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

- Learn to solve the Rubik’s Cube
- Learn to solve the Rubik’s Cube properly
- Seriously, with this method, you’ll be able to solve the Rubik’s Cube in <60 seconds. I’ve seen people spend years of practice on the cube and take over 5 minutes to solve it.

Not for Today

- Learn to generally solve an NxNxN Rubik’s Cube
- Learn to solve the Rubik’s Cube blindfolded

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:

- Basic Information - what you need to know to solve the cube.

In addition, additional information may be provided:

- Supplementary Guidance - if you are having trouble, reading this may gave you some additional insight.
- Non-essential Enrichment - information that you strictly do not need, but smart people tend to have insights and so this may answer any additional questions that come up.

Stick with the basic information first to minimize what you have to consume.

A Brief History

- 1974 - Ernő Rubik invented the Rubik’s Cube
- Please don’t spell it “Rubix.”
- 1980-1983 - 200M cubes sold
- 1982 - NY Times reports “the craze has died”
- 1982-2000 - Dark ages, small pockets of enthusiasts
- 2004 - World Cube Association formed
- 2020 - 142k WCA competitors around the world

A Brief Cubing Bio

- 2003 - Learned to solve the Rubik’s Cube
- 2004 - Founded the World Cube Association
- 2005 - Set the WR for 3x3x3 blindfold solving (example)
- 2005 - Taught Will Smith for Pursuit of Happyness
- 2008 - Released You Can Solve the Cube
- 2013 - Hosted the World Championships
- 2019 - Filmed WIRED Tutorial

A Brief Non-Cubing Bio

Personal

- Born in San Francisco, grew up in San Mateo, currently live here
- One brother (former WR holder - 3x3 single @ 10.48 seconds)
- Wife (Joyce) married in 2013, son Victor born 2016, daughter Valerie born in 2021.
- B.S. in Astrophysics from Caltech

Professional

- High-frequency trading from 2007 to 2011, mostly energy futures
- Product management since 2011 (Zynga, Lyft, currently Google)
- Other: Dev shop, Head of Ops @ Zoox, Grape & Grain / Wursthall

Misc

- Contestant on Beauty and the Geek Season 2

Competitive Cubing

Nerds of the world UNITE!

World Cube Association - the international governing body that regulates competitive cube solving events:

- 5 solves - drop the fastest and the slowest, and average the middle three times
- Single solves are tracked, but not used to determine the winner due to variance and ‘luck’
- 4x4x4, 5x5x5, one-handed solving, blindfolded solving, many different 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.

- Proper method and technique for beginners is the difference between solving the cube in 60 seconds vs 5 minutes → two people who spend 4 hours working on the cube will have vastly different outcomes due to differences in method and technique.
- This method is not more difficult than others that are on the internet. It’s probably easier...
- This tutorial is also available at WIRED - How to Solve a Rubik’s Cube, Step by Step.

FAQs for Entertainment

- Yes, Will Smith actually learned to solve the Rubik’s Cube. (You can recognize the algorithms.)
- Will Smith has forgotten everything and cannot solve a Rubik’s Cube today, and after this tutorial, you will understand why.
- Solving a cube blindfolded is similar to a selection sort.
- My PBs are 12.75 single, 15.60 average, and 1:22.56 blindfolded. These times are not competitive in 2021.

Step 0 - Actually Getting Started

You need to know a few basic facts to start:

- White/yellow, blue/green, red/orange are opposites (unless you bought your cube from Japan). This will be important in Step 1.
- Three types of pieces:
- Centers (one sticker) never move. They only rotate.
- Edges (two stickers)
- Corners (three stickers)
- You are moving pieces, not stickers. A green sticker on a corner will never end up as a sticker on an edge. (That’s pretty simple logic, but I can’t tell you how many times I’ve had someone ask.)

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”

- Pick a color and find its center. For the purposes of this tutorial, find the yellow center.
- Place four white edges (we will call these “petals”) of the opposite color around your center.

Try doing this on your own. This can be done intuitively, but it can be broken down into several situations. Some notes:

- Once you place an edge, you won’t need to move it again.
- Be careful to keep your frame of reference; don’t turn the cube so your chosen center moves away from you. Keep in mind that turning a middle slice will move the centers.
- Don’t worry about the corners. They’re not relevant in this step.

