So I've been thinking about new puzzles and come up with a few ideas.

1) 4x4 Bump/Mirror cube - this one shouldn't be too hard, using a ball core and the same outer workings as a 3x3 bump/mirror cube.

2) Gravity-based bandaged cube - uses pins inside the cube to change the bandaging based on the up face (i.e. if white is up some pieces bandage but not the same as if green were up).

3) 2x1xn slide puzzle - a 2x1xn puzzle that has a sliding mechanism so different layers can interact with each other, this one is harder to describe but essentially it is simple, for example on a 2x1x7 the 2nd layer can only swap with the 6th layer, but if you could slide one of the sides to line up the left half of the 2nd layer with the right side of the 3rd it would be able to move all the edges around, for the puzzle to work properly it would need like a gradient fill sticker set down the 2xn side.

I will add to this thread in due course but for now Tell me what you think.

Thanks,
prof.

Why a ball core?

It makes it easier.

How exactly could you make the centers on the 4x4 different sizes?

I've played with Mirror Cube ideas past 3x3x3 and the only way you could pull it off is by having the outside layers being different lengths; the center pieces will have to remain the same length. This is based on my research of the idea.

Try an evil twin 4x4. those are just like a bump 4x4
You can get them of HKNowstore.