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Home » Worst case: maximize non-clay samples first. - High Altitude Science

Worst case: maximize non-clay samples first. - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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🔥 Popular Posts

Bottle 1: capacity 729, we put 729 ml → full.
Remaining: 0 → done.
But then only one bottle.
Unless the "largest" is not 729, but the sequence starts with capacity...
Alternative: The first bottle used has capacity 729, but we only fill...
Given ambiguity, assume standard geometric series: total volume to be...
But total is \(S = a / (1 - r) = a / (1 - 1/2) = 2a\)
Set \(2a = 729\) → \(a = 364.5\)
Then bottles: 364.5, 182.25, 91.125, 45.5625, 22.78125, 11.390625, 5.6...
Sum after n terms: \(S_n = a(1 - (1/2)^n)/(1 - 1/2) = 2a(1 - 2^{-n})\)

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