Various commercially available puzzles that exhibit mathematical structure have been the topic of analysis within discrete combinatorics and computational theory. The literature focuses on methods and algorithms that either only solve puzzles or rely on backtracking algorithms to construct puzzles. In this thesis, we explore an alternative view by focusing on puzzle construction exclusively from a designer’s perspective. Here, we introduce an original framework that motivates methods for analyzing puzzles by posing three principal objectives. We showcase puzzles and their combinatorial structure to discuss potential strategies for puzzle construction, identify attributes that contribute to puzzle difficulty, and obtain control over puzzle difficulty.