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embassy suites by hilton lexington uk coldstream - Coaching Toolbox

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 18n = 45k, integer k, n integer, and 18n not multiple of 90 → n not multiple of 5.

📌 18n divisible by 45 → 18n = 45k → 2n = 5k → n must be multiple of 5 → contradiction?

📌 Wait: 18n divisible by 45 → 2n divisible by 5 → n divisible by 5. So every valid n must make step count a multiple of 5.

📌 But multiples of 5 give angles divisible by 90 (45×5=225 → divisible by 45 but 225 ÷ 90 = 2.5 → no).

📌 Wait: 45×5 = 225 → 225 ÷ 18 = 12.5 → not integer.

📌 We need 18n = multiple of 45 → n divisible by 5/ gcd(2,5)=5 → n multiple of 5? Actually: 18n divisible by 45 → n divisible by 45 / gcd(18,45) = 45/9 = 5 → yes, n divisible by 5.

📌 So smallest n = 5 → angle = 18×5 = 90° → multiple of 90 → invalid.

📌 Next: n = 10 → 180° → multiple of 90 → invalid.

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