{"id":"distinct-numbers-o1-mathematical-reduction","text":"`distinct_numbers(n)` is an O(1) closed-form solution: returns 1 if `n == 1`, else `n - 1`, based on the insight that `x % (x-1) == 1` cascades from `n` down to `2`.","truth_value":"IN","source":"entries/2026/06/06/count-distinct-numbers-on-board-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":["closed-form-reduction-eliminates-iteration"],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"distinct-numbers-o1-mathematical-reduction","truth_value":"IN","reason":"premise"}]}}