# My 40ish year old Rubik's Cube

• Averagesupernova
Wrong. Reality is more complex, and the two sequences of moves will not always solve the puzzle. However, if you follow a sequence of moves that swaps two corners and does nothing else, and another sequence of moves that swaps two sides and does nothing else, you'll usually end up with the same result.

#### Averagesupernova

Gold Member
As the title implies, I have a cube that was given to me new around 1980-1981. All the info I have found online indicates my cube is likely not an original. I would have thought at that time there wouldn't have been knock offs, but it's entirely possible I am wrong.
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The colors on my cube do not match what a genuine cube is supposed to be. The center blocks do not match what the genuine Rubik is supposed to be. With yellow on top, and white towards me as I hold it, green is on the bottom, red is on the left, orange is on the right, and blue is opposite white. That in and of itself does not bother me in the least. But a tutorial I found works up until solving the last layers corners. I'm wondering if the fact that it does not match a genuine Rubik is why. I can't imagine it would. One thing I'll throw out there, I have solved it in the past, and as far as I know it has never been pried apart and put together wrong.
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Here is the site I am using: https://www.youcandothecube.com/solve-it/3x3-solution
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Edit: Wiki article says early cubes did not follow a specific ordering of color orientation. I'll keep trying.

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Puzzle solved. As long as I translated the colors to what my cube actually is, it went well. I had missed a step which caused the initial problem. How many here can say they have the cube given to them as a Christmas gift in 1980-1981? Lol

My understanding is that a "standard" cube is oriented White (Top), Yellow (Bottom), Red (Facing you) and Blue, Orange, Green going counterclockwise. Yours is Yellow (Top), Green (bottom), White (towards you) and Orange, Blue and Red, going counterclockwise. Feel free to correct me.

Take the instructions. Replace every instance of White with Yellow, Yellow with Green, Red with White, Blue with Orange, Orange with Blue, and Green with Red. And you're on your way.

Averagesupernova
I got one around then. Mine was opened and six moves made, with the note that if it takes more than six moves to solve, I was making it worse, not better.

sysprog
I tried to find my way back from the first moves I made and was unsuccessful in solving it until it occurred to me I should look up the solution online about 10 years ago. So it sat for 30 years with one side solved for much of that time.

Keith_McClary
If you play around long enough, you learn combinations of moves that swap certain combinations of squares while leaving the others unchanged. That was my key in solving it. That and learning that a cube that looks almost solved may be quite far from a solution and one that looks like a mess might be quite close.

If you play around long enough, you learn combinations of moves that swap certain combinations of squares while leaving the others unchanged. That was my key in solving it. That and learning that a cube that looks almost solved may be quite far from a solution and one that looks like a mess might be quite close.
So you ended up solving it all by yourself? I "gave up" after about 2 weeks or 3 of trying. Then I brainlessly followed an "algorithm" that came with the cube, but I didn't memorize it. Without knowing it, I used to follow a few steps of the algorithm on my own. I would rather figure out a solution by myself, different from the given algorithm (which is, I know, extremely far from the most efficient solution).

Mine never had a solution included.

fluidistic said:
So you ended up solving it all by yourself?

Sure. Lots of people did. The trick was understanding that learning to operate the cube was the critical step, and solving was just a special case - and learning to operate it was not insanely difficult.

People's default plan seemed to be:
1. Turn randomly until one side was mostly one color.
2. Get the remainder of that side one color.
3. Without disturbing the single color side too much, get the other sides one color or close to one color
4. Fix up whatever is left after step 3.
This is a terrible plan. It just makes a mess.

While I don't remember any of the specific steps, a more useful way of thinking about this is:
• The colors are useless. Their only role is in determining if you have an answer or not.
• Corner squares have three colors and move in a particular way.
• Side squares have two colors and move in a particular way.
• Center squares have one color and do not move at all.
If you had a sequence of moves that swapped two corners and did nothing else, and another sequence of moves that swapped two sides and did nothing else, you'd be done, right? Reality is more complex, but that's the thinking.

It's been a long time, but I believe the path to solution was a set of moves that allowed the corners to be positioned while making a mess of the sides, and a second set of moves that exchanged a subset of sides without moving corners (or did so in a predictable and reversible way).

