On the left, we have Sam Loyd's puzzle,
Back From the Klondike, with a correction. Apparently, the following are
Sam Loyd's original instructions: Return to my Puzzle pages
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© Copyright 2003, Jim Loy
On the left, we have Sam Loyd's puzzle,
Back From the Klondike, with a correction. Apparently, the following are
Sam Loyd's original instructions:
Euler, the great mathematician, discovered a rule for solving all manner of maze puzzles, which, as all good puzzlists know, depends chiefly upon working backwards. The accompanying puzzle, however, was built purposely to defeat Euler's rule, and out of the many attempts is probably the only one that twoarts his method.
Start from the heart in the center. Go three steps in a straight line in any one of the eight directions, north, south, east, west, or on the bias, as the ladies say, northeast, northwest, southeast, or southwest. When you have gone three steps in a straight line you will reach a square with a number on it, which indicates the second day's journey, as many steps as it tells, in a straight line in any one of the eight directions. From this new point, march on again according to the number indictaed, and continue on in this manner until you come upon a square with a number which will carry you just one step beyond the border. You will then be out of the woods and can holler all you want, for you will have solved the puzzle!
See the solution, below. As Martin Gardner pointed out in one of his Scientific American columns, Sam Loyd's diagram contained a typo which allowed two solutions. This has been corrected, perhaps by more than one person in more than one way, by changing one of the numbers. Here the 1 in the white box with the square inside, below center, was originally a 2. This particular correction was made by John Hallyburton.
Nowadays, we sometimes see simpler puzzles based on this idea, including hexagonal grids. See http://www.logicmazes.com/n1mz.html.
Solution:
SW, SW, NE, NE, NE, SW, SW, SW, NW (or SE).