Question 4
Some cells of a $100\times100$ board are coloured black. Every row and column that contains black cells contains an odd number of them. The middle black cells of different rows lie in different columns; the middle black cells of different columns lie in different rows. (a) Prove that some cell is simultaneously the middle black cell of its row and of its column. (5 points) (b) Must every middle black cell of a row also be the middle black cell of its column? (5 points)
Neutral editorial illustration.
Neutral editorial illustration.