BillTre, Averagesupernova, DaveE and 1 other person
When the Rubik's cube first came out, I was a maths undergraduate at university. The maths department was aware of this cube several months before it became well known to the general public. The group theorists got quite excited as they could apply group orbit theories to analyse the cube. Some produced algorithms that could solve a cube within a few hours.

Some months later, the cube became very popular with the general public and we heard of eight-year-olds who could solve it in a minute or two.

Keith_McClary, 2milehi, fluidistic and 1 other person
Mine never had a solution included.

Sure. Lots of people did. The trick was understanding that learning to operate the cube was the critical step, and solving was just a special case - and learning to operate it was not insanely difficult.

People's default plan seemed to be:
1. Turn randomly until one side was mostly one color.
2. Get the remainder of that side one color.
3. Without disturbing the single color side too much, get the other sides one color or close to one color
4. Fix up whatever is left after step 3.
This is a terrible plan. It just makes a mess.

While I don't remember any of the specific steps, a more useful way of thinking about this is:
• The colors are useless. Their only role is in determining if you have an answer or not.
• Corner squares have three colors and move in a particular way.
• Side squares have two colors and move in a particular way.
• Center squares have one color and do not move at all.
If you had a sequence of moves that swapped two corners and did nothing else, and another sequence of moves that swapped two sides and did nothing else, you'd be done, right? Reality is more complex, but that's the thinking.

It's been a long time, but I believe the path to solution was a set of moves that allowed the corners to be positioned while making a mess of the sides, and a second set of moves that exchanged a subset of sides without moving corners (or did so in a predictable and reversible way).
I wonder if there are easy/quick ways to swap any 2 squares leaving the rest invariant. Maybe by trying to figure out those sequences could lead to a solution, although I have no idea how long (i.e. average number of sequences) a "game" would last, compared to the popular algorithms.

fluidistic said:
I wonder if there are easy/quick ways to swap any 2 squares leaving the rest invariant.

I believe there are not only no easy ways, there are no possible ways. Working on a proof now.

fluidistic
I believe there are not only no easy ways, there are no possible ways. Working on a proof now.
Wow, I didn't even consider this possibility. Could it be possible for certain squares only?
How did you get the insight? From intuition, group theory knowledge or something else?

I'm thinking about square colors as stickers. I can only exchange two squares if I can exchange their color stickers and have the same pieces I had before. Thinking about the corner pieces, I can't turn a right-handed combination into a left-handed combination. I am thinking there is an extension of this for the whole cube - this is a fairly restrictive condition.

The way I am thinking about proving it is by defining a global parity-like variable that is not changed by a single turn of the cube, but is changed by swapping two squares. If I can do that, I'm done.

I definitely remember being shown a "recipe" based on rules similar to those @Vanadium 50 mentions. It started with a single correct layer (which is relatively easy) and then called for a series of operations each of which swapped several blocks (I believe it was 4 each time) in a cyclic way without moving others. So you had one layer ready first, then four remaining corners of the second layer, and the last layer was also done in two steps (each step being a combination of several moves, repeated if necessary).

I don't remember details, but I do remember how happy my cousin was that he knows how to "solve" the cube. I never told him (nor his parents) one can train monkey to do it this way. And no, he didn't came up with this solution, he was shown it by someone.

DrGreg said:
Some months later, the cube became very popular with the general public and we heard of eight-year-olds who could solve it in a minute or two.

See my post - my cousin was doing it in 35 sec (he even won some city level contest). Doesn't mean he knew what he was doing nor why it worked.

DrGreg said:
eight-year-olds who could solve it in a minute or two
Did you ever watch this "live?" I was astounded, this kid said "you take as long as you like to mess it up, and if I put it back in a minute you owe me a dollar." Then he proceeded to do just that. Amazing. I guess you can probably see it on youtube now, but seeing it "live" was special. And worth a buck!

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I'm not sure how old this one is. At least 15 years (?) maybe much older.

Bottom is white. Right is green. Left is orange.

The way I am thinking about proving it is by defining a global parity-like variable that is not changed by a single turn of the cube, but is changed by swapping two squares. If I can do that, I'm done.