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

- Pick a white “petal” next to your yellow center. (See left picture.)
- Find the other color that’s connected to that piece. In the left picture, that color is blue.
- Turn the top so the “blue” sticker matches (see center picture) to its corresponding center. (Each “petal” will have a different corresponding color. It’s not always blue.)
- Because (in these pictures) you matched the blue side, turn the blue face (the side with the blue center) 180°. (See right picture.)
- Now repeat steps 1-4 for the other three “petals.” You will do this a total of four times.
- When you are done, you should have a white cross on the bottom.

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:

- Turn the right side 90° clockwise (“up”)
- Pull the top towards you with your right index finger
- Turn the right side 90° counterclockwise (“back down”)

Left trigger:

- Turn the left side 90° counterclockwise (also “up”)
- Pull the top towards you with your left index finger
- Turn the left side 90° clockwise (“back down”)

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

- Place the left thumb on the center of the 2x2 grid in the lower left on the front face.
- Left middle and ring finger are on the other side, centered on the 2x2 grid. Left index finger is free (so you can turn the top).
- Place the right thumb on the center of the 2x1 grid in the lower right on the bottom face.
- Right middle and ring finger are on the other side. Right index finger is similarly free.
- Mirror this for the left-handed trigger.

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:

- R U R’

Left trigger:

- L’ U’ L

Step 3 - Solving the Bottom Layer

- Take the white cross and place it on the bottom. The white cross should be on the bottom for the rest of the solve. If it is not, then something has gone wrong.
- Look in the top layer for white corner stickers that face you. (Ignore corners that face the top for now.)
- That “white” corner has two other stickers. There’s a green sticker on top. Ignore that. Look at the red sticker.
- Turn the top and match the red sticker to the red center.
- Once you’ve matched the corner to its corresponding center, face that matched center to you. This is your front.
- If the corner is on the right, do a right trigger.
- If the corner is on the left, do a left trigger.

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:

- Turn the top so that the white sticker that faces the top is over something that’s not white.
- Do the trigger, but pull the top twice instead of once.

[Center Image] Corner sticker in the bottom, facing the wrong way:

- Yank it out with a trigger.

[Bottom Image] Corners in the wrong place:

- Yank it out with a trigger.

Basic Information

Step 4 - Solving the Middle Layer

Your bottom layer should be solved. It’s now time to solve the middle layer.

- Look on the top for edge pieces that don’t have yellow stickers.
- Turn the top so the sticker (red) on the side matches to its corresponding center.
- Look at the sticker on the top of the same piece (blue). Look to see if the blue wants to go to the left or the right. (In this case, it’s left.)
- Because it wants to go left, pull the top once with your left index finger. Now do a left trigger. You should have done four moves all with the same hand. (Note: this isn’t intuitive, because it looks like you’re moving the edge away from where it wants to go. This is correct. You are setting up the corner and edge properly.)
- Lol… CS majors… recursion. You messed up your “white” corner. Solve it with Step 3 - Solving the Bottom 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:

- U = Up, R = Right, F = Front
- L = Left, B = Back, D = Down

How does it work?

- A single letter means turn that face 90° clockwise. You need to look at the face to make sure you have the correct perspective.
- A “2” (e.g. “R2”) means turn the face 180°. Please don’t ask me which way to turn it.
- A ‘ symbol means to turn the face 90° counterclockwise.

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?

- 4 - you’re done… go to Step 7 (1/27 probability… which is (⅓)^3… interesting...)
- 2 - make sure you “target” something that’s not yellow on top
- 0 - make sure you “target” something that’s yellow on the left side closest to you
- 1 - the fish swims southwest
- 3 - this is mathematically impossible… the cube is not solvable (you may not be done with Step 3)

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:

- 2 corners → 0 corners → 1 corner → 4 corners
- 2 corners → 1 corner → 1 corner → 4 corners

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

- Find two corners in the top layer that have the same color on the same side. (In this case, there are two blue stickers.)
- Once you find them, turn the top so the match with their corresponding face.
- Hold the cube so the matching corners are on the left.
- If you look at all four sides and you don’t see matching corners, it means you need to switch corners diagonally. Just do the algorithm once, and then repeat this step.

