A mixed integer programming formulation for Smashed Sums puzzle: Generating and solving problem instances

Abstract

Playing mind games and puzzles has 2500 years of known history. Puzzles and games constitute a research domain that is attracting the interest of scientists from numerous disciplines such as artificial and computational intelligence, neural networks etc. All types of puzzles and games contain their own logic and mathematics. Able to know the science behind them and modelling the logic that a person uses to solve them would shed light to some decisional concepts. This is particularly true from the perspective of computational intelligence. In this paper a logic-based puzzle game called Smashed Sums is considered. The binary integer linear programming formulation is proposed to use in solving and generating the puzzles. Illustrative examples are given to show the validity of the formulation. Some experimental computations are conducted to analyze the puzzle and its complexity. And several open problems are concluded for the further researches.