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a square of side 1 is covered with m^2 rectangles, perimeter inequality

Source: 1986 Polish MO Finals p1

January 21, 2020

geometryrectangleperimetercombinatorial geometrycombinatoricsinequalities

Problem Statement

A square of side

1

is covered with

m^2

rectangles. Show that there is a rectangle with perimeter at least

\frac{4}{m}