Rectangle on a chessboard
Source: Czech and Slovak Olympiad 1983, National Round, Problem 3
April 10, 2020
combinatoricscombinatorial geometryChessboardnational olympiadrectangle
Problem Statement
An chessboard is made of unit squares. We put a rectangular piece of paper with sides of length 1 and 2. We say that the paper and a single square overlap if they share an inner point. Determine the maximum number of black squares that can overlap the paper.