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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?
thesilican
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3 Answers3

42

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.

bobble
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15

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.

lineage
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3

1

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

Alexey Burdin
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