How to Solve Rubik's Cube with a combination of just 10 Numbers

Rubik's Combination
by Todd Schannuth

Ever wish Rubik's Cube had a simple solution? Well, it does. And it's just ten numbers:

2413-1526
642-315
4232-4223
2417-2318
394-10

Write them down or copy them into the notes on your smartphone.
They're all you need to solve Rubik's Cube, every time.

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The Solution

Try this:

Imagine assigning numbers to the faces of the Cube.

Holding the cube in front of you, imagine the top face is 2, the right face is 4, the face straight in front of you is 6, left face 8, and bottom face 10. Forget the back face that's furthest from you. It doesn't need a number.

Rubik's Cube Simple-Ten Solution

In this Combination method's nomenclature, 'even numbers' mean you should dial that face one quarter turn clockwise. If you are meant to turn a face counter-clockwise, we'll just subtract 1. So, on paper, turning face #6 clockwise would be expressed simply as "6" and turning face #6 counter-clockwise would be expressed as "5".

That's all there is to it.

Note: You might find it easier to practice all this on a 'virtual cube' -- inside the official Rubik's Cube smartphone app -- than on a 'real cube'. The app (free, as of this writing) has one very helpful feature -- a "Back" button to retrace your steps to the point where you think you messed up. A real cube is far less forgiving.

Just to be clear on Notation:

10 = Turn face #10 one quarter turn clockwise.
9 = Turn face 10 counter-clockwise.
8 = Turn face 8 clockwise.
7 = Turn face 8 counter-clockwise.
6 = Turn face 6 clockwise.
5 = Turn face 6 counter-clockwise.
4 = Turn face 4 clockwise.
3 = Turn face 4 counter-clockwise.
2 = Turn face 2 clockwise.
1 = Turn face 2 counter-clockwise.

Let's get crackin'

Solve a Single Face. I don't have any instructions for this. It's not hard. Just do it. After you solve one face (blue in the following example), spin the 'equator' beneath it until the colors of the side-centers align correctly (in this case, the white and red center pieces). Your cube should look like the one below. This is your starting point. From here, ten numbers are all you need to unlock the solution.


	The place to start.

Step 1 : Dial 2413-1526 to Solve the Middle Layer Edges.
Flip the cube over so the face you just solved is on the bottom (face #10 in this scheme) - the blue face in this example. Spin the top face (face #2) until an edge piece is in one of the positions depicted below. To get that piece into its final position with correct color alignment, use the combination of moves shown below: 2413-1526 or 1526-2413. Repeat as needed until all the middle layer edges are in the right place with the right orientation of colors. If an out-of-place edge piece is already on a middle edge, don't fret. Just perform one of these combinations to move it up to the top edge and then solve as you would any other.

In truth, you can solve the entire middle layer using only 2413-1526, it just takes longer to power though with only the one combination. Making smart use of its inverse (1526-2413) will knock at least 30 seconds off your time.


2413-1526	Depending on which way you want to turn the edge piece, just flip the two numbers: 2413-1526 becomes 1526-2413.	1526-2413


	How your cube should look at the end of this step.

Step 2 : Dial 642-315 to Solve the Upper Cross.
Rotate the top layer (face #2) until the top edges look like one of these three possibilities. Perform the 642-315 sequence. If you still don't have a cross, again rotate the top (face #2) until it looks like one of the possibilities below -- and then perform the 642-315 sequence again. Eventually, you will have a cross on top of your cube. Note that throughout this step there will likely be other green pieces on top, in addition to those depicted here.


642-315	642-315	642-315


	How your cube should look with a cross.

Step 3 - Dial 4232-4223 to Fix Those Top Edges.
Rotate the top face (face #2) until one of the top edges is in the right place. If the others are out of place, this sequence will shuffle them around, counter clockwise, leaving the one good edge piece in place. If you end up solving two adjacent sides (in this example the orange and yellow sides) while the other two remain unsolved (here, the unseen white and red sides), just rotate the whole cube so that face 8 becomes face 6 and then dial this sequence again.


4232-4223 Dial this sequence one or more times.		How your cube should look at the end of this step. The two top center edges you can't see in this view are also color-aligned -- or you need to keep working until they are.

Step 4 - Dial 2417-2318 to Solve the Top Corners (positions).
Solving the top corners is a two step process. First you need to get the corners into their correct overall positions, then (Step 5 below) you can rotate those corners into their correct color alignment. To change the positions of the top corners, rotate the whole cube until you find a corner in the right position (whether or not the colors on that corner are in the correct alignment) and put that corner directly in front of you (at the corner where faces 2, 4 & 6 meet). If you can't find a corner already in its correct position, just perform this sequence once and at least one will fall into place. Perform this sequence until they all find their positions, regardless of color alignment.


