Wednesday, August 20, 2014

Complete guide to solve Rubik's cube

Hi! Today's topic is solving Rubik's cube.

After spending a lot of time reading various guides, I've come up with instruction compilation that fit on a small 13 by 9 cm cheat sheet like this.

Photo from Samsung Galaxy Y. Sorry for photo quality.

Let's get the notation out of the way (naming). This is the cube that I bought. It's called Dayan. Maybe a Chinese notation, I don't know. I learned from the Russians.
When you hold it in your hands, the left hand touches left side Л and the side facing you is face Ф. Right is правый П. There's also a back side in Russian called тильный T. Pretty sure it's misspelled, but I'll try to correct it later. Bottom side is нижний H, roof plane верх B (bee is read as V for Vendetta).

Ok, now. This follows what people call the easy way. Start by choosing any colour you like. Locate the centre piece 5. When you look at numpad of computer keyboard, the numbers are arranged like
789
456
123
so 5 is the centre piece. 4862 are edges, 7913 are corners.
Try your best to assemble a cross on the top, matching colours with centre pieces of other colours. Basically, if  yellow is on plane B, then arrange 5 yellow to match B 2 yellow to Ф 8 orange, and Ф 8 orange to Ф 5 orange.
I'll borrow a picture from this guide to illustrate

Then do the corners to complete B plane. This is the first time I will include a formula. That means locate the pattern and execute instructions. If you've got the corner you need in pattern Ф 3, and you need to place it in B 3 (Ф 3 is the same colour as B 5), then execute:
H, П↓, H, П
if colour you need is in the corner H 9 in relation to B 3 where it should sit, then execute:
П↓, 2x H←, П↑, H→, П↓, H←, П
For the last combination of  П 1 to B 3 execute:
П↓, H←, П

At this stage the top layer should be solved, and all the sides Ф П T Л in alignment of a tetris figure.

Now is the time to shift edges of Ф 4 and Ф 6 into position. After this only the H plane will be unsolved. Find the colour you need, rotate H until Ф 2 forms a "T" with the solved part. Then, if it needs to go to position Ф 6 (to the right and up), execute:
H, П↓, H, П↑, H, Ф, H, Ф
The formula for shifting to left (Ф 2 to Ф 4) is
H, Л↓, H, Л↑, H, Ф, H, Ф

Sometimes the edge already sits in place, but is aligned wrong to colours. Just execute one of the formulas to replace the edge back to H plane, align and put it back.

This is where you flip the cube. Bottom side H should have the solved part thus far, and top part B should be the only left unsolved.
Take a good look at the corners B 1, B 3, B 7, B 9. The corners should be aligned in pairs, like B1 and B3 should either be in correct positions or need to be exchanged to fit.
The other case is that B1, B3 and B7 and B9 should exchange positions to take the correct position. By correct position I mean the corner should be where it would complete the cube after rotation. It does not matter what direction they are rotated. For now we need to place them to correct position.
There are two approaches, depending on where the corners are located. Go ahead and rotate B plane, until you have identified which case applies to you. The corner position will determine which side becomes Ф, so you know how to hold the cube to get the desired effect after formula. If the corners are already in place, then skip this step.
So, to exchange B1 and B3 only, use (2x means twice the same move):
Л, B→, Л, Ф, B, Ф, Л, B, Л, 2x B
to exchange B1 with B3 and B7 with B9, use:
Л, B→, Л, Ф, 2x B, Ф, Л, B, Л

Now take another look at the top B plane. The goal is to rotate corners so that the unsolved colour forms a solved X. The best case is if only one corner is rotated correctly. If you see two or more upturned corners (I imagine the tiles in corners as lights turned on or off in relation to the centre piece), then execute the "scenario B1 Ф9" formula (described below) once and check again. Side Ф is revealed by the colour in Ф7 that matches to B5 (this sentence sounds confusing only because it's important that plane B remains unmoved while the Ф plane is identified. Check the sides of cube without moving planes to align edges).

When there is only single upturned tile in corners of B, then examine neighbouring corners. We are looking for pattern where B3 colour is same as B5 and Ф7, or B1 is same colour as B5 and  Ф9. I've simplified this step from other guides.
Now, if you're in the scenario B3 Ф7, execute: 
Л↑, B, Л, B, Л, 2x B, Л, 2x B
scenario B1 Ф9:
П, B, П, B, П, 2x B, П, 2x B

Now it's important that you don't turn B plane. Visually inspect the cube and determine which case applies.
The next formula can shift edges in triangle formation clockwise or counter-clockwise. The edges B4, B6 and B8 will be swapped with:

up, down, B, up, C

I'll explain the abstraction. Up corresponds to centre up followed by top in the direction you want to swap. Down means centre down, B in the direction the corners need to go and it's the same throughout the formula. Repeat B once more after down as shown.

The full formula for edge shifting in triangle formation clockwise is
C, B→, C, 2x B→, C, B→, C
anti-clockwise edge shifting:
C↑, B←, C↓, 2x B, C↑, B←, C

After experimentation I've found that if you have two correctly positioned edges, then align the cube so that they both will be shifted by the formula, and check again.
If all four edges are out of position, then align the cube so that after shifting, only one edge will be in the correct position. Then inspect the cube again.

I'm sure you'll get the hang of it. The last part is rotating edges into position.
Sometimes cube is solved before this step.
So, now edges can be in three patterns:
either two neighbouring edges, like B2 and B6, or B2 and B4 need flipping, or B2 and B8.
Sometimes all four need flipping. Then it's just the case of repeating dedmore H pattern twice.

Basically, dedmore H rotates edges B2 and B8:
3x Co↑, B←, 3x Co↓, B
Update: the direction of B only matters in dedmore fish formula. So in essence only one formula  need remembering.

Dedmore fish pattern rotates B2 and B6 (so adjust the cube appropriately):
П↑, T←, 3x Co↑, B, 3x Co↓, B, T, П,

By now I trust you can decipher this writing. Replace Co with centre and top movements with the direction corresponding as it's used in the formula. So, in H pattern the plane B will always be rotated left (as used inside Co), and just repeat B movement after the third Co as shown. Plane T is the back one, opposite Ф. In the cheat sheet image I use dot, triangle, circle and cross to denote the four possible stages, but here I've simplified it for execution speed.

Good solving!

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