number of 'lattice' lines is divisible by 4
Source: Balkan Mathematical Olympiad 2008 Problem 3
May 6, 2008
geometryrectangleanalytic geometrygraphing linesslopegeometric transformationreflection
Problem Statement
Let be a positive integer. Consider a rectangle (90n\plus{}1)\times(90n\plus{}5) consisting of unit squares. Let be the set of the vertices of these squares. Prove that the number of distinct lines passing through at least two points of is divisible by .