I was surfing on internet when I came across a really interesting question -
How many scrambled Rubik's Cube configurations exist such that it takes exactly 7 moves to solve the cube.
Now while the problems sounds easy from the view that we just need to find the number of ways to shuffle a Rubik's Cube in 7 moves, it will be incredibly hard to prove that there doesn't exist a shorter way to solve the cube.
Can only one provide solution to the problem?
Details and Assumptions
You are supposed to solve any given configuration in fewest moves possible.
Any \(90°\) or \(180°\) turn counts as a single turn while \(-90°\) and \(-180°\) counts as a single turn. Meaning, we are using half or semi turn metric.
To familiarize yourself with Rubik's Cube's notations, please check this website - Rubik's Cube Notation:
Bonus, can you find the answer for other value in place of 7?