I have already written about the labyrinth on Rubik’s Cube. I had presented a template for making a model. I’ve used that myself and made a labyrinth cube out of it. This is how it looks like: Ariadne’s thread runs on the surface of the vsible miniature cubes. The 9 faces of the miniature cubes on “down” and the 7 on “up” were not used.
That gave me the idea of whether it would not be possible to include all the miniature cubes?
And I offer a solution for this:
The Rubik’s Cube has all in all 26 pieces. The core mechanism is fixed and holds the 6 center pieces with one coloured face. The 12 edge pieces show two coloured faces, and the 8 corner pieces have three coloured faces.
Ariadne’s thread should now run through all the little cubes. So 6 times one face is visible, 12 times two faces and 8 times three faces.
It looks like this on the template:
Ariadne’s thread is shown in color here. The labyrinth should be the type Knossos labyrinth with the path sequence 3-2-1-4. Green stands for 3, blue for 2, brown for 1. The center is white (4), and can only be reached if you pass through the invisible center (= core mechanism) from the “up” surface.
The beginning of Ariadne’s thread is the green edge cube with three coloured faces in the lower left “front”. Then you run up to the next edge cube with three coloured faces, you run around the “up” surface, following the “back” surface, then the “right” surface to the green/blue coloured face edge cube, which initiates the line of the blue cubes. The next change is in the “left” surface from blue to brown.
There is also a template that can be used to build a model. Here you can see, print or download the template as a PDF file.
I tried it myself and made a more or less successful cube.
In the large picture on the left you can see the “up” surface, the “left”, and the”front” surface from above. In the three smaller pictures the cube is each rotated by 90 degrees.
Here in a tilted representation:
In the large picture on the left, you can see the “front”, “left” and “down” surface from above. In the three smaller pictures the cube is rotated by 90 degrees again.
I cannot judge how difficult that would be to solve. Especially if you do not say beforehand what that should be and you should find the beginning and the end of the thread yourself.
Perhaps one could make the specification: connect the green cube with the white cube and go over all miniature cubes.