MathDB

Let

n

be an odd positive integer and consider an

n \times n

chessboard of

n^2

unit squares. In some of the cells of the chessboard, we place a knight. A knight in a cell

c

is said to attack a cell

c'

if the distance between the centers of

c

and

c'

is exactly

\sqrt{5}

(in particular, a knight does not attack the cell which it occupies). Suppose each cell of the board is attacked by an even number of knights (possibly zero). Show that the configuration of knights is symmetric with respect to all four axes of symmetry of the board (i.e. the configuration of knights is both horizontally and vertically symmetric, and also unchanged by reflection along either diagonal of the chessboard).
NIkolai Beluhov

Problem Statement