Puzzles belonging to this category require repeated manipulation of an object in order to obtain the desired shape and state. The most well-known puzzles of this kind are the Rubik's Cube and the Tower of Hanoi.
Furthermore, this category includes those puzzles where several parts must be put in the right position, among which the best known is the 15 Puzzle.
Rubik's Cube caused an unprecedented boom in this category. The number of variants is amazing: cubes of 2×2×2, 3×3×3, 4×4×4, 5×5×5, 6×6×6 and 7×7×7 dimensions were created, as well as tetrahedral, octahedral, icosahedral and dodecahedral variants based on different types of cylinders.
With a variant orientation of the rotation axis, various puzzles with the same basic figure could be generated. In addition, other cube-shaped puzzles could be obtained by cutting one of the sides from a cube. These puzzles take irregular shapes when manipulated.
The picture below is a lesser known example of this kind of puzzles. It's quite easy, so it could be solved by trial and error, keeping in mind some details, unlike Rubik's Cube which is too difficult to solve only by trial and error.
Some examples are: