In April 2124, the International Chess Federation made a big splash by announcing that it wanted to modernize the rules of the game, unchanged for centuries. A new piece, called tourfou, was introduced onto the chessboard.
How the tourfou works is simple: every other move, it behaves like a tower, that is to say it can move horizontally or vertically as many squares as desired. And, every other move, like crazy, which means that it then moves diagonally, as many squares as desired. Figure A shows the movement of a single tourfou on the chessboard which crosses 20 squares.
Game specialists quickly studied the possibilities of this new piece. In particular, we asked ourselves this question:
Can a single player on the chessboard travel a path that passes through each of the 64 squares once and only once?
We know that such a route is easy to find for the rook (see figure B), while it is impossible for the bishop, the latter being condemned to always stay on squares of the same color. Which side was the turmoil on?
Of course, the same question arose when in 2224 the federation decided to introduce the cavalou, half-rider, half-madman.
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