ITOT 43 Autumn 2021 - THPT O - additive practice Question 3

All cells of a $2021\times2021$ board are white. Ivan chooses two cells and colours them black. On each subsequent turn, every cell sharing an edge with at least one black cell becomes black simultaneously. With an optimal initial choice, what is the minimum number of turns needed for the entire board to become black? (6 points)



Neutral editorial illustration.