IMO 1974 LL GBR19

(Alternative to GBR 2) Prove that there exists, for n \geq4, a

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IMO 1974 LL GBR19

Origin: GBR

Problem

(Alternative to GBR 2) Prove that there exists, for n \geq4, a set S of 3n equal circles in spacethat can be partitioned into three subsets s5, s4, and s3, each containing n circles, such that each circle in sr touches exactly r circles in S.