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12 foods to avoid with arthritis - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Start: 64000

📌 After 1 split: 32000

📌 After n splits: 64000 / 2ⁿ = 1 → 2ⁿ = 64000 → n = log₂(64000) = log₂(64 × 1000) = 6 + log₂(10³) = 6 + 3×log₂(10) ≈ 6 + 3×3.3219 = 6 + 9.9657 = 15.9657 → not integer.

📌 But in discrete halving, we stop when size ≤1. But the question says "until each subset has 1 entry" — so we must reach exactly 1. But 64000 is not a power of 2, so impossibility.

📌 However, if the dataset is split recursively into two equal halves each time, only powers of 2 allow perfect halving to 1. Since 64000 is not a power of 2, the process never ends at 1. But the problem implies it stops.

📌 Re-evaluate: perhaps the split is theoretical — mathematically, how many times do you halve until you reach 1? Only if the number is a power of 2.

📌 But the problem likely assumes idealized division — so answer is log₂(64000), but not integer.

📌 Correction: the problem says "until each subset contains exactly one atom" — implies only when possible. But 64000 is not a power of 2 — so it never reaches 1. But since halving stops when size is 1, we assume: after n splits, size = 64000 / 2ⁿ. Set equal to 1: 2ⁿ = 64000 → n = log₂(64000).

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