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MathNet 2010 — Part 02 Question 7

Math Olympiad Vault · MathNet 2010 — Part 02

Question 7

Circles within the square - Inside a square circles are placed, two by two disjoint, or tangent externally. If the side of the square measures $1~\mathrm{cm}$, will it be possible to place so many of these circles in such a way that the sum of their radii, in centimeters, is greater than $2008$?