Rubik's Cube V1.0by James Killian 22 Jun 98
Purpose... To Document the sequences I have memorized, because the book which had some of the sequences didn't really cover how to solve the bottom side, and I made up the most efficient sequences (I think) to solve the bottom as well. I don't want to have to try and remember each time how I do all of my sequences I'd like to have a hard copy to refresh my memory on how to solve it. Perhaps in the future I may implement a virtual program to simulate a Rubik's cube, and even go as far as to develope an intelligence program to reason out a solution to find if in fact there is a more efficient way, and to make it compromise the least amount of sequences in every situation so that these sequences can be remembered... so far I have discovered to solve the cube in these following sequences... To make this readable I'll make a key... I'll always declare a constant topside unlike the book, which states to turn the cube upside down. The topside remains the top for the duration of the solution. In fact since the original Rubik's cube had the logo written in the center white square, we'll solve the white side first, and it will be the constant topside. Next I'll have a constant front side, this will be constant per any given sequence, and I'll state when to change front side, because really when you think about it its easier to rotate the cube and maintain vertical moves than to keep a constant front face trying to move it any other way. This means I'll specify which front side you are working on at any given time in the sequence. Here's a layout of my cube for color reference
Where white is the top, blue is the bottom this would be constant throughout solution and so the 4 working colors gryo, are also constant throughout solution; Now in this case the front side is red the left is green right yellow and back is orange, if I say rotate 90 to the right (Ror) yellow would be the new front as red=left orange=right and green=back. Note there are 3 types of cube pieces,center piece 1 side side piece 2 sides corner piece 3 sides so this means there are 6*1 center 12*2 side, and 8*3 corner = 54 = 9*6 total colors to solve My method of solving the cube is in the following order: 1. Solve the TopSide first (no sequences listed) a. Solve the sides b. Solve the corners 2. Solve the Top Sides (2 sequences) 3. Solve the Top Corners (2 sequences) 4. Solve the Middle Row (1 sequence) 5. Solve the Bottom Corners a. Place corners in right area (2 sequences) b. Flip corners (1 sequence) 6. Solve the Bottom Sides a. Flip sides (3 sequences) b. Place corners in right area (2 sequences) So that's roughly 13 sequence's to memorize not bad and they are pretty efficient too. so here it goes... Note any two turn combination doesn't matter which direction There is never a case in my sequences where the middle will be turned horizontally, you never do TL+BL T2+B2 TR+BR instead do LU+RU LD+RD L2+R2 (used M2 instead in sequence of course since there are no L2's or R2's separately) see key below... horizontal- (note no sequences are written for Tl T2 Tr, because these turns only apply in step one, and I have not written any sequences for this step) Bl=Bottom Left B2=Bottom Twice Br=Bottom Right (Think of bottom moves as the ideal piece manipulation moves, especially since these are the only horizontal moves I use, as the vertical moves simply bring the pieces down to be manipulated) Vertical- Other- (refer to the cube layout above for more details for RoR and RoL) Let Start1. Solve the TopSide first (no sequences listed)
a. Solve the sides
Solving the topside there is no way to document all the possible
sequences its too vast, it's easy enough to figure out, simply start
with the side pieces to make a plus sign then find the corners put
them in....
b. Solve the corners
Now to solve the corner tops I am not going to explain its too many
possibilities if you have problems have someone show you or keep
trying its a matter of time you'll see my point perhaps when I make
the intelligence program I'll find a way to document these ideas in
step 1.
2. Solve the Top Sides (2 sequences) Now you should have one side solved (In our example white); however its not really until step 2 & 3 are completed, basically the white pieces have to be in the right places which takes care of the whole top row so first we start with the white side pieces there are 2 types of manipulation in this step, one is to swap Front Top and Back Top side pieces See Sequence 1, the other is to swap Front with left or Right side pieces See Sequence 2. Sequence 1: M2 B2 M2 Sequence 2a: Md (Rol) Md Bl Mu B2 (Ror) Mu 3. Solve the Top Corners (2 sequences) Now the white side tops are in the right place now position the corners in the right place determine whether you wish to manipulate a corner from say left to right (sequence 3) or diagonal corners like front left to back right for example (sequence 4) Sequence 3: Rd Br Ru Ld Bl Lu Rd Br Ru Sequence 4a: Rd Lu B2 Ru Ld 4. Solve the Middle Row (1 sequence) So finally the top row on your four working sides all match as now you truly solved the top side, it now looks like "T's" on all four sides now were ready for the middle horizonal pieces. The trick here is to put the ideal side piece at the bottom if it isn't there already and then do this one sequence to move it into the right middle row... the only way to explain this is by example... Lets say the topside is white and you wish to to move the orange/yellow side piece from the bottom row to its right spot. First face the cube to where white is top and you can see both yellow on the right and orange on the left (substitute colors if your cube is different). Look at bottom side piece. If the front side is yellow and bottom side is orange, line the front side yellow color with yellow center piece and move one more direction Bl opposite of the orange yellow destination and do sequence 5a; however if it were orange with yellow bottom you'd move it Br and do sequence 5b also note the front face for both these sequence is the face color of the front side color of the piece on the bottom that you just move so in this example 5a your front face would be yellow, and 5b your front face would be orange Sequence 5a: (yellow) Rd Br Ru Br (Ror orange) Ld Bl Lu 5. Solve the Bottom Corners Now if you're confused this far, I have news for you, it gets more complex! As you have more pieces to maintain, the sequences get more extensive to manipulate and preserve a greater scale of pieces. The bottom corners, consists of placing them in the correct place and then to flip them...
