A regular Rubik's cube has a staggering number of possible states. However, that number is most decidedly finite; after all, a quintillion is just as far from infinity as seven is. From this finiteness it immediately follows, that any sequence of rotations, twists and turns, however complex, will have a cycle.
What I mean by that is that if you perform the sequence again on the resulting cube, and just keep on repeating, the cube will at some point return to the original position. (The cube will eventually run out of states that weren't already visited.)
These sequences are usually called algorithms. For the purpose of this puzzle, I'll redefine "algorithm" in terms of real world appearance of the cube:
An algorithm is any sequence of physical manipulation of the cube that results in the cube being in the same shape as before, in the same place as before, and at least one of the sticker positions now showing a different colour. $^*$
You are to keep this definition as a given, even if it might contradict with any other definitions, including the one you think is the correct one.
Now then, all algorithms can be categorised by the length of their cycle.
For example, the algorithm typically denoted with U (a quarter turn of the topmost layer) will return the cube to the original position after exactly 4 repetitions. Therefore, U has a cycle length of 4.
Some examples of algorithms with cycle length 2 would be
- 180° turn on the left face (L2)
- swapping any two pieces while preserving orientation
- turning the cube upside down
- flipping any given pair of edges
- ..and so on and so forth.
It's pretty easy to come up with algorithms with a cycle length of any N, as long as N is a power of two. Finding cycles of other lengths is a bit more challenging. Especially the ones that have a cycle length of 3 are not so common, and the first ones that spring to mind are usually quite complicated. So here, finally, we get to the puzzle:
Find the simplest algorithm (as defined above) that returns the original colours to all sticker positions when performed exactly 3 times.
The intended solution is simple both in terms of the physical movements involved, and speed, as in "time required to perform on a cube initially lying on a timer pad".
$^*$: You probably already noticed why it's important to disallow "null algorithms" and twists that are not a multiple of 90°. Also, you probably agree that even though the definition basically allows disassembling and reassembling the entire cube, it doesn't really matter here.