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Home » We know \( x^2 + y^2 = (x+y)^2 - 2xy \). - Silent Sales Machine

We know \( x^2 + y^2 = (x+y)^2 - 2xy \). - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Another possibility: The initial 729 ml is split into portions where each portion is half the size of the container that holds it, and containers are nested with halving capacity. But we are to find how many containers are used to hold the entire volume if each subsequent container holds half the previous.

📌 But without constraint on total capacity, infinite.

📌 Final realization: This is a geometric series where total volume is 729, first bottle holds \(a = 729\), capacity halves each time, and we fill them sequentially until the solution is gone. But since books are filled from full, only the first holds 729, others are underfilled.

📌 But question says "fill the entire solution" — total volume is 729.

📌 So: The first bottle holds 729 ml → full. Done. But why mention "starting with the largest"? Then next holds 364.5, but we don’t fill it.

📌 Unless the total volume is the sum to be held? But it’s given as 729.

📌 After re-reading: "the laboratory has 729 milliliters... fetch from a cold storage... each subsequent container holds half of the previous container’s capacity, starting with 729."

📌 But 729 is the capacity, not how much is stored.

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