Just a little idea: What if you made a 4x4x4 with a fifteen puzzle on every side? It would turn like a 4x4x4 and slide like a fifteen puzzle. The pieces could either be colored or all one color. I don't know how you could make this or even if it is even possible, but it would be one of the hardest puzzles I could think of.

So this but a higher order version?

I tried making this puzzle by cutting rails into the puzzle. As I'm not a great modder, I never finished, and I used up that 4x4x4 on a different mod. You must be very careful about cutting up a 4x4x4 for this because while you should go deep enough for a tile to grip in, you can't go too deep before destroying a center piece, which I only narrowly escaped doing.

It is possible with simply modifying the cube by constructing add-ons. I actually plan on printing these add-ons and the tiles to go with within the next few months, as I had wished to do for years now. Feel free to beat me to it.

Solving is something I also thought a lot about. You would have to worry about orientation of the tiles that are on either an edge or a corner. The center tile orientation is alike a super-cube but according to my predictions, there is a parity case that requires the sliding feature to correct.

Yes, I would probably do this: get 6 think fun 15 puzzles, cut them up into equal sized pieces, and glue them on to a 4x4 with a slightly larger cubie size so it turns smoothly.

Unfortunetly I don't have 100$ to blow on a cube that might not even work.

So like an arrow cube with numbers instead? If so, how does it slide?

Before spending the money, try with just one 15 puzzle. In fact, I can try it out now and tell you how that goes. I have several spare 4x4x4s still and I never play with my 15 puzzle.

EDIT: Wow, I kinda like the truncated corners on this 15 puzzle.

Double-posting, but as an update. The 15 puzzle does work on the 4x4x4. It is much more rough and catches more easily, and the parts can easily fall out in mid turn. I've only applied it to one face, as I only have one 15 puzzle. If this is to be followed through, I highly suggest there being access to 5 of the 6 "16" tiles, leaving just one empty slot on the whole cube.

I don't have a working camera. Sorry about the lack of visualization of the idea. If you want to do this, you can buy 6 15 puzzles and put them on a spare 4x4x4 like this, but the empty slot total of 6 would be annoying, and the parts do easily slide off in mid turn with just one.

Did you use a wooden 15 puzzle? What 4x4 did you use?

ThinkFun Inc, a metal one.

Could you use legos? It would be alot cheaper and possibly catch less. Ill try to order them online, see how much it would cost. Any suggestions for cheap 4x4's with cubist size 15 mm?