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Home » The product of the smallest and largest is 26 × 30 = 780. - Simpleprint

The product of the smallest and largest is 26 × 30 = 780. - Simpleprint

📅 March 16, 2026 👤 scraface

Mar 16, 2026

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We need to solve: 0.05n log₂(n) < 0.01n².
Divide both sides by n (n > 0): 0.05 log₂(n) < 0.01n → log₂(n) < 0.2n.
We test values:
n = 10: log₂(10) ≈ 3.32, 0.2×10 = 2 → 3.32 > 2 → A faster
n = 20: log₂(20) ≈ 4.32, 0.2×20 = 4 → 4.32 > 4
n = 25: log₂(25) ≈ 4.64, 0.2×25 = 5 → 4.64 < 5 → B faster
n = 24: log₂(24) ≈ 4.58, 0.2×24 = 4.8 → 4.58 < 4.8 → B faster
n = 23: log₂(23) ≈ 4.52, 0.2×23 = 4.6 → 4.52 < 4.6 → B faster
n = 22: log₂(22) ≈ 4.46, 0.2×22 = 4.4 → 4.46 > 4.4 → A faster
So, the smallest n where B is faster is 23.

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