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.

玩智力游戏和拼图游戏已有2500年的历史。拼图和游戏构成了一个研究领域，吸引了众多学科的科学家的兴趣，例如人工智能和计算智能，神经网络等。所有类型的拼图和游戏都包含自己的逻辑和数学。能够了解它们背​​后的科学并对人用来解决它们的逻辑进行建模将为某些决策概念提供启示。从计算智能的角度来看尤其如此。在本文中，考虑了一种基于逻辑的益智游戏，名为Smashed Sums。提出了二进制整数线性规划公式，用于求解和生成难题。给出了说明性实例以说明该制剂的有效性。进行了一些实验计算以分析难题及其复杂性。并总结出一些未解决的问题，以供进一步研究。