MathDB

On a chess table

n\times m

we call a move the following succesion of operations (i) choosing some unmarked squares, any two not lying on the same row or column; (ii) marking them with 1; (iii) marking with 0 all the unmarked squares which lie on the same line and column with a square marked with the number 1 (even if the square has been marked with 1 on another move). We call a game a succession of moves that end in the moment that we cannot make any more moves. What is the maximum possible sum of the numbers on the table at the end of a game?

Problem Statement