This is a challenge for 3x3 that I came up with a while ago. The main idea is to limit what you can do by "gluing" your fingers to the cube (not literally!). By that, I mean that you imagine some fingers being stuck to certain stickers, and you're not allowed to move/lift them at all (until you solve the cube). You're allowed to rotate the fingers around the stickers though (in particular, you can turn a face even if a finger is glued to its center). In the most basic version, you have 4 fingers glued to the cube. The left thumb is glued to the F center, the left middle finger is glued to the B center, the right thumb is glued to the FR sticker and the right middle finger is glued to the BR sticker. In order to make sure that the cube is solvable, simply scramble the cube with the fingers glued like that. Other than that, you're free to solve it any way you like.
I'll explain one more variant that I found pretty challenging, but there might be other interesting ways of gluing the fingers as well! You start just like with the basic version, gluing four fingers to the cube. On top of that you glue the left pinky to the D center, the left ring finger to the BD sticker and the right ring finger to the BDR sticker. This limits what you can do by a lot.
Please let me know if anything is unclear
I'll explain one more variant that I found pretty challenging, but there might be other interesting ways of gluing the fingers as well! You start just like with the basic version, gluing four fingers to the cube. On top of that you glue the left pinky to the D center, the left ring finger to the BD sticker and the right ring finger to the BDR sticker. This limits what you can do by a lot.
Please let me know if anything is unclear
