“Euler, the great mathematician, discovered a rule for solving all manner of maze puzzles, which as all good puzzlists know, depends chiefly on working backwards. This puzzle was, however, built purposely to defeat Euler’s rule and out of many attempts is probably the only one which thwarts his method.” Sam Loyd, in Cyclopedia of Puzzzles, page 106.
Back from the Klondike is one of Sam Loyd's most famous puzzles, first printed in1898. In introducing the puzzle, Loyd describes it as having been constructed to specifically foil Leonhard Euler's rule for solving any maze puzzle by working backwards.
The following are Sam Loyd's instructions in “Cyclopedia of Puzzles”.
“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, 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 indicated, 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, when you are out of the woods and can holler all you want, as you will have solved the puzzle.”
The solution to this puzzle will be post on 6/25/2016.