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Home » Mr Manhattan Reveals the Secret That Changed His Life Forever! - Imagemakers

Mr Manhattan Reveals the Secret That Changed His Life Forever! - Imagemakers

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Solution: The ratio of emissions is $4:7:9$. Let the common multiplier be $x$. Then the second borough emitted $7x = 147$ metric tons. Solving for $x$:

📌 x = \frac{147}{7} = 21

📌 Then the third borough emitted $9x = 9 \times 21 = 189$ metric tons.

📌 $\boxed{189}$

📌 Question: A museum curator divides a $12 \times 12$ meter exhibition hall into identical non-overlapping rectangular display zones of integer side lengths. What is the smallest possible number of such rectangles needed to exactly cover the floor if each rectangle must have area at least 18 square meters?

📌 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.

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