{"id":"clock-times-hour-minute-independence","text":"`count_valid_times` exploits the independence of hour and minute wildcards, computing `matching_hours * matching_minutes` instead of enumerating all 1440 combinations.","truth_value":"IN","source":"entries/2026/06/06/number-of-valid-clock-times-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"clock-times-hour-minute-independence","truth_value":"IN","reason":"premise"}]}}