Memorizing Rubik's Cubes (and similar puzzles)

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#1 8 October, 2012 - 06:08
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Memorizing Rubik's Cubes (and similar puzzles)


Okay, this is gonna be a post summarizing how I personally memorize a 3x3x3 (normal) rubik's cube. I can also memorize a 4x4x4 (4 layers on each side/16 stickers per face) and a 2x2x2 (2 layers on each side/4 stickers per face. Commonly known as the "4 cube" (or something like that) by non-speed cubers).

I can memorize a normal cube in about 1 minute, a 4x4x4 cube in about 25 minutes (I'm still a beginner), a 2x2x2 cube in about 15-18 seconds. Some people can memorize a normal cube between 7-10 seconds. Yes. 7 SECONDS. The WR for 4x4x4 blindfolded is around 2min, 30 sec, I believe. I think the memorization took about 1 min, 45 sec (pretty sure, but I can't remember now. lol)

Now, many of you may think that we look at the cube for a few seconds and know exactly what turns we have to do to solve it. This is entirely false. There is an event that some practice called Fewest Moves. Each competitor gets 1 hour to solve a rubiks cube in the least number of turns possible. Any cube can be solved in 20 or fewer moves, and most can be done in 17. The WR was recently set at 20 moves. I believe God's algorithm (fewest moves to solve it) for that scramble was under 20, perhaps 17 or 18. Blindsolvers start memorizing at the same time the timer starts, so if a cuber says they blindsolved a 3x3 in 30 seconds (WR is 27, people have done under 20 unofficially at home) that includes the time used to memorize the cube.
What we actually do is memorize where each piece has to go and then use commutators (A B A' B' or some variant) to solve only a few pieces at a time (usually just 2).

How do we memorize these pieces though? Some people do it visually in some way - perhaps viewing an airplane flying from one piece to the next - but that is not as strong of a memorization. If you lose your focus, chances are you will have lost the flight plans. That's why we assign letters to stickers. If you hold your Rubik's cube (solved) with White on the top and Red on the front, here is how I letter my stickers:
U = top (up), D = bottom (down), L = left, R = right, F = front, B = back
UB (Up[top]-Back) - A - White sticker on the edge with white and orange
BU (Back-up(top)) - B - orange sticker on the edge with orange and white
UR (up-right) - C - white sticker on the edge with white and blue
RU - D - blue sticker on the edge with blue and white
UF - E - white sticker on White/red edge
FU - F - red sticker on red/white edge
UL - G - white on white/green
LU - H - green on white/green
LB (Left-back edge) - I - green sticker on green/orange
BL - J - orange on green/orange
BR - K - orange on orange/blue
RB - L - blue on orange/blue
RF - M - blue on blue/red
FR - N - red on blue/red
FL - O - red on red/green
LF - P - green on red/green
BD - Q - orange on orange/yellow
DB - R - yellow on orange/yellow
RD - S - blue on blue/yellow
DR - T - yellow on blue/yellow
FD - U - red on red/yellow
DF - V - yellow on red/yellow
LD - W - green on green/yellow
DL - X - yellow on green/yellow

That's how I letter my [edge] stickers. I do a similar thing for the corners, but I don't need to go into that here. I use the same techniques as for edges.

So I'll mix up my cube and explain what I do and how I'd do it.
I have to pick a location (not piece) on the cube that I am going to use to solve the rest (called the buffer). I use the Down-Front location (the piece is the yellow/red piece, but that does not matter). I look at the edge between the red center and the yellow center (on the Front and Bottom respectively). In my scramble, this is the Orange on orange/blue. I know from practice that it's letter is K (Back/right position). I will then temporarily remember K while I look at the back/right sticker+edge and see what that letter is. In my case this is the Blue on blue-white edge. Again, from practice, I know this is D. So now I have KD. I use a journey/roman rooms method to memorize these. I usually start my blind cubing sessions with my living room as the first room. On the piano (first thing I see when I enter; you guys know how roman rooms works [I hope :P ]) I put my friend named Kadie. She's just sitting there, doing nothing for now. I interact two images/letter pairs per location. I'll look at the right/up sticker ("D" location). It is the yellow on yellow-green. That is X. I temporarily remember this and look at that spot on the cube. White on white/orange. That is A. I now have KDXA. For the X's I usually just electrocute (makes me think of X) whatever the first thing is that pops into my mind with the following letter. A is alligator, so I add that to my image of Kadie. She is tasering an alligator. It's writhing around, electricity shooting off of it, etc. You guys understand the concept. I look at the piece in U/B (white/orange location). It is yellow on yellow/blue. T. I look there. It's green on green/red. P. So I've got Kadie electrocuting an alligator, TP. TP is toilet paper. At my next location in the room (computer) I put a huge roll of toilet paper. Perhaps it is wrapping around the computer like a mummy. The sticker at L/F (green/red) is the orange on orange-yellow. That is Q. Q's are usually hard, so I swap out Q with the "sh" sound when there isn't a nice image. I'll look at that piece; it is red on red/white. That is an F. So now I've got QF. I'll either incorporate a quaffle into the image with toilet paper or a chef (sounds like shef). In this case I'll picture a chef being strangled by the toilet paper. He's struggling, trying to get free, and knocks over the chair, computer, and books nearby in the process. I look at that sticker, and it is the blue on blue-red. That is M. I see that the piece in this spot is my "buffer", so I know that I am done (usually, but I won't go into that unless you guys really want me too. I'd probably just send you to a video on youtube anyway, since it's kinda hard to explain over text.) So since that is the end of the edges (cause I got to the yellow-red edge), I just need to memorize M somehow. I'll usually double up the letter and say MM, so I'd toss a huge bag of M&Ms on the couch.
So now I've got KDXATPQFM: Kadie electrocuting an alligator, toilet paper strangling a chef, M&Ms.

