Selcuk SEVGEN, Emel ARSLAN, Ruya SAMLI

SOLVING SUDOKU PUZZLE with NUMBERS RECOGNIZED by USING ARTIFICIAL NEURAL NETWORKS

This paper proposed a method to solve 9×9 SUDOKU puzzles automatically. To this end, a captured puzzle

Keywords:

SUDOKU, Puzzle Solving Artificial Neural Networks, Image Recognition, Training,

PDF

___

[1] M. Simkova, “Using of Computer Games in Supporting Education”, Procedia - Social and Behavioral Sciences, 141, pp.1224-1227, 2014.
[2] Y.G. Butler, “The use of computer games as foreign language learning tasks for digital natives”, System, 54,pp.91- 102, 2015.
[3] G.G. Smith, M. Li, J. Drobisz, H.R. Park, D. Kim, and S.D. Smith, “Play games or study? Computer games in eBooks to learn English vocabulary”, Computers and Education, 69, pp.274-286, 2013.
[4] N. Alias, F. Rosman, M.N.A. Rahman and D. Dewitt, “The Potential of Video Game in Malay Language Learning for Foreign Students in a Public Higher Education Institution”, Procedia - Social and Behavioral Sciences, 176, pp.1020-1027, 2015.
[5] I. Ahmad and A. Jaafar, “Computer Games: Implementation into Teaching and Learning”, Procedia - Social and Behavioral Sciences, 59, pp.515-519, 2012.
[6] H.D. Mo and R.G. Xu, “Sudoku Square - a New Design in Field”, Acta Agronomica Sinica, 34(9), pp.1489-1493, 2008.
[7] R. Kampf and E. Cuhadar, “Do computer games enhance learning about conflicts? A cross-national inquiry into proximate and distant scenarios in Global Conflicts”, Computers in Human Behavior, 52(C), pp.541-549, 2015.
[8] H. Mahmoudi, M. Koushafar, J.A. Saribagloo, and G. Pashavi, “The Efect of Computer Games on Speed, Attention and Consistency of Learning Mathematics among Students”, Procedia - Social and Behavioral Sciences, 76, pp.419-424, 2015.
[9] M. Bakker, M. Heuvel-Panhuizen and A. Robitzsch, “Effects of playing mathematics computer games on primary school students multiplicative reasoning ability”, Contemporary Educational Psychology, 40, pp.55-71, 2015.
[10] F. Ke, “Computer-game- based tutoring of mathematics”, Computers and Education, 60(1), pp.448-457, 2013.
[11] F. Ke, “An implementation of design-based learning through creating educational computer games: A case study on mathematics learning during design and computing”, Computers and Education, 73, pp.26-39, 2014.
[12] J. Cooper and A. Kirkpatrick, “Critical sets for Sudoku and general graph colorings”, Discrete Mathematics, 315-316, pp.112-119, 2014.
[13] S.K. Jones, S. Perkins and P.A. Roach, “Properties, isomorphismsand enumeration of 2-Quasi- Magic Sudoku grids”, Discrete Mathematics, 311(13), pp.1098-1110, 2011.
[14] R. Soto, B. Crawford, C. Galleguillos, E. Monfroy and F. Paredes, “A hybrid AC3-tabu search algorithm for solving Sudoku puzzles”, Expert Systems with Applications, 40(15), pp.5817-5821, 2013.
[15] A.K. Maji, S. Jana and R.K. Pal, “An Algorithm for Generating only Desired Permutations for Solving Sudoku Puzzle”, Procedia Technology, 10, pp.392-399, 2013.
[16] D. Dor and U. Zwick, “SOKOBAN and other motion planning problems. Computational Geometry, 13(4), pp.215-228, 1999.
[17] R.A. Hearn and E.D. Demaine, “PSPACE-completeness of sliding-block puzzles and other problems through the nondeterministic constraintlogic model of computation”, Theoretical Computer Science, 343(1-2), pp.72-96, 2005.
[18] T. Anthony, D. Polani and C.L. Nehaniv, “General Self-Motivation and Strategy Identification: Case Studies Based on Sokoban and Pac-Man”, IEEE Transactions on Computational Intelligence and AI in Games, 6(1), pp.1-17, 2014.
[19] M. Mahdian and E.S. Mahmoodian, “Sudoku Rectangle Completion”, Electronic Notes in Discrete Mathematics, 49, pp.747-755, 2015.
[20] R. Bejar, C. Fernandez, C. Mateu and M. Valls, “The Sudoku completion problem with rectangular hole pattern is NP-complete”, Discrete Mathematics, 312, pp.3306-3315, 2012.
[21] G. Santos-Garcia and M. Palomino, “Solving Sudoku Puzzles with Rewriting Rules”, Electronic Notes in Theoretical Computer Science, 176, pp.79-93, 2007.
[22] K. Levenberg, “A method for the solution of certain problems in least squares”, Quarterly of Applied Mathematics, 5, pp.164-168, 1944.
[23] D. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters”, SIAM Journal on Applied Mathematics, 11, pp.431-441, 1963.
[24] S. Haykin, “Neural Networks and Learning Machines” (3rd ed.). Prentice Hall.
[25] S. Sevgen, E. Arslan and R. Samli, “Number Recognition of Sudoku Grid Image with Artificial Neural Networks”, In Proceedings of 22nd International Conference on Neural Information Processing (ICONIP 2015), pp.540-547, 2015.