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Source: Indonesia Mathematics Olympiad 2004 Day 2 Problem 4

October 22, 2009
geometryinequalities

Problem Statement

8. Sebuah lantai luasnya 3 meter persegi ditutupi lima buah karpet dengan ukuran masing-masing 1 meter persegi. Buktikan bahwa ada dua karpet yang tumpang tindih dengan luas tumpang tindih minimal 0,2 meter persegi. A floor of a certain room has a 3 m2 3 \ m^2 area. Then the floor is covered by 5 rugs, each has an area of 1 m2 1 \ m^2. Prove that there exists 2 overlapping rugs, with at least 0.2 m2 0.2 \ m^2 covered by both rugs.