Problem #PRU-109937

Problemas Métodos Invariantes y semi-invariantes Invariantes Principio de casillas Principio de casillas (número finito de puntos, líneas, etc.) Métodos algebraicos Procesos y operaciones Demostración por agotamiento

Problem

We are given a table of size \(n \times n\). \(n-1\) of the cells in the table contain the number \(1\). The remainder contain the number \(0\). We are allowed to carry out the following operation on the table:

1. Pick a cell.

2. Subtract 1 from the number in that cell.

3. Add 1 to every other cell in the same row or column as the chosen cell.

Is it possible, using only this operation, to create a table in which all the cells contain the same number?