Changing-Rule Number Maze            

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for the rules
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to restart

To the 6x6 Number Maze.

To the 7x7 Number Maze.

To the No-U-Turn Number Maze.

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Further notes: I think this is the best of my number mazes. It first appeared in Mad Mazes, published in 1990. I hadn’t looked at the maze since 1990 and I’d completely forgotten the solution. After I wrote this program, I tried solving the maze and discovered it was pretty hard. And it was a lot of fun. I think the solution follows a rather amusing route.

If you’ve been visiting, you may have noticed that Ed Pegg refers to my puzzles as “multi-state mazes.” The 6x6 Number Maze and the 7x7 Number Maze didn’t quite fit that description because when you are on a particular square in one of those mazes you can only be in one state. But the Changing-Rule Number Maze is truly multi-state. When you’re on a particular square here you can be in one of two states, depending on which rule is currently in effect. The next maze in the series, the “No-U-Turn Number Maze,” is also multi-state. When you’re on a particular square in that maze you can be in one of four different states depending on the direction you entered the square. By the way, although the the 6x6 and the 7x7 maze use rules that go back at least as far as Sam Loyd, the Changing-Rule and the No-U-Turn mazes use rules that are original inventions of mine.