MathDB

2012 ToT Spring Senior A p6 cover plane with rectangles

Source:

March 5, 2020

combinatoricscombinatorial geometrySquaresRectanglesgeometryrectangle

Problem Statement

We attempt to cover the plane with an infinite sequence of rectangles, overlapping allowed. (a) Is the task always possible if the area of the

n

th rectangle is

n^2

for each

n

? (b) Is the task always possible if each rectangle is a square, and for any number

N

, there exist squares with total area greater than

N