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The Mazing (Posted on 2003-10-02) Difficulty: 3 of 5
A maze is to be constructed on an X by Y grid of squares by creating "walls" between them.

The process starts with an enclosed rectangle X squares wide and Y squares tall, with walls on the outside edges of the outermost squares. Here's an example of a (6 x 2) rectangle:

       |                 |
       +  +  +  +  +  +  +
       |                 |
We then build additional walls in the following manner:
  • Pick an existing wall (A) at random.
  • Pick (also at random) a potential non-existent wall (W) that will be adjacent to (A). (W) must be a valid wall - it must be inside the maze.
  • Ensure that (W) will not connect wall (A) to any other wall - that is that there is no existing wall (B) that is is distinct from (A) and non-adjacent to (A) but that would be adjacent to (W).
  • Place wall (W) only if the above condition is satisfied.

    By following in these steps, what is the theoretical maximum number of walls that can be placed? Is there a situation where walls can be placed in such a way that achieving this maximum will no longer be possible?

  • See The Solution Submitted by levik    
    Rating: 3.3333 (3 votes)

    Comments: ( You must be logged in to post comments.)
      Subject Author Date
    Going in CirclesBrian Smith2003-10-03 09:29:32
    why didn't my <pre> work?Charlie2003-10-02 22:25:40
    SolutionsolutionCharlie2003-10-02 22:16:07
    Hints/TipsFor startersCharlie2003-10-02 15:45:16
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