Wildcard Sequence Mazes
1st May 2019
The May competition maze on Mazelog was a type of logic maze I haven't featured before which I call the Wildcard Sequence Maze.
One of the things that started my interest in unusual mazes was a paperback I found in a secondhand bookshop many years ago called "For Amazement Only" by Walter Shepherd. It was originally published by Penguin Books during the Second World War in 1942:
It features 50 mazes, many of which have unusual layouts or rules. My copy is very yellowed, and the pages are falling out.
One of the mazes was called "Scissors Cut Paper", and to my knowledge it's the first published example of what I call a Sequence Maze. You have to start from the top left corner and move one square at a time, horizontally, vertically, or diagonally, to find the shortest path to the bottom right-hand corner. You must follow the sequence scissors, paper, stone, scissors, etc.:
In the Answers section Walter Shepherd gives the following 15-step solution:
In fact there's a 12-step solution which he must have overlooked. Can you find it?
Easy as ABC
I created my own Sequence Maze several years ago called "Easy as ABC". In this maze you start at the top left corner and you can only move horizontally or vertically. You must follow the sequence a, b, c, a, etc., and find the shortest path to the bottom right-hand corner.
If you try it you'll see that it really is easy; you probably don't even need a pencil and paper to work it out:
You can try solving it interactively using the Maze Walker here: Easy as ABC.
A better Sequence Maze
For a long time I considered Sequence Mazes to be a bit of a dead end because it's not possible to make them particularly difficult, and so I didn't include them in Mazelog.
However, it recently occurred to me that you could introduce a wildcard, representing any letter, which would have the effect of converting the maze into a state maze. In other words, it might now be necessary to visit the same square more than once at different points along the route, depending where you came from.
Another improvement is to add the "no U-turn" rule; in other words you are not allowed to jump straight back in the direction you've just come from.
Here's an example; as before, start in the top left corner, move horizontally or vertically, follow the sequence a, b, c, a, etc., and find the shortest path to the bottom right-hand corner. When you land on an asterisk you can choose to use it as any letter, and you are not allowed to jump straight back in the direction you've just come from:
If you try solving this you'll see that it's much harder than the simple Sequence Mazes. With the addition of the wildcard and the "no U-turn" rule the Wildcard Sequence Maze theoretically has six states: it may be necessary to visit the same square six times to solve the maze!
If you find yourself unable to solve it the solution is here: Wildcard Sequence Maze Solution.
Try the larger Wildcard Sequence Maze given as May's Monthly Maze Competition: Abacus.
There's another, even harder, Wildcard Sequence Maze given as June's Monthly Maze Competition: Alphabet.
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