Skip to main content Accessibility help
×
Home

Redundant Sudoku rules

  • BART DEMOEN (a1) and MARIA GARCIA DE LA BANDA (a2)

Abstract

The rules of Sudoku are often specified using 27 all_different constraints, referred to as the big constraints. Using graphical proofs and exploratory logic programming, the following main and new result is obtained: Many subsets of six of these big constraints are redundant (i.e., they are entailed by the remaining 21 constraints), and six is maximal (i.e., removing more than six constraints is not possible while maintaining equivalence). The corresponding result for binary inequality constraints, referred to as the small constraints, is stated as a conjecture.

Copyright

References

Hide All
Demoen, B. and Garcia de la Banda, M. 2012. Maximal Sets of Redundant Constraints in Latin Square. Monash University, no. 2012/269. Technical Report.
Ist, I. L., Lynce, I. and Ouaknine, J. 2006. Sudoku as a SAT problem. Proceedings of the 9th International Symposium on Artificial Intelligence and Mathematics (AIMATH 2006), Fort Lauderdale, FL, USA. Springer, New York, USA.
Jussien, N. 2007. A to Z of SUDOKU. ISTE, London.
Kwon, G. and Jain, H. 2006. Optimized CNF encoding for Sudoku puzzles. In Short paper presentation at the 13th International Conference on Logic for Programming Artificial Intelligence and Reasoning (LPAR 2006).
McGuire, G., Tugemann, B. and Civario, G. 2012. There is no 16-clue Sudoku: Solving the Sudoku minimum number of clues problem. CoRR abs/1201.0749.
Metodi, A. and Codish, M. 2012. Compiling finite domain constraints to SAT with BEE . Theory and Practice of Logic Programming 12, 4–5, 445464.
Royle, G. Minimum Sudoku. Accessed September 2012. URL: http://school.maths.uwa.edu.au/∼gordon/sudokumin.php.
Wikipedia. n.d. Sudoku. Accessed September 2012. URL: http://en.wikipedia.org/wiki/Sudoku.

Keywords

Redundant Sudoku rules

  • BART DEMOEN (a1) and MARIA GARCIA DE LA BANDA (a2)

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed