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Meandering Monk Maze

Every afternoon the Monks of Knosm retire to the garden of the monastery for meditation. The garden has several clearings connected by curving paths. While the monks meditate each one stands in a different clearing and occasionally strolls along a path from one clearing to another. Only one monk moves at a time and when walking a monk always travels the entire length of a path, never stopping at any clearings he passes through along the way, and never starting a path from the middle. Most of the paths are open to anyone, but some paths are reserved for certain monks.

At no time does a monk enter or pass through a clearing occupied by another monk. Every day the monks continue walking until they are back to their starting positions except that the monks wearing the red and blue cloaks have swapped positions.

Can you move the monks to their final locations in the garden?


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The Meandering Monk Maze is one project where I feel like the software shouldered a significant fraction of the creative burden. I started with some general ideas about using some simple parameters to create sliding coin puzzles and the Java program took it from there. For example, it is interesting to note that the software does not constrain the starting and ending positions to occupy the same circles, nor does it require that the starting and ending positions differ by the exchange of two pieces. The start and end locations vary randomly and the software looks for the puzzle with the longest solution using a few constraints. However, if the program is allowed to run long enough the random mutations always converge on mazes with the start and end related by a single exchange.

I found puzzle 3 to be very difficult and so I challenged people to send me the shortest solution. In very short order I received two correct answers. Yogy Namara submitted the first correct solution, and Jacob Mandelson submitted the second. The shortest solution found by them (and by the software that created the puzzle) is 174 moves, but the best I've been able to do solving by hand is 180.

The Meandering Monk Maze was inspired by Robert Hearn's excellent Martin Gardner coin puzzle. (See the 19 April 2004 entry at MathPuzzle.com.)

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Puzzles and applet copyright 2004 by James W. Stephens.
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