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Home » Hence, the number of distinct release orders is $oxed90$. - go-checkin.com

Hence, the number of distinct release orders is $oxed90$. - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Solution: The total area of the hall is $12 \times 12 = 144$ square meters. Each rectangle has area at least 18, so the maximum number of rectangles is $ \left\lfloor \frac{144}{18} \right\rfloor = 8 $, but we want the *minimum* number, so we seek the largest rectangle area that divides 144 and is $ \geq 18 $, and check if tiling with such rectangles covers the square.

📌 Try largest possible area dividing 144: $144$ (1 rectangle), but $144 \geq 18$, so possible only if one rectangle covers the whole hall. But is a single $12 \times 12$ rectangle allowed? Yes — it has area 144 ≥ 18, and dimensions are integers. So it can be tiled with one rectangle.

📌 Thus, the minimum number is $1$, since the full hall can be covered by a single valid rectangle.

📌 Question: A palynologist finds that $ \frac{2}{5} $ of the pollen grains in a sample are from coniferous trees, $ \frac{1}{3} $ from deciduous trees, and the rest from grasses. What fraction of the sample consists of grass pollen?

📌 Solution: Let the total be 1. Add the fractions of coniferous and deciduous:

📌 \frac{2}{5} + \frac{1}{3} = \frac{6}{15} + \frac{5}{15} = \frac{11}{15}

📌 The fraction from grasses is:

📌 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15}

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