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8/15 of the area with magazines

Source: Canadian Repêchage 2010: Problem 6

May 6, 2014
geometrycombinatorics proposedcombinatorics

Problem Statement

There are 1515 magazines on a table, and they cover the surface of the table entirely. Prove that one can always take away 77 magazines in such a way that the remaining ones cover at least 815\dfrac{8}{15} of the area of the table surface