Does this make sense? Should I clarify some things, or is it fairly clear? I tried to keep it as simple as possible. This is the same method I use for memorizing even larger cubes such as the 4x4x4. One person used this method to memorize and blindsolve an 8x8x8.

whew. That was a long post...

9 October, 2012 - 05:27
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It made a lot of sense to me, only because I've been blindsolving since 2011. To someone new to this; there is an awful lot of interesting, but unrelated filler. You need to clarify a lot of the terminology used in your post and explain commutators/algorithms, what they are and how they are actually used during a solve.

12 October, 2012 - 07:12
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MOOP! I know who you are! (on ss) (I think... Kristopher de Asis?)
I'll clarify some later, but perhaps you could do some too. I won't have much time tonight, with homework, and I've got a cube comp in the morning, but I'll try to do some clarification.

12 October, 2012 - 21:24
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Thanks for the explanation. How do you keep track of things once you star solving it? Do you just move a few pieces and then rememorize based on where you think you moved things?

That is an amazing video:

25 October, 2012 - 06:52
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Well, that's where it gets a bit complicated. Basically, you solve 1 or 2 pieces at a time without disturbing any other pieces. So I would solve the first 1 or 2 pieces I memorized, and I would know exactly where the next 1 or 2 pieces would be, cause they hadn't moved at all. I would continue this until I had solved all of the pieces. If that doesn't make sense, check out this video. It's a bit long, but it explains everything and you probably won't need to watch it all.

21 January, 2013 - 20:35
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I'm quite new to Rubik's cubes generally... I solved a 4x4x4 cube myself ONCE - only by painstaking analysis of my trial and error moves. It was a terrible ordeal over many days ;)

However, more recently I decided to read up and learn how to complete a 3x3x3 cube blindfolded. I was led to believe it was more a feat of memory than anything else. Obviously there are the mechanics of several key sequences - but otherwise it's all about remembering the initial state of the cube. The mechanical sequences are muscle automations.

I am not aiming to be a speed cuber... just to practice and learn how to do it. But I do have some thoughts to contribute to the memorisation while I am still learning. It is quite possible that I am learning a basic technique using more steps than necessary... but hopefully this might be of interest to those who enjoy mnemonics and would like to try something a bit different!

This is the link i used for my instruction.
http://www.personal.psu.edu/pfg115/rubiks/blind.htm

I've read several suggestions for how to remember the state of the cube... but I definitely prefer the numerical representation described in the article. The author states you simply need to remember a sequence of around 35 digits. This will probably interest anyone who uses a major or Ben system for memorising numbers. Let me stress that we are ignoring explicit memorisation of colours and only memorising position and orientation of each piece.

His example of a random scrambled up cube is this:

0 2 1 0 1 1 2 - 1 1 0 0 0 0 1 0 0 1 0 - 5 8 4 7 9 3 7 3 - 10 3 7 8 4 12 9 5

Obviously, this numerical sequence can be condensed way down, meaning only 8 or 9 images required to remember the entire state of the cube.

The cube is solved in 4 parts:

1) Corner Orientation (spin the corner pieces)
2) Edge Orientation (flip the edge pieces)
3) Corner Permutation (move the corner pieces to where they should be)
4) Edge Permutation (move the edge pieces to where they should be)

How does the numerical sequence work?

