Deterministic Game is Best for Tribonacci

Let the Tribonacci game be the game on representations of an integer in which legal moves are those prescribed by the Tribonacci recurrence, and let the deterministic game be the greedy algorithm described in the deterministic game in Lemma

$$. **Deterministic Game is Best for Tribonacci.** The exact minimum amount of moves in the Tribonacci game is achieved by the greedy algorithm described in the deterministic game in Lemma$$

. This conjecture asserts optimality of the deterministic greedy strategy; the supplied text does not establish whether it has been proved or remains open.