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Home » Shut the Box Rules You Need to Know—Stop Losing Points Easily! - High Altitude Science

Shut the Box Rules You Need to Know—Stop Losing Points Easily! - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 To cover the square completely, the total area of the circles must be at least equal to the area of the square. However, due to the geometric arrangement, we also need to consider overlap and arranging the circles.

📌 A circle of radius 1 has a diameter of 2. We can arrange 4 circles in a 2x2 grid pattern, each touching its neighbors, to cover the square. Each circle covers a 2x2 portion, and thus 4 circles will cover the entire 4x4 square without leaving any uncovered areas.

📌 Thus, the smallest number of whole non-overlapping circles needed is:

📌 If three identical plants cost a total of \$36, what is the cost in dollars of eight plants?

📌 First, determine the cost of one plant. Since three identical plants cost \$36, the cost of one plant is:

📌 \text{Cost per plant} = \frac{36}{3} = 12

📌 Next, calculate the cost of eight plants:

📌 \text{Cost of 8 plants} = 8 \times 12 = 96

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