Answer:
The number of possible permutations of the squares on a Rubik’s cube seems
daunting. There are 8 corner pieces that can be arranged in 8! ways, each
of which can be arranged in 3 orientations, giving 38 possibilities for each
permutation of the corner pieces. There are 12 edge pieces which can be
arranged in 12! ways. Each edge piece has 2 possible orientations, so each
permutation of edge pieces has 212 arrangements. But in the Rubik’s cube,
only 1
3
of the permutations have the rotations of the corner cubies correct.
Only 1
2
of the permutations have the same edge-flipping orientation as the
original cube, and only 1
2
of these have the correct cubie-rearrangement parity, which will be discussed later. This gives:
(8! · 3
8
· 12! · 2
12)
(3 · 2 · 2) = 4.3252 · 10The number of possible permutations of the squares on a Rubik’s cube seems
daunting. There are 8 corner pieces that can be arranged in 8! ways, each
of which can be arranged in 3 orientations, giving 38 possibilities for each
permutation of the corner pieces. There are 12 edge pieces which can be
arranged in 12! ways. Each edge piece has 2 possible orientations, so each
permutation of edge pieces has 212 arrangements. But in the Rubik’s cube,
only 1
3
of the permutations have the rotations of the corner cubies correct.
Only 1
2
of the permutations have the same edge-flipping orientation as the
original cube, and only 1
2
of these have the correct cubie-rearrangement parity, which will be discussed later. This gives:
(8! · 3
8
· 12! · 2
12)
(3 · 2 · 2) = 4.3252 · 10
Step-by-step explanation:
