May 18, 2021
tyson.mao@gmail.com (if you have questions, best is to leave a comment in the deck)
Totally Not Related to Work
Tyson’s Rubik’s Cube Tutorial (go/rubiks-tutorial)
Executive Summary
COVID-19 has impacted the world tremendously. As we face an uncertain future, finding sources of entertainment amidst the collapse of civilization may prove difficult. The Rubik’s Cube has 43 quintillion combinations and offers endless entertainment without the requirements of either electric power or friends.
Today’s Objective
Not for Today
Tutorial Guide
This tutorial contains 8 steps.
There is a balance of giving enough information for a user to learn this method, and giving too much information such that it is overwhelming. Each step will have:
In addition, additional information may be provided:
Stick with the basic information first to minimize what you have to consume.
A Brief History
A Brief Cubing Bio
A Brief Non-Cubing Bio
Personal
Professional
Misc
Competitive Cubing
Nerds of the world UNITE!
World Cube Association - the international governing body that regulates competitive cube solving events:
It is important to have standards so that results can be compared around the world. Look… the IAAF does this with the 100m dash. It makes sense for cubing too!
Before We Get Started
If you know how to solve the Rubik’s Cube, this tutorial may still be valuable.
FAQs for Entertainment
Step 0 - Actually Getting Started
You need to know a few basic facts to start:
Basic Information
Step 0 - Non-Essential Enrichment
The pictures you see on the right are actually impossible if the rest of the cube is solved. In the cubes on the right, a corner/edge is twisted/flipped on the other side of the cube.
It turns out, if you were to disassemble a cube and reassemble it randomly, your cube would only have a 1/12 probability of being solvable. Corners must either be twisted in opposite pairs, or in groups of three. Edges must be flipped in pairs. Finally, you can’t switch the position of just two corners or two edges. You need to switch three corners or edges, or two corners AND two edges.
Why is this important? For those of you who may have an old cube lying around the house, if it has been taken apart and put back together, it may not be solvable. Similarly, if a corner is twisted in place, you can only solve it by twisting it back.
Non-Essential Enrichment
Step 1 - The “Daisy”
Try doing this on your own. This can be done intuitively, but it can be broken down into several situations. Some notes:
This is one of the four “petals” of your daisy.
Basic Information
Step 1 - Supplementary Guidance
There are a few ideas that may be helpful. In the following images, the yellow center is the top.
Supplemental Guidance
Base Case | Adjust the Top | Facing Wrong Way | Wrong Way Bottom |
| | | |
The white sticker can be placed next to the yellow center with a single turn. In this example, turn the right side “up” (or clockwise 90°). Some of your white stickers might be on the bottom of the cube. In these cases, it requires a 180° turn. | This is similar to the base case, but if you turn the right side “up” now, you will knock out one of the white edges. Adjust the center (by turning it 90° clockwise in this example) so that the free slot (where the green sticker is) is in position. Now you have the “Base Case.” | Remove the edge from the top (90° turn either way). This will bring you to the situation “Adjust the Top.” | Place edge under the free slot by rotating the bottom or the top, and then turn it 90°. In this case, you are turning the front. This will bring you to situation “Adjust the Top.” |
Step 1 - Non-Essential Enrichment
Non-Essential Enrichment
If you learn and practice starting with different colors, you’ll build the ability to understand color relationships from all six colors. I did not do this, and so my brain is only mapped to one color.
The advantage of being able to start with any color means that you have choices when you start, and you can start with the color that may present the easiest initial steps in your solution.
This is a very minor optimization, and is the difference between solving the cube in 12 seconds vs 8 seconds. However, I think it’s worth noting because as you are first learning to solve the cube, building this ‘agnostic’ color preference is easy. If you spend 17 years solving the cube starting with the white edges, it’s going to be hard to change later.
Step 2 - Making the Cross
Basic Information
Step 2 - Non-Essential Enrichment
Non-Essential Enrichment
The image on the right shows what the cube should look like after you have completed Step 2. People sometimes ask the question why we first put white edges around the yellow center, instead of putting them around the white center.
This is a teaching tool. I could tell you to put the white edges around the white center, which would allow you to skip Step 1, but it would require the user to pay attention to the order of the centers around the cube. On the white cross, notice that the blue and red stickers line up with their centers. In order to do this, all four white edges need to be in the correct order (with white on top going clockwise, that order is blue, red, green, and orange). Instead of burdening the user with this information, we instead have users make the “daisy.”
The Trigger
The trigger is a basic building block of Rubik’s Cube manipulation.
Right trigger:
Left trigger:
Notice, all three moves are done with the same hand. When you use your index finger, make sure you are pulling the top as you would pull the trigger of a gun. This helps ensure that the top of the cube is being turned in the correct direction.
