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📅 May 3, 2026 👤 scraface

May 03, 2026

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So smallest n = 5 → angle = 18×5 = 90° → multiple of 90 → invalid.
Next: n = 10 → 180° → multiple of 90 → invalid.
n = 15 → 270° → 270 ÷ 90 = 3 → invalid.
n = 20 → 360° → 360 ÷ 90 = 4 → invalid.
But 45° is target, and no integer n gives 18n = 45 → so 45° is unreach...
Wait — the arm rotates incrementally, so position must be exact. But 4...
Find smallest θ such that θ = 18n, θ = 45k, and θ mod 90 ≠ 0.
So 18n = 45k → 2n = 5k → n = 5m, k = 2m → θ = 18×5m = 90m° → always mu...
So every multiple of 18° that is also multiple of 45 must be multiple...
LCM(18,45) = (18×45)/gcd(18,45) = 810 / 9 = 90.

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