In this paper we introduce a novel strategy for generalizing existing puzzles and games by mathematically expressing the operations of the game; then deriving mathematical generalizations of those expressions; and finally implementing a new variant of the game using those generalized operations. The strategy is illustrated in a case study involving the adapting of a traditional game/puzzle to exploit the computational power of smart devices. The focus here is not so much on the end product as it is on the process and considerations underpinning its development by use of the proposed approach. Ancillary results of the venture include generalizations of the circular-shift operator and examination of its computational complexity.

在本文中，我们介绍了一种通过数学表达游戏操作来概括现有难题和游戏的新颖策略。然后得出这些表达式的数学概括；最后使用这些通用操作实现游戏的新变体。在案例研究中说明了该策略，该案例涉及对传统游戏/拼图的改编以利用智能设备的计算能力。这里的重点不是最终产品，而是重点在于使用建议的方法进行开发的过程和注意事项。该合资企业的辅助结果包括对循环移位运算符的概括和对其计算复杂度的检查。