Basic Information
Quick Ergonomics Lesson
The trigger is a common component of many algorithms in cubing. This slide attempts to teach you how to do it properly. In the image on the right, the white center is on the bottom, and the green center is on the front.
Right-handed trigger hand positioning
Non-Essential Enrichment
Why do we do this?
By holding the cube this way, you can now turn the right side clockwise and counterclockwise while keeping your index fingers free. Your index fingers can turn the top, left index finger for counterclockwise and right index finger for clockwise.
I am really annoying about finger positioning, because it makes things efficient. Your fingers are placed in a precise location, so that when you turn the right side, none of your fingers are in the way of the top layer which allows your index fingers to turn the top layer without any obstacles. This is critical to becoming good.
Spend the effort learning this now so you can optimize your learning. Don’t suck and then have to re-work your fundamental ergonomics 30 years later (which is the case with my violin technique).
Non-Essential Enrichment
The Trigger - (With Notation)
Non-Essential Enrichment
In the previous slide, the trigger was described in a way that promotes good ergonomics. I want you to use the fingers specified in the instructions as it is the right way to turn the cube. You could use other fingers, but I would encourage you to learn this the correct way now, and then you won’t have any bad habits to correct.
Refer to this slide for notation.
Right trigger:
Left trigger:
Step 3 - Solving the Bottom Layer
Basic Information
Step 3 - Pesky Edge Cases
If you really have no corners that are on top that face you, you might have one of three edge cases:
[Top Image] Corner sticker facing on top:
[Center Image] Corner sticker in the bottom, facing the wrong way:
[Bottom Image] Corners in the wrong place:
Basic Information
Step 4 - Solving the Middle Layer
Your bottom layer should be solved. It’s now time to solve the middle layer.
Basic Information
Step 4 - Pesky Edge Cases
You’re solving pieces, not stickers. If the colors aren’t lining up, it’s because you don’t have the right piece there. In the case shown in the image, the edge is in the correct position, but it is flipped the wrong way. If something is not in its proper position, we remove it and then place it correctly using Step 4.
A trigger will yank out the offending edge. Yanking out an edge will also yank out the corner. The corner can be solved with Step 3, which will replace it and leave the offending edge in the top layer. Now you can work with the offending edge using Step 4.
Basic Information
Quick Lesson on Notation
The Rubik’s Cube has six sides. We will reference them as:
How does it work?
If you do (R U R’ U’)^6, it will do nothing to the cube. If you do (R U)^105 or (R U’)^63, you’ll end up where you started. (R U R’ U’) has been called “the sexy move” since it’s easy to execute fast.
Basic Information
Step 5 - Making the Top Cross
The goal here is to make a yellow cross. With ⅔ of the cube solved already, you can’t do this the same way as Step 1 and Step 2. Instead, we use our first algorithm:
Algorithm: F U R U’ R’ F’
The third image is marked because at that step, it is important to hold the cube in the correct orientation. You need to hold it so the edges from “9 o’clock”. Remember, the yellow side is on top. You’ll need to pick whatever front (or adjust the top) so that you have “9 o’clock” on the cube.
Basic Information
Step 5 - Non-Essential Enrichment
Need help remembering this step? Seals have fur and they say “urf.”
THIS IS OPTIONAL! DO NOT READ THIS UNTIL YOU HAVE MASTERED THE PREVIOUS SLIDE!
If your yellow edges form a line, hold the line horizontally and do:
Algorithm: F R U R’ U’ F’
Non-Essential Enrichment
Step 6 - Solve the “Top”
The goal is to get all four corners to have “yellow” on top. How many corners do you have?
Algorithm: R U R’ U R U2 R’
Basic Information
Step 6 - Supplemental Guidance
To clarify orientation, in this scenario, the yellow center is on top, and the red center is in front. Because the fish is swimming “southwest,” the Step 6 algorithm will correctly solve this cube.
You may need to repeat Step 6 up to three times in order to get all four corners to have yellow on top. There are two possible trees:
If it feels like you are solving the 1 corner case twice, it’s because it exists in one of the trees.
One way of remembering this algorithm is:
“Right trigger, pull, right double trigger.”
Supplemental Guidance
Step 6 - Non-Essential Enrichment
Why is it that sometimes you have to do the 1 corner case twice? It’s because the case with 1 corner can has chirality. The top image is right-handed and the bottom is left-handed, and the chirality is determined by the three yellow stickers on the sides of the cube. The stickers will be on the right or left depending on which case you have.
For the left-handed case, the first application of the algorithm will convert it into the right-handed case, at which point, it can be then solved with a second application of Step 6 (you’ll need to do U2 after the left-handed case to have the correct orientation).
