A372224 The size of the smallest critical set of hints needed to uniquely solve a generalized n X n Sudoku board.
0, 1, 2, 4, 6, 8, 12, 14, 17
Offset: 1
Examples
Below is a critical set of size 17 on the 9 X 9 Sudoku grid: . +-------+-------+-------+ | | 8 1 | | | | | 4 3 | | 5 | | | +-------+-------+-------+ | | 7 | 8 | | | | 1 | | 2 | 3 | | +-------+-------+-------+ | 6 | | 7 5 | | 3 | 4 | | | | 2 | 6 | +-------+-------+-------+ . which uniquely determines the solution: . +-------+-------+-------+ | 2 3 7 | 8 4 1 | 5 6 9 | | 1 8 6 | 7 9 5 | 2 4 3 | | 5 9 4 | 3 2 6 | 7 1 8 | +-------+-------+-------+ | 3 1 5 | 6 7 4 | 8 9 2 | | 4 6 9 | 5 8 2 | 1 3 7 | | 7 2 8 | 1 3 9 | 4 5 6 | +-------+-------+-------+ | 6 4 2 | 9 1 8 | 3 7 5 | | 8 5 3 | 4 6 7 | 9 2 1 | | 9 7 1 | 2 5 3 | 6 8 4 | +-------+-------+-------+
References
- J. N. Cooper and A. Kirkpatrick, Critical Sets for Sudoku and General Graphs, Discrete Mathematics, 315-316 (2014), 112-119.
- C. Lass, Minimal number of clues for Sudokus, Central European Journal of Computer Science, 2 (2012).
- G. McGuire et al., There Is No 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration, Experimental Mathematics, 23 (2012), 190-217.
Links
- H. Chel, D. Mylavarapu, and D. Sharma, A novel multistage genetic algorithm approach for solving Sudoku puzzle, IEEE International Conference on Electrical, Electronics, and Optimization Techniques (2016), 1.
Comments