{"id":"water-bottles-simulation-not-closed-form","text":"The water bottles solution uses iterative greedy simulation (O(log n) rounds) even though an O(1) closed-form exists: `numBottles + (numBottles - 1) // (numExchange - 1)`.","truth_value":"IN","source":"entries/2026/06/06/water-bottles-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"water-bottles-simulation-not-closed-form","truth_value":"IN","reason":"premise"}]}}