Question 59
Given positive integer $n$. Several cells of a $n \times n$ board were coloured green in a way that no two green cells share a common segment. Is it always true (i.e. no matter which cells were coloured green) that it is possible to place exactly $n$ rooks in some not green cells of board such that no rook captures any other rook if:
1. $n=20$
2. $n=19$ ?
1. $n=20$
2. $n=19$ ?