[Illustration:
+-----+-----+-----+-----+-----+-----+-----+-----+
| | | | | | | | |
| ............. ....... ............. |
| . | | . | . | . | . | | . |
+--.--+-- --+--.--+--.--+--.--+--.--+-- --+--.--+
| . | | . | . | . | . | | . |
| ....... ....... ....... ....... |
| | . | | | | | . | |
+-- --+--.--+-- --+-- --+-- --+-- --+--.--+-- --+
| | . | | | | | . | |
| ....... ....... ....... ....... |
| . | | . | . | . | . | | . |
+--.--+-- --+--.--+--.--+--.--+--.--+-- --+--.--+
| . | | . | . | . | . | | . |
| ............. ....... . ....... |
| | | | | | . | . | |
+-- --+-- --+-- --+-- --+-- --+--.--+--.--+-- --+
| | | | | | . | . | |
| ............. ....... . ....... |
| . | | . | . | . | . | | . |
+--.--+-- --+--.--+--.--+--.--+--.--+-- --+--.--+
| . | | . | . | . | . | | . |
| ....... ....... ....... ....... |
| | . | | | | | . | |
+-- --+--.--+-- --+-- --+-- --+-- --+--.--+-- --+
| | . | | | | | . | |
| ....... ....... ....... ....... |
| . | | . | . | . | . | | . |
+--.--+-- --+--.--+--.--+--.--+--.--+-- --+--.--+
| . | | . | . | . | . | | . |
| ............. . P ............. |
| | | | | | | | |
+-- --+-- --+-- --+-- --+-- --+-- --+-- --+-- --+
]
A French prisoner, for his sins (or other people's), was confined in an
underground dungeon containing sixty-four cells, all communicating with
open doorways, as shown in our illustration. In order to reduce the
tedium of his restricted life, he set himself various puzzles, and this
is one of them. Starting from the cell in which he is shown, how could
he visit every cell once, and only once, and make as many turnings as
possible? His first attempt is shown by the dotted track. It will be
found that there are as many as fifty-five straight lines in his path,
but after many attempts he improved upon this. Can you get more than
fifty-five? You may end your path in any cell you like. Try the puzzle
with a pencil on chessboard diagrams, or you may regard them as rooks'
moves on a board.