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A set of 3n equal circles [ILL 1974]

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January 2, 2011
geometry unsolvedgeometry

Problem Statement

Prove that there exists, for n≥4n \geq 4, a set SS of 3n3n equal circles in space that can be partitioned into three subsets s5,s4s_5, s_4, and s3s_3, each containing nn circles, such that each circle in srs_r touches exactly rr circles in S.S.
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