0 2 1 0 1 1 2 - reminds us which corners need to be rotated

Corner 1 = 0 (no turn)
Corner 2 = 2 (two turns clockwise)
Corner 3 = 1 (one turn clockwise)
Corner 4 = 0 (no turn)
Corner 5 = 1 (one turn clockwise)
Corner 6 = 1 (one turn clockwise)
Corner 7 = 2 (two turns clockwise)
Corner 8 (don't worry - this turns itself)

1 1 0 0 0 0 1 0 0 1 0 - reminds us which edges need to be flipped.
This is 11 binary digits

5 8 4 7 9 3 7 3 - reminds us which corners need to move to a new place (it's kind of an ordered chain)
This is around 8 decimal digits

10 3 7 8 4 12 9 5 - reminds us which edge pieces need to move (in a chain)
This is around 8 "numbers". Unfortunately the numbers range from 1 to 12 which is not as nice for chunking.

After memorising this initial state, we perform the same sequence several times to rotate corners, then another sequence to flip edges, then another sequence to move the corners, then a last sequence to move the edges.
That's all discussed in detail in the article. I believe there is no substitute for practice to let your hands learn these automatic sequences - "muscle memory"

However for the state of the cube, using something like the major or Ben system really condenses it.

The chunking of digits is open for personal preference with some complications, and I'm still deciding exactly what to do. For now I will explain the corner orientation memorisation as it is probably the strangest of my current decisions:

Corner Permutation
0 2 1 0 1 1 2
I memorise this in two images.

I break it into 0 2 1 0 (top corners) and 1 1 2 (bottom corners)

the 112 is straight forward - a Ben system style decimal image. For me, it is TIN (teen)

the weirder bit is the 0 2 1 0. This could be treated as four decimal digits but most people need two images for that, I prefer to use one image for the top corners, one for the bottom.

0 2 1 0 is technically "Ternary", every corner is 0,1 or 2

I chunk this into 02-10 and translate to decimal
02 = 0x3 + 2x1 = 2
10 = 1x3 + 0x1 = 3

So the image for the top corners is my two digit 23. For me, it is UM (umu)

An umu is like a fire pit for cooking food in Polynesian islands.
So remembering a teen (cheerleader) jumping into a firepit is enough for me to recall the orientation of all the corners of the cube.

I have quite a number of reasons for settling on this approach and will elaborate if anyone is interested :) But for now, I think this might be enough of a curiosity for mnemonists and cubers.

Cheers!

23 February, 2013 - 19:58
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What blindsolving methods do you guys use?

I use 3OP, it took me awhile to learn how it worked and to learn the algorithms but I'm pretty good at it now except for solving some parity errors blindfold.

I number all my edge 1-12 going clock-wise starting from the U (top) layer with the edge piece facing me being 1 and 5 being on the F (front) side left.
For corners I have them numbered 1-8 going counter clock-wise starting from the U (top) layer with number 1 being the corner facing me on the left side.

For edge orientation I visualize shapes such as traingles, lines or balls (a triangle would be 3 cublets, a line 2, a ball 1) and try to visualize these shapes connecting the cublets that need to be solved. I do the same thing for corner orientation but I use the L shape. I don't try to memorize them for very long because I will end up solving edge and corner orientation fairly quickly and there's not a point to remembering it more than 10-30 seconds at most.

I do however use my own PAO system and the method of loci for the edge and corner permutation which is at most 20 digits because it is useful to remember them for a longer period of time.

1 March, 2015 - 23:19
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Joined: 3 years 9 months ago

I use TuRBo edges and OP corners, although I'm trying to make the switch from OP to commutators for corners right now. (I hate having to come on to an old thread.)

P.S. Hey Ickathu! Nice to see you here (if you're still active).

27 December, 2015 - 11:59
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With a PAO system you can reduce it to 5-7 images

28 December, 2015 - 10:08
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I am very interested in 3op method. I resolved 3x3 rubix fine with m2 old pochman method. I assigned letters to each edge and corner from which I create words. The words are my images but this is slow method I want something faster.

Do you have good instructions for 3op method, especialy parity part?

17 April, 2017 - 11:57
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Joined: 1 year 8 months ago

Solve Rubik's cube - ONLY 4 STEPS (RU'R'U) !!!
https://youtu.be/QweskMWKHhc

Only 4 steps (RU'R'U) , no need to endless repeat same steps!
No algorithms, no notations, no memorization!
You can also download application (see link in description) and practice!

I hope this tutorial will help you!