MathDB

Joey is playing with a

2

-by-

2

-by-

2

Rubik’s cube made up of

8

1

-by-

1

-by-

1

cubes (with two of these smaller cubes along each of the sides of the bigger cubes). Each face of the Rubik’s cube is distinct color. However, one day, Joey accidentally breaks the cube! He decides to put the cube back together into its solved state, placing each of the pieces one by one. However, due to the nature of the cube, he is only able to put in a cube if it is adjacent to a cube he already placed. If different orderings of the ways he chooses the cubes are considered distinct, determine the number of ways he can reassemble the cube.

Problem Statement