We know that 9-clue SudokuPX and SudokuWX puzzles exist, but 8-clue puzzles seem unlikely.
hkociemba1 uncovered this grid, which is a SudokuPX grid, but also has the DP property, ie no pair of diagonally-adjacent cells have the same value, thus allowing specification of clues in SudoKakuro form.
- Code: Select all
+-------+-------+-------+
| 8 6 4 | 3 2 7 | 5 1 9 |
| 3 2 7 | 5 9 1 | 8 4 6 |
| 5 1 9 | 8 4 6 | 3 2 7 |
+-------+-------+-------+
| 2 4 6 | 1 7 5 | 9 8 3 |
| 1 5 3 | 9 6 8 | 2 7 4 |
| 9 7 8 | 2 3 4 | 6 5 1 |
+-------+-------+-------+
| 4 3 1 | 6 5 2 | 7 9 8 |
| 6 8 5 | 7 1 9 | 4 3 2 |
| 7 9 2 | 4 8 3 | 1 6 5 |
+-------+-------+-------+
Remarkably, HK found a SudoKakuroPX puzzle on this grid with just 6 clues:
- Code: Select all
+----------+----------+----------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . 22 | . 30 . | . . . |
+----------+----------+----------+
| . . . | . . . | . . . |
| . . 28 | . . . | 30 . . |
| . . . | . . . | . . . |
+----------+----------+----------+
| . . 22 | . 12 . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------+----------+----------+
I took this grid, and tested it with a HS engine configured for SudokuPXD (ie SudokuPX + DP), and although I found no 8-clue puzzle, I did find a large number (2498) of 9-clue puzzles.
So I morph-tested all of these via {+1, -2} and found an 8-clue puzzle:
- Code: Select all
+-------+-------+-------+
| . . . | . . . | 5 1 . |
| . . . | . 9 . | . . . |
| . . . | 8 4 . | . . . |
+-------+-------+-------+
| . . . | . . . | . . 6 |
| . . . | . . 2 | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . 3 |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
