The original Rubik's cube is 3 inches tall and has a width of 3 inches. They decided to create a new Rubik's cube with a height of 2 inches and a width of 2 inches.
1. If you round the scale factor to the nearest thousandth (if possible), are these
Rubik's cube similar? Justify your conclusion. Show all work.

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: