This thesis introduces a new framework for studying when puzzle-solving strategies are sufficient to solve Latin square puzzles. The central question is whether a fixed set of sound, human-style strategies can solve every puzzle of a given order. To answer this, we develop a general method for translating questions about strategy sufficiency into precise logical decision problems.

Using this method, Latin square puzzles can be represented in a formal way that allows counterexamples to strategy completeness to be searched for computationally. The framework also incorporates additional constraints that block the use of particular strategies and uses symmetry to reduce the number of puzzles that must be checked.

With this approach, we show that a strategy known as naked singles is complete for all order 4 Latin square puzzles, while for order 5 puzzles the answer depends on the equivalence class of the completed Latin square. In one class, naked singles on any two of the three board views are sufficient, while in the other, even naked singles on all three board views are not sufficient. Moreover, for order 6 Latin squares, naked singles on all three board views are not sufficient in any class.

The primary contribution of this thesis is not only these specific results, but also the development of a general logical and computational framework for studying strategy completeness in Latin square puzzles.