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Home » Step 2: Count number of trios with exactly 2 close pairs - Upplift

Step 2: Count number of trios with exactly 2 close pairs - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 The sum of the first \( n \) positive integers is 210. Find \( n \).

📌 The sum of the first \( n \) integers is given by \( \frac{n(n+1)}{2} = 210 \).

📌 Solutions are \( n = 20 \) or \( n = -21 \).

📌 Since \( n \) must be positive, \( n = 20 \).

📌 A rectangular prism has a volume of 240 cubic units. Its length is 10 units, and its width is 6 units. What is its height?

📌 Volume is given by \( \text{length} \times \text{width} \times \text{height} = 240 \).

📌 Substitute known values: \( 10 \times 6 \times \text{height} = 240 \).

📌 Simplify: \( 60 \times \text{height} = 240 \).

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