A Minimal Rubik’s Cube Solution.

An easy-to-remember method for solving the Rubik’s cube. This method is not for speed cubing but it is great for beginners. Experienced cubers can teach this to their friends and relations.

Avishalom Shalit
HackerNoon.com
Published in
7 min readJun 25, 2019

--

Sneak Peek, last step
Review of the first three sequences. Note that all of them follow a similar pattern, see explanations below.

Is this post for you?

This post is written for two audiences.
It is written for cube-enthusiasts, and cube mostly-indifferentists. If you are in the first group, you’ve probably tried teaching it, this method is very easy to teach.
If you are in the second group, you’ve considered learning it recreationally, but only if it takes about 15 minutes. You are in luck!

Some cube solving methods are fast. This one is small and can be worked out from first principles. (as opposed to memorized arbitrarily.)It is composed of a minimal set of easy moves with much in common between the steps.

We will review these commonalities at the end to make it easy to remember.

The edge colors line up nicely.

Step 0: Bottom cross.

You are on your own. You can put an edge in its place without disturbing others. Don’t waste RAM on this, just do it. If you get stuck, there are links to tutorials at the bottom of this post.

Step 1: “Drop In” — place first layer corners.

Remember the front face has the piece of interest (the white side of the piece.)

Do this for all 4 corners.

Alternative:

What if the corner was twisted and the white facelet was facing the blue side? Nothing changes in principle. The front face is now the blue face, because it holds the The active side is orange. (color match)

Alternatives ¹ :
A) Corner is already in place but twisted:
“Step 1: Drop In” x 2
B) White side is on top (not one side):
“Step 1: Drop In” x 3
C) Wrong corner is on the bottom:
move any corner down and continue.

Step 2. Connect the edge — second layer edges.

This step involves making use of what we’ve learned.
It has two parts, Step 2a moves the corner up and connects it to the edge
Step 2b is actually Step 1. Make use of what you know.

Remember- the Front face has the edge piece we are interested in. Color match of the center and the edge forms an upside down T.

Do this for all 4 middle layer edges.

Mnemonics :

The Moves are the same as in step 1, But definition of what the front face is and what the active side is changes. In step one the front is the face that has the white side (facelet) of the corner, because that’s what we are interested in, in this step, the front is the face that has the piece we are interested in.

If you don’t have an edge that you need in the top row, it must be in the wrong place in the middle layer. move it up by moving the wrong one in.

Alternative:

If you can’t find a suitable edge piece on the top row, it must be in the wrong location on the second row, or in the right location but flipped, use this algorithm to put a “wrong” edge into that location, and it will pop the edge up. Then: Step 2.

Step 3: “Ping pong”, Place 3 top layer corners.

This algorithms keeps one corner in place and swaps the other 3.

The Yellow, Orange, Blue corner piece is in its right place; nestled between the Yellow, Orange and Blue faces. It may not be oriented correctly. That’s fine.

Orientation

At this stage of the solve we are only concerned with each corner being placed in the right place (the 3 faces match the sides’ colors) but the piece might be rotated in one of 3 ways. We’ll take care of that next.

Don’t bother remembering the direction, instead remember that 3 repeats return to the first state, so repeating the pattern twice is like going the other way.

Alternatives:

  • You still have 3 wrong corners? Do it a second time. (a third time will revert to the initial position.)
  • If you don’t have exactly one edge in the right place…. You might have:
    0 Corners: Keep turning the top face something should line up.
    4 Corners: All done. congrats.
    3 Corners: Impossible. the 4th one must be in place.
    2 Corners (adjacent): keep turning, you’ll find a stop with one right corner. (Then rotate the cube so that one is top right)
    2 Corners (opposite): pick an arbitrary corner as “Good”, and run the algorithm once, then you’ll be in the 1 corner situation. (you may have to turn the top and rotate the cube.)

Mnemonic:

Pay attention to the top right corner, it will ping pong along the top row, always staying in front, always moving out of the way before a side moves up or down

Step 4 : Twist 3 corners

Don’t bother remembering the direction, instead remember that 3 repeats return to the first state, so repeating the pattern twice is like going the other way. Also notice that the edge corner pair is never broken by the active edge moving up and down (this is depicted as the green-orange-white pair in the final illustration)

Alternatives:

What if you need to “twist close” instead of “twist open” ?
Easy! Just twist open again!
(or you could do a mirror image, and keep the top left corner unchanged)

What if you need to twist a different number of corners, i.e. 2 or 4 ?
You will need to act twice each time with a different top-right corner.
Pick a corner that is not right, and run the sequence (once or twice).
The result of the first sequence will be a single corner that is twisted correctly.
Make the correct corner top-right for the next run.

I could give more rules about which corner to pick to minimize moves, but I’d rather you do a move twice than memorize another fact. (you can figure this out on your own later.)

Step 5: Shuffle the last edges

Don’t bother remembering the direction, instead remember that 3 repeats return to the first state, so repeating the pattern twice is like going the other way.

If all 4 are out of place you will need to do this method to get one edge in place, then use that face as the front face. At the end of this stage you are either done or you need to flip some edges where they are. if you need to flip edges go to step 6.
You might avoid needing step 6 by using this extra trick (which is out of scope for this recipe list because it uses the back edge.)

Advanced move (not needed for solve):

Step 5 also flips two of the edges (the shorter arrows). You can avoid the flip by replacing the first and last move of step 5 each by a double turn of the back face.
Mnemonic: The first move of the sequence takes the edge at the back of the top face and puts it at the back of the bottom face. Just like turning the back twice.

Step 6: Flip the last edges.

You already saw this, this is the first image right below the title.

This is the same as the sneak peek you saw at the start.

Summary

This is a minimal solution to the cube.
You shouldn’t have to remember much. These moves have been selected because they all conform to a small set of rules.

  • Minimal ingredients.
  • Moves either cancel out, or repeat 4 times to complete a circle
  • Top moves away from active edge
  • Moves 1–3 start with the top face turning away, 4–6 start with “up”
  • All moves feature up before down
The ingredients for any sequence include the top face, and a vertical move

Reference:

Links :

Images were created with Ruwix.
Arrow notation was taken from chessandpoker.com.
Solution for the white cross also on Ruwix

Video Walkthrough,

Requests:

I’ve tried to make sure to cover all possible cases, if you got stuck anywhere, and the instructions weren’t enough — let me know.

Footnotes:

[1] Every application of the 4 moves that make up “Step 1” swaps the top and bottom corners -> applying it twice returns the corners to where they were, but twists them a ⅓ of a turn. (Applying it 6 times is like doing nothing.)

--

--

Avishalom Shalit
HackerNoon.com

Data Science & Analytics, ML , AI and all the buzzwords (I used to be called an “Algorithm Developer”, which was the style at the time)