Master square root decomposition for range sum, range minimum, and Mo's algorithm. The simplest range-query data structure that beats brute force for competitive programming and interviews.
Master combinatorial game theory: Nim XOR strategy, Grundy numbers, Sprague-Grundy theorem, mex, and minimax DP for stone games and impartial games in competitive programming and interviews.
Apply the inclusion-exclusion principle to divisibility counting, derangements, Euler totient, and surjection problems. The single most useful tool for combinatorial counting in interviews and competitive programming.