The puzzle of making a complete tour of the chessboard with the queen in
the fewest possible moves (in which squares may be visited more than
once) was first given by the late Sam Loyd in his _Chess Strategy_. But
the solution shown below is the one he gave in _American Chess-Nuts_ in
1868. I have recorded at least six different solutions in the minimum
number of moves--fourteen--but this one is the best of all, for reasons
I will explain.
[Illustration:
+---+---+---+---+---+---+---+---+
| | | | | | | | |
| ............................. |
| . | | | | | | | . |
+-.-+---+---+---+---+---+---+-.-+
| . | | | | | | | . |
| . | ..........................|
| . | .| | | | | | . |
+-.-+---.---+---+---+---+---+..-+
| . | |. | | | | . . |
| . | ................. | .| . |
| . | .| .| | |. | . | . |
+-.-+---.---.---+---.---+.--+-.-+
| . | |. |. | .| . | . |
| . | . | . | . | . | .| . | . |
| . | ..| .| .|. | . |.. | . |
+-.-+-.-.---.---.---+.--.-.-+-.-+
| . | . |. |. .|. . .| . | . |
| . | . | . | . | ..| . | . | . |
| . | . | .|. .| ..|. | . | . |
+-.-+-.-+---.---..--.---+-.-+-.-+
| . | . | .|. .. .|. | . | . |
| . | . | . | ..| . | . | . | . |
| . | . |. | ..|. .| .| . | . |
+-.-+-.-.---+.--.---.---.-.-+-.-+
| . | ..| . .|. |. |.. | . |
| . | . | .| . | . | . | . | . |
| . |.. | . |. | .| .| ..| . |
+-.-.-.-+.--.---+---.---.-.-.-.-+
| ..| . . .| | |. |.. |.. |
| . | ..| ............. | . | . |
| | . | | | | | | |
+---+---+---+---+---+---+---+---+
]
If you will look at the lettered square you will understand that there
are only ten really differently placed squares on a chessboard--those
enclosed by a dark line--all the others are mere reversals or
reflections. For example, every A is a corner square, and every J a
central square. Consequently, as the solution shown has a turning-point
at the enclosed D square, we can obtain a solution starting from and
ending at any square marked D--by just turning the board about. Now,
this scheme will give you a tour starting from any A, B, C, D, E, F, or
H, while no other route that I know can be adapted to more than five
different starting-points. There is no Queen's Tour in fourteen moves
(remember a tour must be re-entrant) that may start from a G, I, or J.
But we can have a non-re-entrant path over the whole board in fourteen
moves, starting from any given square. Hence the following puzzle:--
[Illustration:
+---+---+---+---*---+---+---+---+
| A | B | C | G " G | C | B | A |
*===*---+---+---*---+---+---+---+
| B " D | E | H " H | E | D | B |
+---*===*---+---*---+---+---+---+
| C | E " F | I " I | F | E | C |
+---+---*===*---*---+---+---+---+
| G | H | I " J " J | I | H | G |
+---+---+---*===*---+---+---+---+
| G | H | I | J | J | I | H | G |
+---+---+---+---+---+---+---+---+
| C | E | F | I | I | F | E | C |
+---+---+---+---+---+---+---+---+
| B | D | E | H | H | E | D | B |
+---+---+---+---+---+---+---+---+
| A | B | C | G | G | C | B | A |
+---+---+---+---+---+---+---+---+
]
Start from the J in the enclosed part of the lettered diagram and visit
every square of the board in fourteen moves, ending wherever you like.