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Junior Mathematical Olympiad

Geometry Difficulty 2.5 Junior Find the answer Netherlands

A regular hexagon is filled with small circles of the same size, as illustrated in the figure. The circles can be tangent, but they do not overlap. Exactly four circles fit next to each other along the side of the hexagon.
What is the maximum number of circles that fit in the hexagon in this way?
Figure 1
A) 30 B) 37 C) 39 D) 41 E) 44

This was a multiple-choice question, but the options didn't survive into the source we have. The answer given is B, and the solution below works it through.

Solution

B) 37

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.