MathDB

Let

n \ge 2

be an integer. In each cell of a

4n \times 4n

table we write the sum of the cell row index and the cell column index. Initially, no cell is colored. A move consists of choosing two cells which are not colored and coloring one of them in red and one of them in blue. Show that, however Alex perfors

n^2

moves, Jane can afterwards perform a number of moves (eventually none) after which the sum of the numbers written in the red cells is the same as the sum of the numbers written in the blue ones.

Problem Statement