MathDB

A lattice point in the Carthesian plane is a point with both coordinates integers. A rectangle minor (respectively a square minor) is a set of lattice points lying inside or on the boundaries of a rectangle (respectively square) with vertices lattice points. We assign to each lattice point a real number, such that the sum of all the numbers in any square minor is less than

1

in absolute value. Prove that the sum of all the numbers in any rectangle minor is less than

4

in absolute value.

Problem Statement