Guarini's Problem

The earliest chessboard puzzle dates from 1512, almost 500 years ago. Guarini's Problem involves four knights, two white and two black, at the four corners of a small 3X3 chessboard. The white knights and the black knights need to exchange places. A knight can move on a chessboard by going two squares in any horizontal or vertical direction, and then turning either left or right one more square. It is a relatively simple puzzle to solve, even by trial and error.
The knights must march around a cycle, all in the same direction, either clockwise or counterclockwise, until their positions are exactly reversed.