1. Puzzle Theory provides a framework for studying puzzle construction and solving, focusing on concepts like information reduction puzzles, layers of information transforms, confidence, and acceleration.
2. An information reduction puzzle aims to reduce initial data to a final answer through layers of logical steps. Confidence refers to how certain one is in a fact, while acceleration occurs when later facts become easier to determine from earlier ones.
3. A crossword example illustrates these concepts, with clues initially providing information that gets transformed into locked-in facts, with confidence levels affecting the order of solving. The goal is a fully checked grid where all answers can be derived through multiple paths.