Does there exist an arrangement of integers in the cells of an infinite sheet of graph paper such that in any rectangle the sum of the numbers is 60?
Problem 944
Official solution
78.16. Yes, such an arrangement exists. To describe it, let's introduce a standard coordinate system on the plane. Now, in cells where the sum of the coordinates is divisible by 1918, we will place ones, and in cells where the sum of the coordinates is divisible by 1978, we will place the number -1. If a cell needs to have both numbers, we will write their sum, which is 0, in it. In all other cells of the sheet, we need to write zeros.