# Nodes & Tunnels

An entry in Fortnightly Topic Challenge #33: Surface Geometry Mazes

Behold, a tricky maze created on the surface of a cube. There are 'nodes' to collect and tunnels to traverse, are you up to the challenge?

I have unfolded the cube and created a legend to aid your mission, you can also find the rules below! (Click images for a closer look):

Here is the maze in all it's unfolded glory, remember even in this condition it is still a cube!:

Answers should adhere to the above parameters, shown preferably with a nice long scrawl over my original image but feel free to improvise!

There is at least one correct path but as with the nature of such a puzzle other solutions may exist. The first answer given that meets the criteria will be awarded the tick, if it's quite different to my solution I will also share mine as a second answer :)

Extra information for those that like to think out of the box, you can't jump walls, climb, fly, reach that node just over there, squeeze past your old paths, re-use tunnels or become a giant to take the whole maze and all it's nodes in one grab, etc ;)

EDIT: Quick rules clarification as a relative brought it up when attempting the puzzles, use of tunnels is optional. Whether completion is possible without them is another thing!

Good luck and I hope you have fun solving it!

• Few we didn't only have one question at the end of the fortnight (and here is 1k, grats! :) ) Jul 14, 2017 at 15:05
• And I just realised I can't spell 'phew' Jul 14, 2017 at 15:33
• Very stylish puzzle! Really nice looking. I like your tunnel innovation on the classic maze. Jul 14, 2017 at 15:49
• I will make a 3D Printable version of the cube maze available (with and without nodes) for anyone that would like a .stl, let me know and I'll upload to Thingiverse. Jul 14, 2017 at 15:50
• I hope we aren't being chased by ghosts while doing this. Jul 14, 2017 at 15:55

This seems to work:

Green is the path. Purple is showing how many times we enter each face.

Highly sophisticated method of solution: Trial and error. (I started by filling in things that were forced, then just drew stuff. I ended up with a couple of loops and some bits that wouldn't connect, and fixed things up incrementally.)

• Wow awesome, some sections are just like mine but your overall route is different, quick work well done! :) Jul 14, 2017 at 16:33

As promised, here is my solution that was made when designing the maze:

I will probably make another in the near future as it was a fun process. For those wondering I used Fusion360 to make the maze and Clip Studio Paint for the additional details.

For the next maze I would like some suggestions and feedback if possible so please comment below or ping me on the chat.

A bigger cube?
A different shape?
Better layout/decorative details?
Bridges (maybe between multiple shapes)?
More restrictions/rules?
Non-Euclidean shapes?
Don't bother? ;)

• I like the bridges idea and also maybe a door/key combo where you need one before taking that path? Perhaps one way paths? Jul 17, 2017 at 19:43
• Fantastic ideas. If I use either I will be sure to credit you :) Jul 17, 2017 at 21:06