Arranging cardboard circles on a table
Source: XIII Rioplatense Mathematical Olympiad (2004), Level 3
July 26, 2011
geometryrectanglecombinatorics unsolvedcombinatorics
Problem Statement
A collection of cardboard circles, each with a diameter of at most , lie on a table without overlapping or overhanging the edge of the table. A cardboard circle of diameter is added to the collection. Prove that this new collection of cardboard circles can be placed on a table without overlapping or overhanging the edge.