Question 23
For $n \gt 1$, consider an $n \times n$ chessboard and place pieces at the centers of different squares.
a. With $2n$ chess pieces on the board, show that there are 4 pieces among them that form the vertices of a parallelogram.
b. Show that there is a way to place $(2n-1)$ chess pieces so that no 4 of them form the vertices of a parallelogram.
a. With $2n$ chess pieces on the board, show that there are 4 pieces among them that form the vertices of a parallelogram.
b. Show that there is a way to place $(2n-1)$ chess pieces so that no 4 of them form the vertices of a parallelogram.