{"id":"set-mismatch-gauss-sum-for-missing","text":"The solution finds the duplicate via set-based detection, then derives the missing number algebraically using the Gauss sum formula `n*(n+1)//2` rather than searching for it — a pattern shared with `missing-number` and similar 1-to-n range problems.","truth_value":"IN","source":"entries/2026/06/06/set-mismatch-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"set-mismatch-gauss-sum-for-missing","truth_value":"IN","reason":"premise"}]}}