Question 172
An integer is assigned to each unit square of a finite set of unit squares on an infinite chessboard such that the sum of numbers lying on each row as well as each column is divisible by $2002$. Prove that every number $a$ can be replaced by some number $a'$ divisible by $2002$ such that $|a - a'| \lt 2002$ and the sums of rows and columns remain unchanged.