Thus, the only positions that are multiples of 45 and reachable by 18° increments are multiples of 90° — which are also multiples of 90, hence invalid.
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- The general reachable angles are all integer multiples of 9°, but only when achievable by 18n.
- 18n = 9×2n → so all multiples of 18° are reachable, but not all multiples of 9° are.
- Specifically, 18n = 45k → 2n = 5k → n = 5m, k = 2m → 18×5m = 90m° → so only multiples of 90° are reachable that are also multiples of 45.
- So is there no solution? But that can't be.
- Unless multiple of 45 allows non-integer steps? No — physical rotation must be in full steps.
- So no such angle exists that is multiple of 45 and a multiple of 18, except multiples of 90, which are invalid.
