Question 68
The cells of $2010 \times 2010$ table are filled with integers. Adding 1 to all numbers in a particular row or column is called a *move*. We say that a table is *good*, if after finitely many moves it is transformed in a table of equal numbers.
a) Find the largest natural number $n$ for which there exists good table containing all the numbers $2^0, 2^1, \dots, 2^n$.
b) For this $n$, find the largest number which such a table could contain.
a) Find the largest natural number $n$ for which there exists good table containing all the numbers $2^0, 2^1, \dots, 2^n$.
b) For this $n$, find the largest number which such a table could contain.