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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?
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  • 7
    $\begingroup$ For those wondering, the trademark symbols in the title were to circumvent this silly rule :P i.imgur.com/A6pKwhO.png $\endgroup$ – thesilican Jul 24 at 17:04
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    $\begingroup$ 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. $\endgroup$ – the default. Jul 24 at 17:29
  • $\begingroup$ @my pronoun is monicareinstate correct! Also you username is really hard to type lol $\endgroup$ – thesilican Jul 24 at 17:35
  • $\begingroup$ @MrSiliconGuy I've found a workaround so that you don't need to add trademark symbols in the title. $\endgroup$ – Toby Mak Jul 25 at 9:32
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    $\begingroup$ @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) $\endgroup$ – the default. Jul 25 at 11:52
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My path:

maze solution

Or,

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

Explanation:

important borders highlighted in purple

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.

cleaned-up maze

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!

enter image description here

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:

This maze is easier to reason through going from the end, so let's follow Frigga, who starts at the Finish. Frigga has to go through N. Now she can choose from C, K, and M. Both C and M lead to dead ends, so she chooses K. Now she can choose from E or L. L leads to a dead-end, so she chooses E. Now she can choose from D or F. D leads to a dead-end, so she chooses F. Now she can choose from G, H, and I. G leads to a dead-end, and I leads to J which leads to a dead-end, so she chooses H. And as luck would have it, H leads to the start! Now all Frigga has to do is retrace her steps and she's solved the maze.

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  • $\begingroup$ Correct! Congrats for solving in just about 35 minutes. $\endgroup$ – thesilican Jul 24 at 17:40
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    $\begingroup$ Good job for adding extensive maze-solving explaination 👏 $\endgroup$ – thesilican Jul 25 at 6:44
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Here's a graph showing the connections:

graph

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

enter image description here

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

Here's the torus maze solution on a torus.

enter image description here

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

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1

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

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