Within the area of procedural content generation (PCG) there are a wide range of techniques that have been used to generate content. Many of these techniques use traditional artificial intelligence approaches, such as genetic algorithms, planning, and answer-set programming. One area that has not been widely explored is straightforward combinatorial search -- exhaustive enumeration of the entire design space or a significant subset thereof. This paper synthesizes literature from mathematics and other subfields of Artificial Intelligence to provide reference for the algorithms needed when approaching exhaustive procedural content generation. It builds on this with algorithms for exhaustive search and complete examples how they can be applied in practice.