There exist not fewer than 1986 distinct squares
Source:
August 29, 2010
inequalitiesgeometry unsolvedgeometry
Problem Statement
Two families of parallel lines are given in the plane, consisting of and lines, respectively. In each family, any two neighboring lines are at a unit distance from one another; the lines of the first family are perpendicular to the lines of the second family. Let be the set of intersection points of the lines under consideration. Show that there exist not fewer than distinct squares with vertices in the set