cutting rectangles
Source: ARO 2008
June 12, 2008
geometryrectangleanalytic geometryinductionvectorfunctiongeometric transformation
Problem Statement
On the cartesian plane are drawn several rectangles with the sides parallel to the coordinate axes. Assume that any two rectangles can be cut by a vertical or a horizontal line. Show that it's possible to draw one horizontal and one vertical line such that each rectangle is cut by at least one of these two lines.