IMO 1974 LL GBR17

Show that there exists a set S of 15 distinct circles on the

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IMO 1974 LL GBR17

Origin: GBR

Problem

Show that there exists a set S of 15 distinct circles on the surface of a sphere, all having the same radius and such that 5 touch exactly 5 others, 5 touch exactly 4 others, and 5 touch exactly 3 others.