Puzzling Asked by athin on September 3, 2020
Is it possible to construct a valid $9 times 9$ puzzle of Total False Sudoku?
Total False Sudoku is a regular Sudoku puzzle where all given clue numbers are wrong. A valid puzzle is a puzzle that has only a single solution.
(Very) partial answer (just a bit too long for a comment):
Proof:
Answered by ManfP on September 3, 2020
I don't have a lot of calculations, but here is my answer.
My reasoning:
Update based on comment feedback:
Answered by Bewilderer on September 3, 2020
I offer no proof, but some evidence:
An 87-clue Pencilmark Sudoku:
+=====+=====+=====+=====+=====+=====+=====+=====+=====+
| 1.. | 123 | 123 | 123 | 123 | 123 | 123 | 123 | ..3 |
| ..6 | 4.6 | .56 | 456 | 45. | 456 | 456 | .5. | ... |
| 789 | 789 | 789 | 789 | 789 | 789 | 789 | .89 | ..9 |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 123 | 123 | 123 | 123 | 123 | 123 | 123 | 123 | .23 |
| 456 | 456 | .56 | 456 | 45. | 45. | 45. | 45. | 45. |
| 789 | 789 | 789 | 7.9 | 789 | 789 | .89 | ..9 | ..9 |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 123 | 123 | 123 | 123 | .23 | 123 | 123 | 123 | 123 |
| ..6 | 4.6 | .56 | 456 | 456 | 456 | .5. | 456 | .56 |
| 789 | 789 | 789 | 789 | 78. | 789 | .89 | .89 | .89 |
+=====+=====+=====+=====+=====+=====+=====+=====+=====+
| 123 | 123 | 123 | 123 | 123 | 123 | 123 | 123 | 123 |
| 456 | 456 | 456 | 456 | 456 | 456 | 456 | 456 | 456 |
| 789 | 789 | 7.9 | 7.9 | 789 | 789 | 7.9 | ..9 | 7.9 |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 123 | 123 | .23 | 123 | 123 | 123 | 123 | 123 | .23 |
| 456 | 456 | 456 | 456 | 456 | 456 | 456 | 456 | 456 |
| 789 | 789 | 789 | 789 | 789 | 789 | 7.9 | ..9 | 7.9 |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 1.3 | 1.3 | 1.3 | 1.3 | 123 | 1.3 | 123 | 123 | ..3 |
| ... | 456 | .56 | ..6 | 456 | ... | 456 | 456 | ..6 |
| 789 | 789 | 789 | 789 | 789 | 789 | 789 | 789 | 7.9 |
+=====+=====+=====+=====+=====+=====+=====+=====+=====+
| 123 | 123 | 123 | 123 | 123 | 123 | 123 | 1.3 | 123 |
| 4.6 | 456 | 456 | 456 | 456 | 456 | .56 | 456 | 456 |
| 789 | 789 | 789 | 789 | 789 | 789 | 789 | .89 | 789 |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 123 | 123 | .23 | 1.3 | .23 | 123 | 123 | 123 | 123 |
| 456 | 456 | .56 | 456 | 45. | 456 | 456 | 456 | 456 |
| 789 | 789 | 789 | 789 | 789 | 789 | 789 | .89 | 789 |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 123 | 123 | 123 | 123 | 123 | 123 | 123 | 123 | 123 |
| 456 | 456 | 456 | 456 | 45. | 456 | 456 | 456 | 456 |
| 789 | 789 | 789 | 789 | 789 | 789 | 789 | .89 | ..9 |
+=====+=====+=====+=====+=====+=====+=====+=====+=====+
Answered by 53x15 on September 3, 2020
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