# A torus maze™™™™™

Since this is a torus maze, the left side of the maze connects to the right side and the top of the maze connects to the bottom. Corresponding openings in the walls of the maze have been labeled for your convenience.

Your goal is to get from the start (top left) to the finish (bottom right).

Be sure to check out this excellent post by humn for tips on maze solving

Unrelated mini-puzzle: The first 14 digits of pi are hiding around the maze. Can you find them?
• For those wondering, the trademark symbols in the title were to circumvent this silly rule :P i.imgur.com/A6pKwhO.png Jul 24, 2020 at 17:04
• I think the digits of pi are the lengths of gaps between letters on the sides, starting from the upper left corner and going counterclockwise. Jul 24, 2020 at 17:29
• @my pronoun is monicareinstate correct! Also you username is really hard to type lol Jul 24, 2020 at 17:35
• @MrSiliconGuy I've found a workaround so that you don't need to add trademark symbols in the title. Jul 25, 2020 at 9:32
• @TobyMak I think your comment is incomplete (especially since you don't seem to have any questions on puzzling.se). (I know about a workaround with zero-width spaces) Jul 25, 2020 at 11:52

My path:

Or,

Start -> H
H -> F
F -> E
E -> K
K ->N
N -> Finish

Explanation:

Here I have highlighted the important walls in purple, splitting the maze into sections. Every area within a section can be reached from every other, and (obviously, since I highlighted walls) there are no ways to go from one section to another.

Here I've cleaned up the maze, leaving just the important borders. (Yes, I manually drew all of those walls in Google Sheets. Where did my life go?). This maze looks much easier!

Now we're talking! I've straightened out the borders so now there are lots of neat rectangles. (Yes, I also did this manually).

Reasoning through the cleaned-up maze:

• Correct! Congrats for solving in just about 35 minutes. Jul 24, 2020 at 17:40
• Good job for adding extensive maze-solving explaination 👏 Jul 25, 2020 at 6:44

Here's a graph showing the connections:

where start is at node "0", end at node "1".

The most straightforward solution is then:

$$0 \longrightarrow H\longrightarrow G\longrightarrow F \longrightarrow E\longrightarrow K\longrightarrow M \longrightarrow N\longrightarrow 1$$

Here's the solution on maze

where the red squares in the maze are the blockades/misdirects.

Here's the torus maze solution on a torus.

where the red and green squares are the start and endpoints.

• (+1) What software did you use to create the torus? Jul 25, 2020 at 19:17
• @TheSimpliFire oh just mathematica....mathematica.stackexchange.com/a/103221/65285. Just an image texture on a torus. Jul 25, 2020 at 20:54
• Cool torus image! Jul 29, 2020 at 8:22

Solution done by the bfs algorithm. And here is the video how does bfs fill the maze and traces back.