A 3x3 Rubiks cube
A 5x5 cube
A megaminx (dodecahedron)
I’ve also had in my possession, over the years, a 4x4, pyraminx, and a few other random rubiksish puzzles (the snake, rubik’s magic, etc) which were pretty straightforward by comparison.
It seems to me, from playing around that:
A 4x4 cube is a reasonable degree harder than a 3x3
A 5x5 and higher is **not **appreciably harder than a 4x4 … once you can do a 3x3 and a 4x4 you can do anything.
A pyramid shape is much easier than a cube.
The dodecahedron shape is **also **possibly easier than a cube - certainly not harder.
So … there’s lots of cubey things out there. A Gigaminx looks promisingly tricky. But is there anything else out there among the many many different Rubik’s Cuboids now available that’s harder than a cube? Particularly **unexpectedly **hard…
Folks who can do all of them report that a 5x5 has a few techniques not found in a 4x4, but that above that, any edge dimension can be done using the same techniques as those two. There’s more steps involved, of course, and God help you if you lose track of what you’re doing in the middle of a move sequence, and the bigger cubes are often mechanically stiffer, but there’s nothing new intellectually.
Once you get beyond the cubes to other shapes, it’s difficult to make proper comparisons, because other shapes aren’t nearly as well-studied. Pick up any given twisty-puzzle, and it might take you a while, just because the techniques needed are unfamiliar to you, but that doesn’t necessarily mean that they’re any more difficult once you learn them.
I’ve modified cubes. Took a standard 3x3x3 and made it so that each face had one cubelet of a color (used nine colors, obviously). So that the goal was not to have each face uniform, but rather as un-uniform as possible. Solved it any number of times and once I started keeping track and none of the solutions were the same. It’s harder than the standard cube because you have to think about where you’re putting the pieces rather than just putting them there.
I also modified a 4x4x4, adding two colors to the standard six. Each corner and edge piece is a single color. It’s harder than a standard 4x4x4 because most folks start those by rebuilding the centers. This is actually my favorite cube and when solved it has eight two by two blocks.
I once tried to modify a cube for a friend with different textures. She could almost solve a regular cube blindfolded. This cube was intended to literally be solved with your eyes closed.
Ooh, that reminds me, I have a sudocube lying around. Each face has the numbers 1 through 9. Which is basically the same thing as E-DUB’s cube of many colors, though it probably has a different specific arrangement.
And I’ve also seen a blind kid using a textured cube.
Back in their hey-day (the 80s) my cousin had one of the pyramid shaped ones (technically a regular tetrahedron). I played with it for a minute of two then decided to just get one face and put it down. After I got one face (which was way easier than getting one side of a 3x3 Rubik’s) I did a double-take suddenly realizing that I had inadvertently solved the whole thing without even trying*!*