You can solve the left-handed case in one step by doing the mirror image: have the fish swim southeast instead and do:
Algorithm: L’ U’ L U’ L’ U2 L
Non-Essential Enrichment
Step 7 - Solve the Corners
The following algorithm switches the two corners on the right. The matching corners (held on the left) are correct, and don’t need to be swapped. This algorithm will swap the two corners on the right.
Algorithm: (R U R’ U’) (R’ F R2 U’) (R’ U’ R U R’ F’)
The parenthesis help you split up the algorithm into execution groups.
Basic Information
Step 7 - Different Algorithm
The solution in WIRED gives a different algorithm for Step 7. This algorithm has the advantage in that the second half of the algorithm is the same as Step 6 which means you can learn fewer new things:
Algorithm: (L’ U R U’) (L U R’) (Step 6)
Notice that the first move of Step 6 cancels with the move before it so if you wanted to be efficient, you could do the algorithm like this:
Algorithm: (L’ U R U’ L) (U2 R’ U R U2 R’)
Supplemental Guidance
Step 7 - Non-Essential Enrichment
Diagonal Corner Swap - the following algorithm allows you to swap corners diagonally, as opposed to swapping adjacent corners twice.
Algorithm:
F (R U’ R’ U’) (R U R’ F’) (R U R’ U’) (R’ F R F’)
The parenthesis help you split up the algorithm into execution groups. Ergonomically, you want to avoid “switching grips” when possible, since that means you’re spending time repositioning your hands instead of turning the cube.
It’s also important to note that while you can learn this algorithm, 75% of the cube solving time is spent in Steps 1-4. If you have to choose where to invest your time, consider improving your execution on Steps 1-4 until you can solve the cube consistently in less than 75 seconds.
Non-Essential Enrichment
Step 8 - Solve the Edges
If you have 3 edges that need to be solved, face the “good” side away from you. There is an misplaced edge that faces you. Does it want to go to the left or to the right? (In this picture, it wants to go to the left.)
Algorithm (left): F2 U R’ L F2 L’ R U F2
Algorithm (right): F2 U’ R’ L F2 L’ R U’ F2
Notice, the only difference is the direction of the “U”. Also, be careful when turning L as it moves “in the same direction” as R’ (and not R as most people are inclined to try).
Basic Information
Parting Thoughts
Appendix
Sub-20 Second Cube Solving
It would be very difficult to solve the cube using this method in under 20 seconds. It would take me about 28-30 seconds, but my friends have gotten it in the 24-26 second range. The cube method that I use combines steps:
Non-Essential Enrichment
Blindfolded Solving
It would be very hard to solve the cube blindfolded using this beginner method, or more advanced speed solve methods. The problem is that when you make a set of moves in a sighted method, it affects other parts of the cube. One would have to track where all those pieces are going. Some people are insane enough to try this, but I do not condone such behavior.
Instead, blindfolded methods allow one to solve just a piece or two of the cube at a time without changing the rest of the puzzle. This allows you to manipulate the cube without “updating your mental picture.” As an example, there are 12 edges on a 3x3x3 cube, which means there are 24 stickers. Let’s say each sticker is given a label from the letter A to the letter X. Now, consider the following sequence:
With a blindfolded method, you could fix the ‘D’ sticker without disturbing “anything else” (in quotes because it’s not strictly true). What you do is you fix D, then you fix J, and you go down the list. When you’re done with the list, the cube is solved.
Non-Essential Enrichment
Want another topic?
Leave a comment and I can write about it.
Non-Essential Enrichment
May 31, 2023
tyson.mao@gmail.com (if you have questions, best is to leave a comment in the deck)
Totally Not Related to Work
A bunch of information about the Rubik’s Cube
A Brief Non-Cubing Bio
Where
Family
Misc
A Brief Professional Bio
Professional
Current
SQLMesh is an open source SQL transformation tool and DataOps platform:
A Brief History
ANYONE Can Cube
Some Demonstrations
While you may think I’m an expert, I am 38 years old with two kids in a world that is dominated by teenagers. (It’s better to be early than good.) For some perspective:�
Okay, but I was never really a competitive 3x3x3 speed solver. But I was world record holder in blindfolded solving, so what does that look like?
I am sadly too out of shape to try a blindfolded solve. Maybe at the end…�Example 1 and Example 2
My Rubik’s Cube Story
How did I get started?
By the way, don’t learn off those sites. That’s why I’m slow.
Competitive Cubing
Nerds of the world UNITE!
World Cube Association - the international governing body that regulates competitive cube solving events:
It is important to have standards so that results can be compared around the world. Look… the IAAF does this with the 100m dash. It makes sense for cubing too!
Oh… That Water is Deep…
Since everyone asks…
FAQ: