WEEKLY WHINE

Let’s solve your cube like a human

So have you been solving your 3×3×3 cube with this method? If so, you should stop solving your cube in that manner immediately. There are numerous better ways to solve it, so let’s talk about one now.

Like the method we showed you earlier, this method depends on a small number of algorithms that are not hard to remember. So why not give it a spin with your cube?

This is the human Thistlethwaite method for solving the cube. For some time, the original Thistlethwaite method was the record holder for the method that requires the least number of moves. However, it has such large lookup tables that it is not really feasible for a human to perform. And that’s why Ryan Heise developed the human Thistlethwaite method, which this method is based on.

1. TOP/​BOTTOM PARITY

The objective is to get the cube into successive configurations that can be solved using only moves from a specific group. First, we will eliminate the need for 90° turns of the front and back faces, then of the left and right faces, and finally of the top and bottom faces.

For most of the process, we will treat opposite colours as equivalent: red and orange, white and yellow, blue and green. To start, select which colours will be your top and bottom colours. We’ll use red and orange.

1.a. Edge Orientation

This is a simple step. We want to make sure that all twelve edge cubies have correct orientation. Correct orientation means:

• No left/​right colours on the top/​bottom faces.
• No top/​bottom colours on the left/​right faces.
• No left/​right colours on the middle row of the front/​back faces.
• No top/​bottom colours on the centre column of the front/​back faces.

So if we have red and orange as U and D, white and yellow as L and R, and blue and green as F and B, these would be correct cubies:

And these would be incorrect cubies:

So, to complete this step, check your twelve edge cubies and find out which ones have incorrect orientation. There will always be an even number of them. If you have four or more, put one on each edge of the front face, without turning the front or back faces 90°. If you have to turn the front or back faces, turn them 180°. You’ll end up with something like this:

FRONT	BACK

Now just turn the front face 90°, and those four incorrect edges have automatically become correct. Repeat until all the incorrect edges are solved.

But if you’re left over with two incorrect edges, put one of them on the front face, and the other someplace else. Turn the front face 90° so that the incorrect one becomes correct and the correct ones become incorrect. Now you have four incorrect edges, including the one that you moved out of the way earlier. Move that one into the position that the newly correct edge is now in, turn the front face 90° again, and you’ve finished this step.

1.b. Top/​Bottom Crosses

If you’ve done the previous step correctly, you should have four or more red/​orange edges on the top and bottom. But we want all eight red/​orange edges on the top and bottom. The edges don’t need to match; they just need to be on the top and bottom. This algorithm moves one red/​orange edge to the top:

	R U R'

So for each red/​orange edge that’s on the front or back face, just turn the top or bottom face until you have a red/​orange edge above it and a blue/​green edge 90° away from that. Then do the above algorithm, or a mirror of it, and repeat until you have a red/​orange cross on both the top and the bottom, like this:

FRONT	BACK

1.c. Top/​Bottom Corners

Now we want to make the entire top and bottom faces red/​orange. There are eight corners, all of which have either a red or an orange face. We want all the red and orange facing up or down. If they’re not already correct, you will always have at least two of them that are not correct. If you can arrange two of them as shown, this is the algorithm to fix them:

	L D' R2 D L'

Do this algorithm, or a mirror of it, for every pair of incorrect corners until they are all solved.

To get your incorrect corners into position, just turn the top and bottom faces, and do 180° turns of the other faces. That will get your corners into the position as shown. But sometimes, if you have three or six incorrect corners, you may not be able to get two of them into the right position. If so, just put two incorrect corners into the positions shown, even if the red/​orange faces aren’t in the right direction:

	L D' R2 D L'

This will correct one of them, and you can then proceed normally.

So when you are done with this step, your cube should look something like this:

FRONT	BACK

The top and bottom faces are completely red/​orange. From here on out, the cube can be solved without ever turning the front, back, left, or right faces 90°. Of course, some of the algorithms will still use some of those moves as a shortcut.

2. SIDE PARITY

Now our goal is to do the same thing with the front, back, left, and right faces: make the front and back blue/​green, and the left and right white/​yellow.

