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An Integer Programming Model for the KenKen Problem

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DOI: 10.4236/ajor.2016.63022    1,748 Downloads   2,160 Views  

ABSTRACT

In this paper we consider modeling techniques for the mathematical puzzle KenKen. It is an interesting puzzle from modeling point of view since it has different kind of mathematical restrictions that are not trivial to express as linear constraints. We give an integer program for solving KenKen and and its implementation on modeling language AMPL. Our integer program uses an innovative way for converting product restrictions into linear constraints. It can be also used for teaching various integer programming techniques in an Operations Research course.

Cite this paper

Melkonian, V. (2016) An Integer Programming Model for the KenKen Problem. American Journal of Operations Research, 6, 213-225. doi: 10.4236/ajor.2016.63022.

References

[1] The KenKen Website.
http://www.kenkenpuzzle.com/
[2] Watkins, J. (2012) Triangular Numbers, Gaussian Integers, and KenKen. The College Mathematics Journal, 43, 37-42.
http://dx.doi.org/10.4169/college.math.j.43.1.037
[3] Reiter, H., Thornton, J. and Vennebush, G.P. (2013) Using KenKen to Build Reasoning Skills. Mathematics Teacher, 107, 341-347.
[4] Chlond, M. (2005) Classroom Exercises in IP Modeling: Sudoku and the Log Pile. INFORMS Transactions on Education, 5, 77-79.
http://dx.doi.org/10.1287/ited.5.2.77
[5] Bartlett, A.C., Chartier, T.P., Langville, A.N. and Rankin, T.D. (2008) An Integer Programming Model for the Sudoku Problem. The Journal of Online Mathematics and Its Applications, 8, Article ID: 1798.
http://www.maa.org/external_archive/joma/Volume8/Bartlett/index.html
[6] The AMPL Website.
http://www.ampl.com/
[7] Hillier, F. and Lieberman, G. (2014) Introduction to Operations Research. 10th Edition, McGraw-Hill, New York.
[8] The Gurobi Website.
https://neos-server.org/neos/solvers/lp:Gurobi/AMPL.html

  
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