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?
- The filled circles are pieces that represent the monks. The open circles represent the clearings in the garden.
- The goal is to move the monks into the clearings of the same color. (The color of the clearings does not otherwise affect
the movement of the pieces.)
- A piece can move along any white path or along a path that is the same color as the piece.
- A piece musts always travel the complete length of a path from dot to dot. A piece may not
start a path in the middle or stop before completing the entire length of a path.
- A piece may not move along a path if the destination or any clearings along the way are occupied by another piece.
- The small numbers beside the clearing are for reference only and do not effect the movement of the pieces.
- To move a piece, click once to select it, and then click again the clearing that is its destination.
(Select the final clearing on the path, not one in the middle of the path.)
- Undo a move - press U or click the undo arrow in the lower right.
- Redo a move - press R or click the redo arrow in the lower right.
- Next puzzle or previous puzzle - Click on the arrows at the upper left and right.
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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