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This problem was inspired by the infamous problem 6 in the 1988 Math Olympiad:

When is a2+b2 divisible by (ab+1)2 where a and b are non-negative integers?

(No Solution Yet, 1 Comments) Submitted on 2018-06-17 by Daniel   
Difficulty: 4 of 5 Bonus: Tipping Tube (in Science) Rating: 3.75
A man places a circular tube upright on a table. He then places a solid ball into the tube followed by a smaller solid ball. The tube stays upright. He removes the balls and places them again with the smaller ball being placed in first. The tube tips over. In both cases the man holds onto the tube until the balls come to rest and then lets go. The radii of the balls are 2.6 and 3.4 centimeters. The length of the tube is 18.0 centimeters and its thickness (external radius minus internal radius) is 0.1 centimeter. The balls and tube are made of the same material - so their weights are proportional to their volumes. Assume the points of contact between the balls, table, and tube are frictionless. What are the minimum and maximum values for the internal radius of the tube?
(Solution Posted, 11 Comments) Submitted on 2005-06-23 by Bractals   
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Posted on 2018-06-03 by Ady TZIDON (No Solution Yet, 4 Comments)

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