2.a. Side Corners

In this step, we are going to start treating opposite colours differently again. To start, make sure all the corners on the top or bottom match the centre cubie on that face:

FRONT	BACK

Do that by turning the top or bottom faces until you have one or two mismatches along one side, and then turn that side face 180°, like this:

BEFORE		AFTER
FRONT	BACK	FRONT	BACK

Now look at the corners on each side face. You want adjacent corners on each face to match, like this:

FRONT	BACK

They don’t need to match that face’s centre, and the top corners don’t need to match the bottom corners. You just want the same colour on the upper left and upper right of each face, and the same colour on the lower left and lower right of each face.

The top and bottom layer can each be in one of three different configurations: all faces mismatched, one face matched, or all faces matched. If everybody on the top and the bottom is mismatched, here is what to do:

		R2 F2 R2
FRONT	BACK

If there is one match on one layer and no matches on the other, do this algorithm:

		R' F R' B2 R F' R
FRONT	BACK

If you have some other configuration, do these algorithms in sequence. Remember that the first algorithm exchanges opposite corners on both the top and bottom layers, and the second algorithm exchanges adjacent corners at the back of the top layer and opposite corners on the bottom layer. So, if you have one face matched on both the top and bottom layers, put the matched faces at the bottom of the front and the top of the back, do the second algorithm, turn your cube over so that the newly matched face is at the top front, and do the second algorithm again. You can work out the sequence for the other possibilities – all and one matches, all and zero matches – on your own.

2.b. Side Edges

So now the top pairs of corners on each face match, as do the bottom faces. For this next step, opposite colours are equivalent again.

Start by making sure that the front and back faces have blue/​green corners, and the left and right faces have white/​yellow corners, like this:

FRONT	BACK

Now look for edges on the sides that don’t match. You’ll always have an even number of mismatches out of the eight. If there are four, use 180° turns to arrange them as shown, and then do this algorithm:

		U M2 U'
FRONT	BACK

Note that we are now using the letter M. This represents the middle slice that falls between the left and right slices. M is a turn in the same direction as R or L', and M' is a turn in the same direction as R' or L.

This may disrupt the corner colour pairings that we established in the previous step. That is to be expected; the work we did in the last step makes it possible to do this step in the first place. And we will fix the corners again in the next step.

If you have two or six mismatched edges, arrange the odd ones next to each other, and do the above algorithm. This will leave you with four mismatched edges, so just arrange them correctly and do the algorithm again.

If you have done this step correctly, every face of the cube should now be made up of the correct colour pairs. For example:

FRONT	BACK

3. FULL SOLVE

For the rest of the solution, opposite colours will no longer count the same.

3.a. Corners

In this step, we want to match all the corners on each face. You can do this with nothing but 180° turns, so there are no algorithms. Just turn the right faces until everything matches, like this:

FRONT	BACK

3.b. Edges

Now, only the edges are wrong. There are a few basic scenarios you will run into:

		U2 R2 U2 R2 U2 R2
FRONT	BACK

		F2 M2 F2 M2
FRONT	BACK

		F2 M' F2 M
FRONT	BACK

		M2 U M2 U2 M2 U M2
FRONT	BACK

These algorithms, in the appropriate combinations, will solve any possible configuration of edges that you will see in this step. The end result, therefore, will look like this:

FRONT	BACK

And that means your cube is solved! Yaaaay!

So this method is light on algorithms, but heavy on understanding how the cube works. This is something of a holistic solution to the cube, as opposed to most speedsolvers who try to solve the cube by layers. Not that there’s anything wrong with that.

ALGORITHM SUMMARY

• 1.b. Top/​Bottom Crosses: Form crosses of edge cubies on top and bottom
  • R U R' [and mirrors]
• 1.c. Top/​Bottom Corners: Orient top and bottom colours on corner cubies
  • L D' R2 D L' [and mirrors]
• 2.a. Side Corners: Orient all corner cubies
  • R2 F2 R2
  • R' F R' B2 R F' R
• 2.b. Side Edges: Match edge cubies on top and bottom layers
  • U M2 U'
• 3.b. Edges: Flip opposite edge cubies
  • U2 R2 U2 R2 U2 R2
  • F2 M2 F2 M2
  • F2 M' F2 M
  • M2 F M2 F2 M2 F M2