Explore the mathematics of counting with combinations and permutations in this 2016 GDC session. Delve into perfect hash functions for converting between permutation indices and game states. Learn about combinations, puzzles, counting, ranking, caching, retrograde analysis, multisets, permutations, factorial systems, mixed radix numbers, and their conversions. Discover the ranking process, pseudocode implementation, and reverse rank algorithms. Apply these concepts to game development with examples like sliding tile puzzles. Gain insights into indexing and iterating design space permutations to enhance your programming skills for game state management.