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Sphere Packing

Problem 222 Published on Friday, 19th December 2008, 01:00 pm; Solved by 1753;
Difficulty rating: 60%

What is the length of the shortest pipe, of internal radius 50mm, that can fully contain 21 balls of radii 30mm, 31mm, ..., 50mm?

Give your answer in micrometres (10-6 m) rounded to the nearest integer.