MathDB

On a

2004\times 2004

chessboard we place

2004

white knights

^1

in the upper row, and

2004

black ones in the lowest row. After a finite number of regular chess moves

^2

, we get the opposite situation where the black ones are on the top and the white ones on the bottom lines. In a turn we make a move with each of the pieces of a color. If you know that each square except those on which the knights originally lie, must not be used more than once in this process, and that after each turn no

2

knights of the same color can be attacking each other

^3

, determine the number of ways in which this can be accomplished.

^1

also known as horses

^2

the knight can be moved either one square horizontally and two vertically or two squares horizontally and one vertically, in any direction on both horizontal and vertical lines

^3

a knight is attacking another knight, if in one chess move, the first one can be placed on the second one’s place

Problem Statement