The puzzle is solved by search, and the completed grid is a valid unique Sudoku solution.
case : sudoku
default puzzle : classic
Puzzle
1 . . | . . 7 | . 9 .
. 3 . | . 2 . | . . 8
. . 9 | 6 . . | 5 . .
| . . 5 | 3 . . | 9 . . |
| . 1 . | . 8 . | . . 2 |
| 6 . . | . . 4 | . . . |
| 3 . . | . . . | . 1 . |
| . 4 . | . . . | . . 7 |
| . . 7 | . . . | 3 . . |
Completed grid
1 6 2 | 8 5 7 | 4 9 3
5 3 4 | 1 2 9 | 6 7 8
7 8 9 | 6 4 3 | 5 2 1
| 4 7 5 | 3 1 2 | 9 8 6 |
| 9 1 3 | 5 8 6 | 7 4 2 |
| 6 2 8 | 7 9 4 | 1 3 5 |
| 3 5 6 | 4 7 8 | 2 1 9 |
| 2 4 1 | 9 3 5 | 8 6 7 |
| 8 9 7 | 2 6 1 | 3 5 4 |
The input contains 23 given clues and 58 empty cells.
The solver fills empty cells with backtracking search, choosing the open cell with the fewest legal candidates first. The search visited 2232 node(s).
The trust gate checks that the original clues do not conflict, exactly one solution is found, every clue is preserved, and every row, column, and 3×3 box contains digits 1 through 9.
Only after those constraints hold does the example emit the completed grid.