Reflect along the other long diagonal (r1c9-r9c1), and replace all silver queens with gold queens and vice versa, and all blue queens with green queens and vice versa.

I suppose the point of the initial setup is that you cannot remove the pieces already "on board" and replace with other pieces? But then I again I might be wrong.

One of the great enjoyment in chess is during a certain stage, one can swap the positions of the white and black queens, and see how the game will turn.

(Is it the standard practice in USA too?)

Smythe Dakota wrote:I suspect the problem is defective, or was not translated properly from the site from which it came.

I'm inclined to believe you on this. My inferior level of English is probably the culprit here.

Smythe Dakota wrote:Somebody on this forum told me that diagonal constraints cannot apply to all nine digits (in an otherwise vanilla sudoku), otherwise there will be no solution. (He may, however, have been talking about wrap-around diagonals, e.g. r1c5-r5c9 and r6c1-r9c4 glued together.) That may be what motivated this problem, whatever it is supposed to be.

I suspect that "somebody" was either myself or

Condor from New Zealand, who just came out to post again after a long period of inactivity. I don't think the wrap-around diagonals are relevant to the "diagonal constraints" though.

Again, thanks for your insights guys!