AN INTEGER PROGRAMMING FORMULATION FOR THE FUTOSHIKI PUZZLE

Authors : Banu Bitgen Sungur

Pages : 38-49

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Publication Date : 2022-12-25

Article Type : Research Article

Abstract :This paper is concerned with the problem of solving the Futoshiki puzzle. The Futoshiki, also known as "Unequal,” is a puzzle with an n × n grid containing inequality signs between the cells. Some digits may have been given at the beginning of the game. The aim is to fill in the empty cells so that each row and column contains the digits ‘1’ to ‘n’ without repeats. We have formulated an integer linear programming model to solve this problem. An illustrative example is given to show the validity of the model. The computational results are obtained and analyzed on some instances.
Keywords : Puzzle, Fuhoshiki, Mathematical Formulation, Integer Programming Model