Melco
Joined: Feb 16, 2015
• Posts: 12
January 2nd, 2017 at 12:50:04 PM permalink
I've been a long time lurker of this site, but this is my first time posting. I'd like to thank the Wizard for the wealth of information on his sites. I've been visiting his odds site for over 10 years.

On Facebook, the Wizard posted his solved 3x3x3, 5x5x5, and 7x7x7 rubik's cubes. My basic understanding of solving rubik's cubes is that there are number of set states that, when seen, require a certain pattern of moves to complete the puzzle. This is why there are people that can solve it without looking once they see the current state.

My question: On a 5x5x5 or 7x7x7 rubik's cube, does the pattern which one memorizes hold? Or do you have to redo all of the pattern recognition?

My hunch is that the pattern remains somewhat the same for a 3x3x3 area, and one just needs to continue once that corner is complete. And then once one has an algorithm for a 5x5x5, going to 7x7x7 would be the same iterative process.

Bonus question: Would a N x N x N cube be harder to solve if N were even?

Thanks.
Romes

Joined: Jul 22, 2014
• Posts: 4223
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January 2nd, 2017 at 1:08:07 PM permalink
Hey Melco, welcome to the forums =).

While I enjoy math and probabilities, I'll fully admit I've never really touched a rubik's cube. I might not have your answer, but I will say I would enjoy reading the answer from one of the many great math minds on this site, as the question intrigues me. From my, clearly uneducated, understanding as posted thus far, I would imagine the Odd Numbered rubik's cubes having a very very similar (but not exact) same patterns, while even numbered would be different but similar to themselves as well.
Playing it correctly means you've already won.
GWAE
Joined: Sep 20, 2013
• Posts: 6222
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January 2nd, 2017 at 3:15:45 PM permalink
Stupid rubiks cube. Wife bought me one for xmas. Spent 3 hours on it. Went on Internet and read how tosolve. Said first step was white cross with each side top and middle the same color. Finally got it there after another 2 hours. I set it down and went to bathroom. Came back and 5 year old son mixed it all up. Have spent abother few hours now and can't get it back to that point.
Wizard
Joined: Oct 14, 2009
• Posts: 16352
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January 2nd, 2017 at 3:28:06 PM permalink
I was thinking about posting about this. On DT I mentioned that I went to pick up my son at a friend's house and the friend's bother had a whole bunch of Rubik's cubes out there and other such puzzles. Then we had a 3x3x3 Rubik's Cube solving race where I got crushed. He was done while I was still on the top layer. It truly made me feel old. When I was in high school I was the king of the Rubik's Cube.

Anyway, this incident got me interested in the other sizes. I had a 4x4x4 in high school but never liked it much. It requires a lot more memorization and if you don't put the centers the right way, then you'll just be wasting your time but won't realize it until you get close to the end. With odd-numbered cubes, the centers can't move.

So, for Christmas I got myself a 4x4x4, 5x5x5, and 7x7x7. I didn't open them until the 25th. Since then I've spent several hours a day on them. At this point I can say that if you can solve the 3x3x3 then with just two extra 7-move combinations you can solve any odd-numbered size.

I'm thinking about making a video on the 5x5x5 to show my technique. I know there are already several others on YouTube but many are vague, go too fast, or require memorization that I think is unneeded. Said video could be used to solve any odd numbered size as long as you can already do a 3x3x3.

As for the 3x3x3 there is a TON of material on it floating out there. Personally I learned from "the book" back in the early 80's. There has got to be some web site that explains how to solve it requiring no prior knowledge, but I haven't looked for it because I can already solve it easily. Maybe somebody else can recommend something.

BTW, my brother challenged me to do the 5x5x5 on a unicycle before the end of the year. I think I'll be able to before the end of the month.
Last edited by: Wizard on Jan 2, 2017
It's not whether you win or lose; it's whether or not you had a good bet.
Melco
Joined: Feb 16, 2015
• Posts: 12
January 2nd, 2017 at 7:35:14 PM permalink
The odd numbered solution seems simpler than I even imagined! I did search for the 3x3x3 solution awhile back. I never did it myself, but I was always intrigued by the league of young folk that could solve it VERY quickly.

Looking forward to your unicycle 5x5x5!
Wizard
Joined: Oct 14, 2009
• Posts: 16352
January 2nd, 2017 at 8:58:32 PM permalink
Quote: Melco

Looking forward to your unicycle 5x5x5!

Thanks! I just need to memorize the sequence to flip a single edge piece and I should be ready. Here is that sequence, not that anyone cares:

Rr2, B2, U2, Ll, U2, Rr', U2, Rr, U2, F2, Rr, F2, Ll', B2, Rr2

Also, here is the site I used to use to remember my 3x3x3 combinations. Beginners may find it too cryptic but those needing a refresher should find it perfect.
It's not whether you win or lose; it's whether or not you had a good bet.
mamat
Joined: Jul 13, 2015
• Posts: 363
January 2nd, 2017 at 9:44:16 PM permalink
Quote: Wizard

On DT I mentioned that I went to pick up my son at a friend's house and the friend's bother had a whole bunch of Rubik's cubes out there and other such puzzles. Then we had a 3x3x3 Rubik's Cube solving race where I got crushed. He was done while I was still on the top layer. It truly made me feel old. When I was in high school I was the king of the Rubik's Cube.

