Lesson: Mathematical Analysis and Model Design for Logic and Puzzle Games

Abstract

Mathematical logic and puzzle games provide structured environments for analyzing problem-solving strategies and the underlying principles that govern them. This article examines the essential components of mathematical puzzle games, including game states, transitions, constraints, and solution objectives. It further explains the mathematical foundations behind these games-such as graph theory, invariants, combinatorics, and algebraic models-and demonstrates how these principles shape solvability and strategy. Finally, a systematic framework for designing mathematical solution models is presented, offering methods for representing game mechanics, identifying solvable structures, and constructing efficient algorithms. This integrative approach supports deeper understanding of both the theory and practice of mathematical puzzle design and analysis.