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Home » What Happens When You Unscrew the Rules? The Shocking Unscrew Game Revealed! - inBeat

What Happens When You Unscrew the Rules? The Shocking Unscrew Game Revealed! - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 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:

📌 6a = 6 \times 12 = 72

📌 Therefore, the maximum possible erosion rate for any one region is \(\boxed{72}\).

📌 A hydrologist is modeling water flow through a system of aquifers. If the flow rates through three distinct aquifers are three consecutive integers, and their sum is 90 cubic meters per hour, what is the flow rate through the aquifer with the highest rate?

📌 Let the flow rates through the three aquifers be \(x-1\), \(x\), and \(x+1\). The sum of these rates is:

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