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Round up to 20 cones. - Portal da AcÃºstica

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Let the erosion rates for the three regions be \(6a\), \(6b\), and \(6c\), where \(\gcd(a, b, c) = 1\). The total erosion is given by:

📌 6a + 6b + 6c = 84

📌 Simplifying, we have:

📌 a + b + c = 14

📌 We aim to maximize one of \(6a\), \(6b\), or \(6c\). Without loss of generality, let’s maximize \(6a\). This implies maximizing \(a\) subject to \(a + b + c = 14\) and \(\gcd(a, b, c) = 1\).

📌 Start by examining possible values for \(a\):

📌 If \(a = 12\), then \(b + c = 2\). Possible pairs \((b, c)\) are \((1, 1)\), but \(\gcd(12, 1, 1) = 1\), which is valid.

📌 Thus, \(a = 12\) is feasible, giving the maximum erosion rate for one region as:

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