by Dudeney, Henry Ernest, 1857-1930
Available in 215 free installments
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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. p 9 " 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.
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 anyA, 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:?
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.
329.?THE STAR PUZZLE.
Put the point of your pencil on one of the white stars and (without ever lifting your pencil from the paper) strike out all the stars in fourteen continuous straight strokes, ending at the second white star. Your straight strokes may be in any direction you like, only every turning must be made on a star. There is no objection to striking out any star more than once.
In this case, where both your starting and ending squares are fixed inconveniently, you cannot obtain a solution by breaking a Queen's Tour, or in any other way by queen moves alone. But you are allowed to use oblique straight lines?such as from the upper white star direct to a corner star.
330.?THE YACHT RACE.
Now then, ye land-lubbers, hoist your baby-jib-topsails, break out your spinnakers, ease off your balloon sheets, and get your head-sails set!
Our race consists in starting from the point at which the yacht is lying in the illustration and touching every one of the sixty-four buoys in fourteen straight courses, returning in the final tack to the buoy from which we start. The seventh course must finish at the buoy from which a flag is flying.
This puzzle will call for a lot of skilful seamanship on account of the sharp angles at which it will occasionally
be necessary to tack. The point of a lead pencil and a good nautical eye are all the outfit that we require. p 9 100
4*44*
A
4
-4
4
d
0
4
4
M
j
This is difficult, because of the condition as to the flag-buoy, and because it is a re-entrant tour. But again we are allowed those oblique lines.
331.?THE SCIENTIFIC SKATER.
<>U t \
40 *» J^_
******** ********
It will be seen that this skater has marked on the ice sixty-four points or stars, and he proposes to start from his present position near the corner and enter every one of the points in fourteen straight lines. How will he do it? Of course there is no objection to his passing over any point more than once, but his last straight stroke must bring him back to the position from which he started.
It is merely a matter of taking your pencil and starting from the spot on which the skater's foot is at present resting, and striking out all the stars in fourteen continuous straight lines, returning to the point from which you set out.
332.?THE FORTY-NINE STARS.
