1. The WHITE Corners
Lesson 3

2. GOAL: The WHITE Corners
Do you see the letter T on the RED, BLUE, ORANGE, and GREEN sides?
GOAL: The WHITE Corners
The goal of this stage is to get the WHITE corners on the UP face with the TOP layer of each face matching the center piece.

3. R Ri L Li D Di U Ui B Bi F Fi ¼ Turns Inverse means opposite.
By using the inverse of a move, the move can be undone.

4. Layers and Faces
When solving the cube, sometimes it’s easier to talk about the layers.
LEFT Face
RIGHT Face
FRONT Face
Faces are the flat sides of the Cube. Faces are two- dimensional (length and width). Think of frosting that goes on all the sides of the cake.
UP Face
BOTTOM layer
TOP layer
Layers are three- dimensional (length, width and height), like layer cake.
MIDDLE
layer

5. SCRAMBLED CUBE 25 Random ¼ Turns
You have to scramble the cube to solve it!

6. REVIEW FROM THE WHITE CROSS
Make sure the WHITE face is UP.
Find a WHITE edge.
Twist the row of the cube that has the WHITE edge until the WHITE edge is on the BOTTOM layer.
GOAL:
To get the WHITE edges matched with the correct faces.
Be Careful! If moving the WHITE EDGE ruins what you’ve already done, turn the BOTTOM layer ¼ turn. Then, undo the move that put the WHITE EDGE on the BOTTOM layer.

7. REVIEW FROM THE WHITE CROSS
Put the WHITE edge directly below the matching colored center piece.
Place on the RIGHT face. Make two R turns, so the WHITE edge
is on the TOP layer.
GOAL:
To get the WHITE edges matched with the correct faces.
Repeat all the steps for each WHITE edge.
If you need to “flip” an EGDE, use this algorithm:

8. ALGORITHM
An algorithm is a set of rules or set of steps that we use to solve math problems.
This is the algorithm that is used for placing the WHITE corners.
Let’s see how.

9. Let’s Start Solving! Hold the WHITE face as the UP face.
Hold the BLUE face on the RIGHT.
Hold the RED face in the FRONT.
GOAL:
To get the WHITE/RED/BLUE corner in the correct position.
Find the WHITE /BLUE/RED corner.

10. Then, twist the DOWN face a D turn.
If the WHITE /BLUE/RED corner is on the TOP layer, make a ¼ turn until it
is on the BOTTOM layer.
GOAL:
To get the WHITE/RED/ BLUE corner in the correct position.
Then, twist the DOWN face
a D turn.
After completing the D turn, reverse the original ¼ turn to the previous position.
Check to see that you still have the WHITE cross!

11. Your cube should look like one of these pictures:
Twist the DOWN face of the cube until the WHITE /BLUE/RED corner is directly below its intended position.
You may have to perform more than one ¼ turn to get the corner underneath its intended position.
Your cube should look like one of these pictures:
GOAL:
To get the WHITE/RED/ BLUE corner in the correct position.

12. Now, do the following algorithm. Remember to hold the cube with
WHITE on TOP
RED on FRONT
BLUE on RIGHT
Repeat until you reach the goal.
GOAL:
To get the WHITE/RED/ BLUE corner in the correct position.

13. GOAL: To get the WHITE/BLUE/ORANGE corner in the correct position.
Position the Cube
Hold the WHITE face as the UP face.
Put the ORANGE face on the RIGHT.
Put the BLUE face in the FRONT.
GOAL:
To get the WHITE/BLUE/ORANGE corner in the correct position.
Find the WHITE /BLUE/ORANGE corner.

14. GOAL: To get the WHITE/BLUE/ORANGE corner in the correct position.
If the WHITE /BLUE/ORANGE corner is on the TOP layer but it’s not in the correct position,
• make a ¼ turn until the corner is on the BOTTOM layer.
GOAL:
To get the WHITE/BLUE/ORANGE corner in the correct position.
• Then, twist the DOWN face
a D turn.
• After completing the D turn, reverse the original ¼ turn to the previous position.
Check to see that you still have the WHITE cross!

