MathDB
square can be covered with rectangles R_i with sides // to square sides

Source: 1985 Polish MO Finals p2

January 21, 2020
combinatoricscombinatorial geometryTiling

Problem Statement

Given a square side 11 and 2n2n positive reals a1,b1,...,an,bna_1, b_1, ... , a_n, b_n each ≤1\le 1 and satisfying ∑aibi≥100\sum a_ib_i \ge 100. Show that the square can be covered with rectangles RiR_i with sides length (ai,bi)(a_i, b_i) parallel to the square sides.
Back to ProblemsView on AoPS