2417-2318 You may need to dial this sequence 2-3 times. Remember, "7" means turn face #8 counterclockwise.		How your cube might look at the end of this step. Colors aren't likely to be in their correct alignments, but the corners are now in their correct relative positions.

Step 5 - Dial 394-10 to Solve the Top Corners (colors).
Now that the corners are in their proper positions, you'll probably need to 'spin' two or three of them 'in place' to get their colors to align correctly. To do that, rotate the whole cube until a problem corner is at the intersection of faces 2, 4 & 6 and perform this sequence 2-4 times. After you solve one problem corner, keep the bottom two layers of the cube in their current position -- even as you turn face #2 to bring another problem corner into the 2/4/6 corner.


394-10		394-10
	Repeat 2-4 times to solve each problem corner. When you solve one problem corner, rotate only the top face (face #2) to bring the next problem corner to the intersection of faces 2, 4 & 6 -- even as the cube is looking quite messed up. Keep doing this until the last problem corner has been addressed -- no matter how messed up the cube looks. Don't cut the sequence short just because 394 seems to bring the problem corner into color alignment -- always finish the whole three-nine-four-ten sequence. Before you know it, everything will fall into place.

	2413-1526 642-315 4232-4223 2417-2318 394-10
	Congratulations! You've just cracked the combination to Rubik's Cube.

Step 6 (optional, quoting from David Singmaster in his 1981 book)
Scream HOORAY! Buy a round of drinks. Send [Singmaster] a check. Tell the orderlies that they can let you out now. Etc, etc.

Now you're done.

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Acknowledgments & Notes

First, a little background on this solution:

Speedcubing is for Cubers (Yes, it's a thing. And so are they) who use all manner of notation to describe the ways they manipulate every piece and plane of 'the Cube' - with algorithms that allow them to solve it in well under 20 seconds. Each face of the cube is assigned a letter (U,R,D,B,etc). Each center slice gets its own letter. To describe turning them counter-clockwise requires a subscript "i" or superscript -1, etc, etc. The nomenclature can get deep quickly.

This ain't one of those methods.

This variation on (what has come to be called) the Beginner's Method assumes you've got a good five minutes to kill, and no one to impress but yourself.

This solution came out of my frustration trying to solve a Cube someone handed my in that spring of 2016. I hadn't touched a cube since the late 1980s, but had vague memories of having been able to solve it (albeit, slowly). I decided to see if I could again memorize a solution.

You can find several simple 7-step Beginner's Method solutions to the Cube online (most are slight variations of the general layer-by-layer approach credited to mathematician David Singmaster, first published in his 1981 book Notes on Rubik's Magic Cube), but one of these Beginner's Method variations in particular lends itself to a 'By The Numbers' approach, so I'll be picking on that one. Dénes Ferenc has a couple of the best illustrated versions of it on the internet.

The official Rubik's Cube I bought came with an easy-to-understand solution developed by Dan Knights (now Dr. Dan Knights), the 2003 3x3 Speedsolve World Champion. It wasn't advertised as an easy-to-memorize solution, or even a fast solution; just an easy-to-understand one. It did the trick for me. Almost.

This layer-by-layer approach was not the method I'd memorized in the '80s when 'the Cube' was still TIME's Hungarian Horror. This was better; a bit easier. And it seemed to me it had two elegant attributes that more advanced and speedier methods just don't have. First, except for maybe the initial simple step, none of the steps involve turning any of the center rows. You only 'dial' whole faces of the cube. Second, only five of the six faces ever get turned. You can forget about the back face.

The moves were simple enough. It was the notation that seemed over-engineered for the job.

So I started looking for a more intuitive way to describe the layer-by-layer method.

I guess I'm more of a numbers guy. So I set out to find a way to solve the Cube with simple integers instead of the notation I had found so cumbersome over 30 years earlier. Turns out it only takes 10 numbers.

So is this a new method for solving Rubik's Cube?? Hardly. At best it's a new twist on a forty-year-old problem. In computer terms, it's hacking a new 'user interface' onto a tried-and-true program. The layer-by-layer approach goes back at least to Singmaster's solution in the early 1980s -- refined, illustrated and popularized anew in the internet age by the likes of Knights in print and Ferenc, Jasmine Lee and others online. Its popularity stems from its use of very few move sequences (err, algorithms) that repeat often - leading to it commonly being referred to as The Beginner's Method. 'Rubik's Combination' is new only in nomenclature. But if dialing 10 numbers helps you get through the memorization phase and enjoy the cube, maybe it has some merit. Let me know what you think. Can you design any other 'By The Numbers' / numerical solutions to Rubik's Cube? I'd love to hear about it.

Todd