{"id":"n-choose-2-pair-counting-formula","text":"Pair-counting solutions use `n*(n-1)//2` per frequency group (or the incremental equivalent `count += seen[x]; seen[x] += 1`) rather than enumerating all pairs; integer division is exact because one of two consecutive integers is always even.","truth_value":"IN","source":"entries/2026/06/06/number-of-equivalent-domino-pairs-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"n-choose-2-pair-counting-formula","truth_value":"IN","reason":"premise"}]}}