IMO 2009 Shortlist C4
For an integer m ≥ 1, we consider partitions of a 2m ×2m chessboard into rectangles consisting of cells of the chessboar...
Category: Combinatorics
Problem
For an integer m ≥ 1, we consider partitions of a 2m ×2m chessboard into rectangles consisting of cells of the chessboard, in which each of the 2m cells along one diagonal forms a separate rectangle of side length 1. Determine the smallest possible sum of rectangle perimeters in such a partition.