4.74 sec speed-cubing 2016 WR.

Anything under 30 sec was really impressive when I first discovered the Rubik's Cube early 1981 (same time as Ringmaster's Scientific American article, sophomore year in high school). Times change. Robots doing cubes.

It took really long...29 more years...for people to show that 20 moves (half-turn metric) was enough to solve any cube (2010).

I liked playing with the centers on the 4x4x4. Never tried anything larger than 5x5x5.

Fun to give the cube to someone else and have them make 3-6+ random turns, and then give it back to you to find God's solution.

I helped Richard Korf (UCLA) a little bit with his first computer algorithm to find optimal solutions (using pattern databases).

Quote: Wizard

BTW, my brother challenged me to do the 5x5x5 on a unicycle before the end of the year.

Cool. Post a video.

There's a video of a Rubik's cube solved while juggling 3 cubes, but unfortunately it's faked.
Wizard
Joined: Oct 14, 2009
• Posts: 16352
January 2nd, 2017 at 9:52:49 PM permalink
Quote: mamat

Anything under 30 sec was really impressive when I first discovered the Rubik's Cube early 1981 (same time as Ringmaster's Scientific American article, sophomore year in high school). Times change.

They now have sequences for every possible bottom arrangement, which is where the 80's method spent most of the time. I think there are short cuts with the middle level too. The downside to today's much faster times is a lot more memorization is required.

Another thing is the cubes are a lot better now. I also got myself a "speed cube" for Christmas. You can make a turn or double turn with just a flick, although I'm sure it takes some practice.
It's not whether you win or lose; it's whether or not you had a good bet.
mamat
Joined: Jul 13, 2015
• Posts: 363
January 3rd, 2017 at 3:23:41 AM permalink
Quote: Wizard

Another thing is the cubes are a lot better now. I also got myself a "speed cube" for Christmas. You can make a turn or double turn with just a flick, although I'm sure it takes some practice.

I was always really slow, since I created my own methods. More interested in playing with congugates (ABA'), commutators (ABAB'), and other stuff from group theory & group representation theory...than doing it fast. 219 space groups (3D) & 17 wallpaper groups (2D, also called "plane symmetry groups"). My Dad used to be an X-ray crystallographer, so he talked about this stuff a lot at home when I was a little boy.

https://en.wikipedia.org/wiki/Space_group
https://en.wikipedia.org/wiki/Wallpaper_group

I liked creating patterns on the cube (and writing down who to make the patterns).

Have you tried blindfold cubing?

Quote: Wizard

They now have sequences for every possible bottom arrangement, which is where the 80's method spent most of the time. I think there are short cuts with the middle level too. The downside to today's much faster times is a lot more memorization is required.

A college friend in 1983 could do 23 sec (if I remember correctly), and I thought that was wicked fast.

I hear what's common in speed-cubing is called Jessica Friedrich's CPOP method (1997).

a) David Singmaster published a layer-based solution in 1980.
b) Guus Razoux Schultz was using an early F2L system in 1982 (solves the first two layers simultaneously).
-> (1) Cross (2) F2L ... rather than (1) Layer-1 (2) Layer-2
-> People also do "color-blind" starts; e.g. start with the most suitable start side (not always white).
c) Friedrich developed better OLL and PLL algorithms (orienting the last layer pieces, then permuting them into their correct positions), which together allowed any last layer position to be solved with two algorithms and was significantly faster than previous last layer systems.

https://en.wikipedia.org/wiki/CFOP_Method

The "big 4" methods are CPOP, Petrus, Roux, and ZZZ.

Philip Marshall's The Ultimate Solution to Rubik's Cube averages only 65 twists yet requiring the memorisation of only two algorithms.
The cross is solved first, followed by the remaining edges, then five corners, and finally the last three corners.

Lars Petrus method - a 2×2×2 section is solved first, followed by a 2×2×3, and then the incorrect edges are solved using a three-move algorithm, which eliminates the need for a possible 32-move algorithm later. The principle behind this is that in layer-by-layer you must constantly break and fix the first layer; the 2×2×2 and 2×2×3 sections allow three or two layers to be turned without ruining progress. One of the advantages of this method is that it tends to give solutions in fewer moves.

Roux Method, developed by Gilles Roux, is similar to the Petrus method in that it relies on block building rather than layers, but derives from corners-first methods.

ZZ method, short for Zbigniew Zborowski (2006). The method was designed specifically to achieve high turning speed by focusing on move ergonomics, and is the combination of a block-building method and a layer-by-layer method. The initial pre-planned step is called EOLine, and is the most distinctive hallmark of the ZZ method. It involves orienting all edges while placing two oppositely placed down-face edges aligned with the correspondingly colored center. The next step solves the remaining first two layers using only left, right, top and bottom face turns, one of the advantages of ZZ. On completion of the first two layers, the last layer's edges are all correctly oriented because of edge pre-orientation during EOLine. The last layer may be completed using a number of techniques including those used in the CFOP method. An expert variant of this method (ZZ-a) allows the last layer to be completed in a single step with an average of just over 12 moves and knowledge of at least 472 algorithms.

https://en.wikipedia.org/wiki/Rubik%27s_Cube
https://en.wikipedia.org/wiki/Speedcubing
Wizard