This is how. Define a parity such that a solved cube has even parity. If it takes n swaps to return to this condition, the parity is (-1)n. A single turn makes four corner swaps and four side swaps, so has even parity. And there you go.

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This is how. Define a parity such that a solved cube has parity zero. If it takes n swaps to return to this condition, the parity is (-1)n. A single turn makes four corner swaps and four side swaps, so has even parity. And there you go.

You're likely aware, but this is the concept of even and odd permutations (https://en.wikipedia.org/wiki/Parity_of_a_permutation). The relevant fact is that when you write a permutation as a product of transpositions, then the parity of the number of transpositions you used is independent of which transpositions you used.

The same concept let's you show that half of the starting positions for the 15 puzzle are unsolvable.

I still have my genuine Rubik's Cube from back then. I could get one face solved but then got stuck - no internet those days - until I discovered David Singmaster's wonderful little book. It had a method using only two move-sequences which, once one face had been solved, were sufficient to solve the cube. It also told you how to disassemble it - something essential as I went wrong so often.

A local pub offered free beer to anyone who could get one face solved and I claimed mine - the publican then disqualified me as a previous winner.

Hold the cube such that the solved bottom layer stays at the bottom. The moves were

a) (R^2.U^2)(R^2.U^2)( R^2.U^2)

Rotate the Right face twice clockwise (ie through 180 degrees), then the Top face twice clockwise; and repeat twice more.

This sequence swaps two mid-edge pieces (front-top and front-right) with their counterparts on the back and is sufficient to complete the second layer without disturbing the completed base. Pre-moves are used to bring the requisite piece into place for moving it; and the pre-moves are reversed after the sequence. Pre-moves could also be used to bring pieces into position so you only affected pieces in the top layer, necessary for the final step.

b) (FR.F'R')(FR.F'R')(FR.F'R')

Rotate the Front face clockwise, then the Right face clockwise; then the Front face anti-clockwise, then the Right face anti-clockwise. Repeat three times. If you do a pre-move, this sequence operates only on the top layer and moves corner and edge pieces, and spins the corner and edge pieces; you then undo the pre-move. At completion, top layer pieces have been moved and spun without affecting the lower two layers.

Similarly doing it 6 times instead of 3, with appropriate pre-moves, swap edge pieces in only the top layer.

If anyone is interested I'll dig it out and post it.

As an aside, we went to a party and were directed to leave our coats in one of the kid's bedrooms. There was a jumbled Rubik's Cube on a shelf and I spent a few minutes solving it and I put it back. We were later told that the extremely excited lad had dashed down the stairs in the morning shouting "Mum! Dad! Someone's solved my cube!" The lad is now a lawyer.

People who solve it in very short times memorise over 160? "starting positions" and the moves to make when they see that position.

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Infrared said:
The same concept let's you show that half of the starting positions for the 15 puzzle are unsolvable.
IIRC the cube operates in one of 12 non-intersecting cycles. You can traverse a cycle but you cannot jump to a different cycle by manipulation.

For example, take a solved cube. Disassemble it and reassemble it with one corner spun (two ways) or an edge piece flipped. You are now in a different cycle from a solved cube ...

... and is an evil trick to play on someone!

Keith_McClary
fluidistic said:
How did you get the insight? From intuition, group theory knowledge or something else?

I realize I didn't answer this. I guess intuition, plus never hearing of a solution that worked that way. As you saw, suspect there was a proof and imagining what a proof might look like was 90% of the way there.

fluidistic
I had one of those as a kid, circa 1980, but never really had the patience to get skilled at its manipulation. However, I did get good at being able to rapidly disassemble and reassemble it in a 'solved' configuration (i.e. the 'Alexander the Great' approach) and mystified a number of people who had left chronically 'unsolved' cubes laying around; discretely 'solving' them as found and then putting them back where I found them in a 'solved' configuration.

--diogenesNY

BillTre
I have dug out Singmaster's booklet. It is a soft cover pamphlet from 1980 stapled together with 62 pages of densely packed information and, if still available, well worth getting.

The four centre pages describe the solution I posted above. His nomenclature is good: the faces colours to which you are solving are determined by their centres and the direction and magnitude of the face rotations easy to follow.

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