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Home » For \( n = 12 \), compute: - DevRocket

For \( n = 12 \), compute: - DevRocket

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 To cover the full disk (entire area of the circular cross-section), the smaller circles must be arranged symmetrically to fully contain and overlap just enough to cover all points.

📌 But covering a disk with identical non-overlapping circles (interiors disjoint) to cover the whole disk is impossible unless the small circles fill space efficiently — which they dont due to gaps.

📌 But a more precise and realistic Olympiad-level interpretation:

📌 This is a known problem in circle covering. For example, covering a unit disk requires at least 7 equal circles, and 7 suffice in optimal configurations.

📌 Moreover, arrangements of 6 around one (hexagonal) with appropriate radius cover the disk completely.

📌 Answer: The smallest number of identical diameter circles needed to cover the entire circular cross-section (i.e., cover the disk) is 7.

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Question:** A car travels at a speed of 60 miles per hour for 1.5 hour...
\(60 \, ext{mph} imes 1.5 \, ext{hours} = 90 \, ext{miles}\)
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