About a year ago I built a bandaged Square-1 variant with single, double, and triple
width pieces. But I didn't unveil it due to endless problems with the laser-cut tiles I had used instead of stickers. They were too thick, they snagged on the puzzle's movements, they picked up fingerprints, they flaked off, and the glue kept showing through the tiles.
I recently built a second one (left) a stickered it with thinner PVC tiles I built on my 3D printer. Sorry, I neglected to use the same color scheme on the two puzzles (built a year apart) so it's hard to make direct comparisons.
File comment: Thin PVC tiles at left, thick acrylic tiles at right.
IMG_2838.JPG [ 170.57 KiB | Viewed 1329 times ]
As an added solving challenge I used an asymmetrical bandaging scheme. At the start, the green side is bandaged so the triple-width pieces are adjacent, allowing movement along only two
cuts. The yellow side is bandaged with matching pairs diagonally opposite each other, allowing movement along three
File comment: Green side
IMG_2840.JPG [ 166.28 KiB | Viewed 1329 times ]
File comment: Yellow side
IMG_2841.JPG [ 177.49 KiB | Viewed 1329 times ]
At first it seems like the puzzle can't get very mixed up because most of the available cuts are at 90-degree angles from each other. But there are enough 30-degree angles to allow an occasional turn, at which point the puzzle can get really tough. You can reach the point where there's only one turnable cut per face, and it's hard to avoid getting stuck in perpetual loops.
File comment: Two possible cuts at 90-degree angles.
IMG_2843.JPG [ 194.28 KiB | Viewed 1329 times ]
File comment: Two possible cuts at 30-degree angles.
IMG_2844.JPG [ 171.3 KiB | Viewed 1329 times ]
File comment: Only one possible cut.
IMG_2845.JPG [ 181.36 KiB | Viewed 1329 times ]
Even simple rearrangements can be difficult because of the bandaging.
IMG_2846.JPG [ 150.08 KiB | Viewed 1329 times ]