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

- 8/12 probability, you will have 3 edges that need to be solved
- 3/12 probability, you will have 4 edges that need to be solved (do either one of the algorithms listed below, and then repeat)
- 1/12 probability, this is called “getting lucky”

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

- Don’t worry about memorizing things to start. That will come later.
- Memorizing the algorithms is muscle memory. The hardest algorithm to memorize is Step 7.
- Using this method, if you spent 20-30 minutes a day, I *think* you will be able to solve the cube consistently under 60 seconds in about two weeks.
- If you do the above and can’t solve the cube in under 60 seconds, send me a video and I’ll try to provide some feedback.
- Back when I was your {cubing} age, I not only had to walk to work uphill both ways in the snow, I had to spend hours sanding and lubricating my cube so it would turn well! Fortunately for you, you can buy an amazing cube for $8 USD with no effort necessary to make it turn well.
- These cubes… they use magnets… how do they work? It’s a miracle...

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:

- Steps 1 & 2 - make the white cross directly. This can be done in 8 moves or fewer.
- Steps 3 & 4 - F2L, instead of putting corners and edges in separately, I place corners simultaneously with their corresponding edge. There are 41 cases, though many of them can be solved intuitively once you understand the principles.
- Steps 5 & 6 - There are 57 different patterns to make the top all yellow. I have memorized an algorithm for each one of these patterns.
- Steps 7 & 8 - Instead of moving corners and then edges, I do them simultaneously. There are 21 different permutations of the last layer pieces.

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:

- DJ WX AL VB IR (a sentence made out of these pairs of letters can help with memorization)

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

- Born in San Francisco, live in San Mateo

Family

- One brother (former WR holder - 3x3 single @ 10.48 seconds)
- Wife (Joyce) married in 2013, son Victor born 2016, daughter Valerie born in 2021
- B.S. in Astrophysics from Caltech

Misc

- Contestant on Beauty and the Geek Season 2

A Brief Professional Bio

Professional

- High-frequency trading from 2007 to 2011, mostly energy futures
- Product management since 2011 (Zynga, Lyft, Google)
- Other: Dev shop, Head of Ops @ Zoox, Grape & Grain / Wursthall

Current

SQLMesh is an open source SQL transformation tool and DataOps platform:

- Automatically parse SQL and know when downstream tables will be affected
- Automates workflows for incremental builds

A Brief History

- 1974 - Ernő Rubik invented the Rubik’s Cube
- Please don’t spell it “Rubix.”
- 1980-1983 - 200M cubes sold
- 1982 - NY Times reports “the craze has died”
- 1982-2000 - Dark ages, small pockets of enthusiasts
- 2004 - World Cube Association formed
- 2020 - 142k WCA competitors around the world

ANYONE Can Cube

- It takes about 2 hours if I’m teaching you in person, maybe a bit longer if you’re learning on your own.
- But contact me if you get stuck.
- I promise you don’t have to be good at math.

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:�

- Tyson’s best time - 12.75 seconds → current world record - 3.47 seconds
- Tyson’s best average - 15.60 seconds → current world record - 4.86 seconds
- Over/under for today → 18.50 seconds

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?

- Tyson’s best blindfolded solve - 1:22.56 → current world record - 12.78 seconds

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?

- Toby learned to solve the cube at CTY (book here)
- Had to chase him, was about 15 seconds slower
- Switched to the method by Lars Petrus
- Eventually learned a method by Jessica Fridrich

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:

- 5 solves - drop the fastest and the slowest, and average the middle three times
- Single solves are tracked, but not used to determine the winner due to variance and ‘luck’
- 4x4x4, 5x5x5, one-handed solving, blindfolded solving, many different 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:

- Yes, he’s a nice guy.
- No, I don’t know anything about the slappening.
- It took him a few hours to learn the cube, but it was spread out over days because we had to do it in between scenes. His learning was impressive.
- The actual Chris Gardner didn’t know how to solve the cube, so he hired me to teach him.