Question

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.

Answer 1

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

Explanation: