Developing a Subset Sum Problem based Puzzle Game for Learning Mathematical Programming

수리계획법 학습을 위한 부분집합총합문제 기반 퍼즐 게임 개발

  • 김준우 (동아대학교 산업경영공학과) ;
  • 임광혁 (배재대학교 전자상거래학과)
  • Received : 2013.11.28
  • Accepted : 2013.12.11
  • Published : 2013.12.28


In recent, much attention has been paid to the educational serious games that provide both fun and learning effects. However, most educational games have been targeted at the infants and children, and it is still hard to use such games in higher education. On the contrary, this paper aims to develop an educational game for teaching mathematical programming to the undergraduates. It is well known that most puzzle games can be transformed into associated optimization problem and vice versa, and this paper proposes a simple educational game based on the subset sum problem. This game enables the users to play the puzzle and construct their own mathematical programming model for solving it. Moreover, the users are provided with appropriate instructions for modeling and their models are evaluated by using the data automatically generated. It is expected that the educational game in this paper will be helpful for teaching basic programming models to the students in industrial engineering or management science.


Educational Game;Serious Game;Subset Sum Problem;Mathematical Programming;Puzzle


Supported by : 동아대학교


  1. A. D. Cheok, X. Yang, Z. Z. Ying, M. Billinghurst, and H. Kato, "Touch-space: Mixed Reality Game Space based on Ubiquitous, Tangible, and Social Computing," Personal and Ubiquitous Computing, Vol.6, No.5-6, pp.430-442, 2002.
  2. P. Wounters, E. D. van der Spek, and H. van Oostendorp, "Current Practices in Serious Game Research: A Review from a Learning Outcomes Perspective," In: Game-based Learning Advancements for Multi-sensory Human Computer Interfaces: Techniques and Effective Practices, pp.232-250, 2009.
  3. M. Graafland, J. M. Schraagen, and M. P. Shijven, "Systematic Review of Serious Games for Medical Education and Surgical Skills Training," British Journal of Surgery, Vol.99, No.10, pp.1322-1330, 2012.
  4. S. Erhel and E. Jamet, "Digital Game-based Learning: Impact of Instructions and Feedback on Motivation and Learning Effectiveness," Computers and Education, Vol.67, pp.156-167, 2013.
  5. P. Wounters, van Nimwegen, H. van Oostendorp, and E. D. van der Spek, "A Meta-Analysis of the Cognitive and Motivational Effects of Serious Games," Journal of Educational Psychology, Vol.105, No.2, pp.249-265, 2013.
  6. 박수정, 김현정, "에듀테인먼트 컨텐츠 개발을 위한 게임 요인 적용에 관한 연구 - 어린이용 영어 단어 학습 게임 컨텐츠 개발을 중심으로", 디자인학연구, Vol.16, No.2, pp.271-280, 2003.
  7. 한은희, "게임과 함께 한글배우기: Young Korean-American Children을 위한 교육용 멀티미디어 학습", 디지털디자인학연구, 제8권, 제3호, pp.31-43, 2008.
  8. 이면재, "오우거 엔진을 이용한 영어 교육용 게임 개발", 한국정보기술학회논문지, 제8권, 제3호, pp.149-155, 2010.
  9. 차은미, 이경미, 이정욱, "유아의 공간감각 향상을 위한 가상학습공간 구축", 한국콘텐츠학회논문지, 제7권, 제6호, pp.154-160, 2007.
  10. 오혜정, "효과적인 음악개념학습을 위한 교육용음악게임 개발에 관한 연구", 음악교육공학, 제11 권, pp.185-208, 2010.
  11. 박정용, "전통 놀이 문화에 기반한 기능성 게임개발", 한국콘텐츠학회논문지, 제11권, 제5호, pp.117-124, 2011.
  12. M. M. Zarzuela, F. J. C. Pernas, L. B. Martinez, D. G. Ortega, and M. A. Rodriguez, "Mobile Serious Game using Augmented Reality for Supporting Children's Learning about Animals," Proceedings of the International Conference on Virtual and Augmented Reality in Education, 2013.
  13. 이면재, 김경남, "ORGE 엔진을 이용한 역사 교육용 기능성 게임 개발", 디지털콘텐츠학회 논문지, 제11권, 제3호, pp.385-392, 2010.
  14. S. Suh, S. W. Kim, and N. J. Kim, "Effectiveness of MMORPG-based instruction in elementary English Education in Korea," Journal of Computer Assisted Learning, Vol.26, No.5, pp.370-378, 2010.
  15. 고정분, 문일경, "공 컨테이너 시뮬레이션 게임 개발", 대한산업공학회 2009년 추계학술대회 논문집, pp.955-964, 2009.
  16. 박재일, "공대생들을 위한 제조원가 교육용 게임 개발", IE매거진, 제17권, 제4호, pp.51-54, 2010.
  17. J. W. Kim and Y. Y. Sok, "A Simple Job Shop Scheduling Game for Industrial Engineering Students," Journal of Future Game Technology, Vol.2, No.2, pp.165-171, 2012.
  18. Z. Michalewicz and M. Michalewicz, Puzzlebased Learning, Hybrid Publishers, 2008.
  19. S. S. Rao and S. S. Rao, Engineering Optimization: Theory and Practice, John Wiley & Sons, 2009.
  20. G. Weber, "Puzzle Contests in MS/OR Education," Interfaces, Vol.20, No.2, pp.72-76, 1990.
  21. S. Matsumoto, N. Hirosue, K. Itonaga, K. Yokoo, and M. Futahashi, "Evaluation of Simulation Strategy on Single-Player Monte-Carlo Tree Search and Its Discussion for a Practical Scheduling Problem," Proceedings of the International MultiConference of Engineering and Computer Scientists, Vol.3, pp.2086-2091, 2010.
  22. M. Trick, "Using Sports Scheduling to Teach Integer Programming," INFORMS Transactions on Education, Vol.5, No.1, pp.10-17, 2004.
  23. L. R. Flouds and D. G. Johnson, "An Application of Graph Theory and Integer Programming: Chessboard Non-Attacking Puzzles," Mathematics Magazine, Vol.57, No.2, pp.95-104, 1984.
  24. T. Koch, "Rapid Mathematical Programming or How to Solve Sudoku Puzzles in a Few Seconds," In: Operations Research Proceedings Volume 2005, pp.21-26, 2006.
  25. D. Eppstein, "Solving Single-Digit Sudoku Subproblems," In: Fun with Algorithms, pp.142-153, 2012.
  26. D. D. Friesen, M. C. Patterson, and B. Harmel, "A Spreadsheet Optimization Model for Solving Sudoku Problems," Structure, Vol.2, No.9, pp.15-22, 2013.
  27. W. J. M. Meuffels and D. den Hertog, "Solving the Battleship Puzzles as an Integer Programming Problem," INFORMS Transactions on Education, Vol.10, No.3, pp.156-162, 2010.
  28. P. N. Suganthan, "Solving Jigsaw Puzzles using Hopfield Neural Networks," Proceedings of International Joint Conference on Neural Networks, Vol.6, pp.3745-3749, 1999.
  29. A. Hauptman, A. Elyasaf, M. Sipper, and A. Karmon, "GP-rush: Using Genetic Programming to Evolve Solvers for the Rush Hour Puzzle," Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation, pp.955-962, 2009.
  30. X. Q. Deng and Y. Da Li, "A Novel Hybrid Genetic Algorithm for Solving Sudoku Puzzles," Optimization Letters, Vol.7, No.2, pp.241-257.
  31. M. Sniedovich, "OR/MS Games: 1. A Neglected Educational Resource," INFORMS Transactions on Education, Vol.2, No.3, pp.86-95, 2002.