![]() Mantere, T., Koljonen, J.: Solving, rating and generating Sudoku puzzles with GA. Madsen, B.A.: An algorithm for exact satisfiability analysed with the number of clauses as parameter. Lynce, I., Ouaknine, J.: Sudoku as a SAT problem. Lewis, R.: Metaheuristics can solve sudoku puzzles. Lawler, E.L.: A note on the complexity of the chromatic number problem. Koch, T.: Rapid mathematical programming or how to solve Sudoku puzzles in a few seconds. Hunt, M., Pong, C., Tucker, G.: Difficulty-driven Sudoku puzzle generation. Herzberg, A.M., Murty, M.R.: Sudoku squares and chromatic polynomials. Held, M., Karp, R.M.: A dynamic programming approach to sequencing problems. ![]() Gordon, P., Longo, F.: MENSA Guide to Solving Sudoku. In: Apolloni, B., Howlett, R.J., Jain, L. Geem, Z.W.: Harmony Search Algorithm for Solving Sudoku. ![]() Press (2002), Įppstein, D.: Nonrepetitive paths and cycles in graphs with application to Sudoku (2005)Įppstein, D.: Recognizing partial cubes in quadratic time. (ed.) More Games of No Chance, MSRI Publications, vol. 42, pp. ![]() Algorithmica 52(2), 226–249 (2008)īrouwer, A.E.: Sudoku puzzles and how to solve them. Schloss Dagstuhl (2010)ījörklund, A., Husfeldt, T.: Exact algorithms for exact satisfiability and number of perfect matchings. Leibniz International Proceedings in Informatics, vol. 5, pp. ACM 9, 61–63 (1962)ījörklund, A.: Exact covers via determinants. IEEE Signal Processing Lett. 17(1), 40–42 (2010)īellman, R.: Dynamic programming treatment of the travelling salesman problem. However, the technique should be used with caution and only as a last resort after other strategies have been exhausted.Arnold, E., Lucas, S., Taalman, L.: Gröbner basis representations of Sudoku. By considering all possible placements of a particular digit in a specific cell, the solver can identify a unique solution to the puzzle. In summary, the Nishio technique is a useful tool for solving Sudoku puzzles when traditional strategies are no longer effective. This is because the technique involves significant trial and error and can be time-consuming, particularly for puzzles with many potential solutions. While the Nishio technique can be an effective tool for solving difficult Sudoku puzzles, it should be used as a last resort after exhausting all other strategies. In such cases, the solver can use the technique to test each of the potential solutions and identify the one that leads to a unique solution. The Nishio technique can be particularly useful when the solver has reached a state where there are multiple possible solutions to the puzzle. If, on the other hand, the solver is unable to find a unique solution, then the placement of the 3 in that cell is not valid. If this leads to a unique solution, then the solver can be confident that the 3 was placed correctly in that cell. Suppose, for example, that the solver places a 3 in the identified cell and proceeds to solve the rest of the puzzle. The goal is to determine if the placement of a particular number in that cell leads to a unique solution for the puzzle. For example, if a cell can only be filled with the numbers 3 or 7, then the solver can proceed to consider each of these possibilities in turn. To apply the Nishio technique, the solver first identifies a cell that has a limited number of possible values. This technique is particularly useful when the puzzle has reached a state where the traditional strategies of elimination and inference are no longer effective. The Nishio technique is a solving strategy used in Sudoku puzzles to identify a unique solution by considering all possible placements of a particular digit in a specific cell.
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