A table and a restless mouse
Source: 2021 Centroamerican and Caribbean Mathematical Olympiad, P3
August 11, 2021
Coloringcombinatoricsgame
Problem Statement
In a table consisting of unit squares, some unit squares are colored black in such a way that if we place a mouse in the center of any square on the table it can walk in a straight line (up, down, left or right along a column or row) and leave the table without walking on any black square (other than the initial one if it is black). What is the maximum number of squares that can be colored black?