- Code: Select all
`+---+---+---+---+---+---+---+---+---+---+---+---+`

| | | 2 | | | | | | | 3 | | C |

+---+---+---+---+---+---+---+---+---+---+---+---+

| | | 5 | | 7 | | | | | | | A |

+---+---+---+---+---+---+---+---+---+---+---+---+

| | | C | | 9 | | | | | | | |

+---+---+---+---+---+---+---+---+---+---+---+---+

| | 4 | | 1 | | | 6 | | | | 2 | 8 |

+---+---+---+---+---+---+---+---+---+---+---+---+

| | 3 | B | | 6 | | | 4 | | | 5 | |

+---+---+---+---+---+---+---+---+---+---+---+---+

| | | | A | | B | | | | | | 6 |

+---+---+---+---+---+---+---+---+---+---+---+---+

| | | | 9 | | | 4 | | | | C | |

+---+---+---+---+---+---+---+---+---+---+---+---+

| A | | | 4 | 2 | | 3 | | 6 | | | |

+---+---+---+---+---+---+---+---+---+---+---+---+

| | 7 | | | 3 | | | C | 9 | | 6 | |

+---+---+---+---+---+---+---+---+---+---+---+---+

| | 9 | | 6 | | | | | | | | |

+---+---+---+---+---+---+---+---+---+---+---+---+

| 2 | B | | | | | | | | | | 9 |

+---+---+---+---+---+---+---+---+---+---+---+---+

| 1 | | 6 | B | | | | | | | | |

+---+---+---+---+---+---+---+---+---+---+---+---+

- Code: Select all
`..2......3.C..5.7......A..C.9........4.1..6...28.3B.6..4..5....A.B.....6...9..4...C.A..42.3.6....7..3..C9.6..9.6........2B.........91.6B........`

DD squares are like Pandiagonal squares, but much simpler ...

- fill the grid so that each row and column has the digits 1 to 12, shown here using the {1-9ABC} system

- no value can appear twice in any row, col or diagonal

- diagonals are like those on a chessboard, they do NOT wrap around the grid

So, we have a slightly smaller grid (12 x 12), and since the diagonals don't wrap around, there should be no problems for P&P solvers. It might be helpful to use a grid that has checkerboard shading ...

DD squares might simply be called "anti-Queen", which implies both the Latin square and the DD properties.

This puzzle, as far as I can tell, is very close to singles-only, but not quite.

I have chose N=12 as the grid size because the only solution grids for N < 12 are all pandiagonal grids (N=5,7,11), and as we have seen these are all cyclic, and scarce.

N=12 seems to be in the "Goldilocks" zone. It 454 distinct solution grids, none of which can be cyclic, since there are no pandiagonal squares for N=12.

N=13 might be interesting to explore ... with 12,386 pandiagonal grids, I would expect millions of DD grids.