In this section, we will explore the following questions.
How can we change the orientation of the corner cubies?
How can we change the orientation of the edge cubies?
How can we apply our four Cube moves to solve the Cube?
In Section 1.3, we considered ways of moving certain edge and corner cubies. The key that allows us to use Cube Move 1.3.1 and Cube Move 1.3.6 to put your cubies in the correct location is that each move affects precisely three cubies. All others are left unmoved. By using just Cube Move 1.3.1 and Cube Move 1.3.6, we can thus put each cubie in the correct location. However, even if a cubie is in the correct location, it may be that its stickers are on the wrong faces —in this case, it needs to be reoriented.
In this section, we will see how to reorient cubies once they are in the correct location. To do so, we’ll learn two moves: one that reorients corners, and one that reorients edges. Once we are able to put each cubie in the correct location, and then orient it correctly, each scrambled Cube becomes a puzzle, solvable by clever application of these moves.
We begin by exploring a move that reorients two corners.
Cube Move1.4.1.
Consider the following sequence of Cube moves.
\begin{equation*}
(R' D^2 R B' U^2 B)^2
\end{equation*}
Exploration1.4.2.Reorienting Corners.
The Cube move described in Cube Move 1.4.1 reorients two corners: one on the Up face, and one on the Down face.
By performing this move several times, identify on the blank Cube below what is happening to the Up face of the Cube. Describe what is happening to the Down face as well.
Using the cubie notation described in Definition 1.2.9, describe what is happens to the Up and Down faces of the Cube after performing this move.
Given what this move does, exercise your human creativity and suggest a short name/abbreviation for this move.
What is the order of the move?
Practice the move until you can reliably execute it.
Figure1.4.3.A blank cube.
Our last Cube move will reorient two edge cubies. Recall Definition 1.3.5.
Cube Move1.4.4.
Consider the following sequence of Cube moves.
\begin{equation*}
(S_R U)^3 U (S_R ' U)^3 U
\end{equation*}
Exploration1.4.5.Reorienting Edges.
The Cube move described in Cube Move 1.4.1 reorients two edges on the Up face.
By performing this move several times, identify on the blank Cube below what is happening to the Up face of the Cube.
Using the cubie notation described in Definition 1.2.9, describe what is happens to the Up face of the Cube after performing this move.
Given what this move does, exercise your human creativity and suggest a short name/abbreviation for this move.
What is the order of the move?
Practice the move until you can reliably execute it.
In this section, we explored the last moves we need to solve the Cube. We also described a strategy for solving the Cube. Our method of solving the Cube is based on the corners-first (CF) method, which is distinct from the layer-by-layer (LL) method which is often the first solving method people learn. The first solution to the Cube, by Erno Rubik himself, was corners-first, and the first world speed-cubing record (22.95 seconds) was done corners-first.
There are advantages and disadvantages to all solution methods. Advantages to corners-first are:
The move sequences are generally shorter in CF
There are just a few important move sequences to memorize
You generally don’t "break" your existing work and so can recover from mistakes more easily
The solution can scale from a leisurely solve of a few minutes or more to quite fast solves
ExercisesExercises
1.
Sam is nearly done with his Cube! Which of the Cube moves from this section does he need? How many times will he have to perform it?
Figure1.4.7.
2.
Lila is nearly done with her Cube! Which move from this section will be helpful? How should she use it?
Figure1.4.8.
3.
Sam has gotten himself into a bit of a pickle. How can he apply our moves to solve his Cube?
Figure1.4.9.
4.
This configuration is known as the superflip. Describe what you see. Can you achieve this on your Cube?
