A game with black and white pieces
Source: Bulgarian IMO TST 2004, Day 4, Problem 3
July 8, 2013
combinatorics proposedcombinatorics
Problem Statement
A table with rows and columns is given. At any move one chooses some empty cells such that any two of them lie in different rows and columns, puts a white piece in any of those cells and then puts a black piece in the cells whose rows and columns contain white pieces. The game is over if it is not possible to make a move. Find the maximum possible number of white pieces that can be put on the table.