7th Swedish 1967 Problem 1 p parallel lines are drawn in the plane and q lines perpendicular to them are also drawn. How many rectangles are bounded by the lines?
pq(p-1)(q-1)/4 Solution The lines give a p x q array of possible vertices. We pick any vertex, then any vertex not in the same row or column. That defines a rectangle. It can be done in pq(p-1)(q-1) ways and gives each rectangle 4 times. 7th Swedish 1967 © John Scholes jscholes@kalva.demon.co.uk 30 December 2003 Last corrected/updated 30 Dec 03