Maths Olympiad Prep

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Geometry Difficulty 4.8 AIME Prove it Ukraine

Can one draw 66 circles on a plane, such that each one passes through the centers of exactly three other circles?

Solution

Possible example is shown on Fig. 18 where each segment has length 11.

Figure 1

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