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I was toying around with grid-based puzzles, and I can up with a format that I'm not sure exists yet, and from my testing leaves only one solution. (If it exists or is broken, please let me know so I can adjust this post.)

I'm calling this a hidden path maze. These are the rules:

  • The objective is to draw a path from the entrance of the maze to the exit.
  • Every square in the grid is either part of the path, or a wall.
  • The numbers indicate how many squares of wall are in a block, including that square. Walls are considered connected into a block if they are orthagonally adjacent
  • A dot represents a section of wall that must be included as part of a numbered wall block.
  • Walls can only exist as numbered blocks. There can be no walls that are not connected to a numbered block.
  • The path may only connect orthogonally adjacent squares.
  • The path may not intersect any of the walls in the maze.
  • The path will always follow the most direct route to the goal. As such, the path may not run adjacent to itself. (example below)

Direct path rule example image

Here is an example of a solved board:

Example puzzle solved image

Using these rules, it should be possible to solve the following boards.

Easy board:

Easy puzzle image

Moderate board:

Moderate puzzle image

And if these are popular I'll make some more :)

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  • $\begingroup$ Are all the numbers always given? $\endgroup$ – SteveV Sep 23 '18 at 12:27
  • $\begingroup$ For the current ruleset, every number is provided, because no walls are allowed to be isolated from a numbered block. $\endgroup$ – Yessoan Sep 23 '18 at 13:26
  • $\begingroup$ Well, I love these! $(+1)$ $\color{darkorange}{\bigstar}$ :D $\endgroup$ – Mr Pie Sep 24 '18 at 6:26
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My solutions.

First

Easy solution

Second

Moderate solution

I think the puzzles are fun, for what it's worth!

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  • $\begingroup$ Thank you very much, I'm glad you liked them. I'm thinking of ways to increase the difficulty beyond just making the board bigger, but I'll also probably make some larger ones too. $\endgroup$ – Yessoan Sep 23 '18 at 13:24
  • $\begingroup$ There are at least three other solutions for the first one. (rot13) Lbh pna bognva bar ol zbivat gur yrsgzbfg jnyy gvyr va gur hccre yrsg oybpx bs 3 vagb gur gbc ebj. Lbh pna qb fbzrguvat fvzvyne ba gur oybpx bs 3 ng gur ybjre evtug, zbivat gur evtugzbfg gvyr gb gur obggbz ebj. N fbyinoyr znmr vf bognvarq vs lbh qb bayl bar bs gurfr zbirf, be obgu, sbe guerr zber fbyhgvbaf. $\endgroup$ – Michael Seifert Sep 23 '18 at 20:57
  • $\begingroup$ @MichaelSeifert I may be misunderstanding what you mean, but doesn't that violate the second rule "Every square in the grid is either part of the path, or a wall."? $\endgroup$ – SteveV Sep 23 '18 at 21:22
  • $\begingroup$ @SteveV: No, you're right. Objection withdrawn. $\endgroup$ – Michael Seifert Sep 23 '18 at 21:49

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