15. GOAL: To get the WHITE/BLUE/ORANGE corner in the correct position.
Twist the DOWN face of the cube until the WHITE /BLUE/ORANGE corner is directly below its intended position, at the bottom, right-hand corner of the cube.
You may have to perform more than one ¼ turn to get the corner underneath its intended position.
Your cube should look like one of these pictures:
GOAL:
To get the WHITE/BLUE/ORANGE corner in the correct position.

16. GOAL: To get the WHITE/BLUE/ORANGE corner in the correct position.
Now, do the following algorithm. Remember to hold the cube with
WHITE on TOP
BLUE on FRONT
ORANGE on RIGHT
Repeat until you reach the goal.
GOAL:
To get the WHITE/BLUE/ORANGE corner in the correct position.

17. GOAL: To get the WHITE/ color/color corner in the correct position.
Using an Algorithm to Place the WHITE Corners
Find a WHITE corner piece. What are the other 2 colors?
GOAL:
To get the WHITE/
color/color corner in the correct position.
If the corner you choose is not in the correct place, do this:
Hold the WHITE face on the UP face.
Put one of the colors of your corner as the RIGHT face.
Put the other color of your corner on the FRONT face.

18. GOAL: To get the WHITE/color/color corner in the correct position.
If the WHITE /color/color corner is on the TOP layer and not in the correct position, make a ¼ turn until it is on the BOTTOM layer.
GOAL:
To get the WHITE/color/color corner in the correct position.
Then, twist the DOWN face
a D turn.
After completing the D turn, reverse the original ¼ turn to the previous position.
Check to see that you still have the WHITE cross!

19. GOAL: To get the WHITE/color/color corner in the correct position.
Twist the DOWN face of the Cube until the WHITE /color/color corner is directly below its intended position, at the bottom, right-hand corner of the Cube.
You may have to perform more than one ¼ turn to get the corner underneath its intended position.
Your Rubik’s Cube should look like one of these pictures:
GOAL:
To get the WHITE/color/color corner in the correct position. or

20. GOAL: To get the WHITE /color/color corner in the correct position.
Now, do the following algorithm. Remember to hold the Cube with
WHITE on TOP
color on FRONT
other color on RIGHT
Repeat until you reach the goal.
GOAL:
To get the WHITE /color/color corner in the correct position.

21. GOAL: The WHITE Corners
Examine your Rubik’s Cube.
GOAL: The WHITE Corners
The goal of this stage is to get the WHITE corners on the UP face with the TOP layer of each face matching the center piece.
Does your Rubik’s Cube look like this?

22. You have achieved The WHITE Corners
Congratulations!
Congratulations!
Congratulations!
Congratulations!
Congratulations!
Congratulations!
You have achieved The WHITE Corners

23. REVIEW Position the WHITE face as the UP face.
Position a WHITE corner on the BOTTOM layer underneath its intended position.
Use the algorithm
as many times as
needed until the
corner is in the correct position.
Repeat the steps for each WHITE corner until all four corners are in the correct positions.
GOAL: To get the WHITE corners matched with the correct faces:

24. PERMUTATION
A permutation is a different arrangement of something or all possible arrangements of something. Each move of a Rubik’s Cube makes a new permutation of the Cube. How many permutations are there for a CORNER?

25. Math Connection How does this lesson apply to math?
When a WHITE corner is on the BOTTOM layer, the algorithm Ri, Di, R, D
is used to place the corner in the correct place.
With each corner, the same algorithm is used to place that corner correctly. 5
56.340
11.268 06 13 10 34 30 40
There is a repeating pattern in the long division algorithm.
÷ Divide
X Multiply
- Subtract
✓ Check
↓ Bring down

26. Vocabulary Give some examples of algorithms you use.
How would you explain how to find a corner on a Rubik’s Cube?

27. Question: Who produced the most expensive Rubik’s Cube
Question: Who produced the most expensive Rubik’s Cube? What was it called?
Answer:
The most expensive Rubik’s Cube was the Masterpiece Cube, produced by Diamond Cutters International in The actual size, fully-functional cube features 185 carats of precious gems invisibly set in 18-karat gold. In its solved state, the cube features a different type of gem on each side—including 22.5 carats of amethyst, 34 carats of rubies and 34 carats of emeralds.