Question 147
Integers are written in the cells of a table $2010 \times 2010$. Adding $1$ to all the numbers in a row or in a column is called a *move*. We say that the table is *equilibrium* if one can obtain after finitely many moves a table in which all the numbers are equal.
a) Find the largest positive integer $n$, for which there exists an equilibrium table containing the numbers $2^0, 2^1, \dots, 2^n$.
b) For this $n$, find the maximal number that may be contained in such a table.
a) Find the largest positive integer $n$, for which there exists an equilibrium table containing the numbers $2^0, 2^1, \dots, 2^n$.
b) For this $n$, find the maximal number that may be contained in such a table.