a. Place corners in right area (2 sequences)
Within placing the corners in the right place, just like the top
side there is left to right sequence 6 and diagonal manipulation
sequence 7. Keep in mind that you'll have to see all three sides to
know which corners belong to which centerpiece on your 4 working
sides, even though they seem to be flipped incorrectly.
Sequence 6a: Rd Bl Ru (Ror) Ld Br Lu (Rol) Rd Br Ru B2
Sequence 6b: Ld Br Lu (Rol) Rd Bl Ru (Ror) Ld Bl Lu B2
Sequence 7a: Rd Bl Ru (Ror) Ld B2 Lu (Rol) Rd Br Ru Bl
Sequence 7b: Ld Br Lu (Rol) Rd B2 Ru (Ror) Ld Bl Lu Br
In diagonal manipulation, you need not do both a and b for 6 & 7.
Just pick the one you like and stick with it. Pick the right front
face to do this one way each time.
b. Flip corners (1 sequence)
This is tricky first check and see if any corners are flipped
correctly. If so see which adjacent corner front side matches the
bottom side. In our example the bottom color is blue, so lets say
your corner red and yellow are flipped correctly check on the red
side and see if the opposing corner on the left is blue if so this is
the first side you'll be working with; however if the yellow side
shows blue this is the side you'll start with. There should be one
side or the other showing a bottom side color on its front face. Now
lets say you find no corners flipped correctly. Find the side which
has 2 colors from the bottom side (blue) this will be your working
side. Now use sequence 8a and 8b to flip, hopefully you only have to
flip a corner once if you had started with the bottom side. If not
it will turn to the bottom side color first and then to its correct
position... here's the sequence
Sequence 8a: Rd Bl Ru Bl Rd B2 Ru B2
Sequence 8b: Ld Br Lu Br Ld B2 Lu B2
6. Solve the Bottom Sides
This part here is where the book, and my documentation is completely
different. Had I have known what I know now for the competition they
had back in the 80's, I believe this might have beaten the other
peoples sequences. I could be wrong but I think it is the most
efficient method to solve the bottom side. This is no doubt the hardest
part to explain, but necessary to explain very thoroughly since the book
doesn't cover it. as you can see in fig a you flip sides to where all 4
sides bottom sides are down to where the bottom side is a solid color
finally, then to manipulate them to the correct working sides to complete
the solution.
a. Flip sides (3 sequences)
Our first objective is to flip all bottom sides down, to where the
bottom side is a solid color (blue in our example).
First look at your bottom side. There are 3 possible ways it is now
1. 2 sides up 2 down in a diagonal fashion
2. 2 sides up 2 down in opposite working sides (bottom looks
like an "H" or "I")
3. 4 bottom sides up and 0 down
refer to sequence 9-11 which correspond to these 3 possible
ways (possibility 1 do Sequence 9 2=10 and so on).
Sequence 9: Md Bl Mu B2 Md Bl Mu
Sequence 10: Md Bl Mu Bl Md Bl Mu Bl Md Bl Mu Br
Sequence 11a: Md Bl Mu (Ror) Md Br Mu (Rol) Md Br Mu (Ror) Md Bl Mu
11b: Md Br Mu (Rol) Md Bl Mu (Ror) Md Bl Mu (Rol) Md Br Mu
For Possibility 1, simply pick the face to where the left and back
sides are the ones needed flipping, after sequence 9 this will finish
this part. For Possibility 2, it doesn't matter which face you pick
to be front, after performing this sequence, the cube will look like
possibility 1, and then you do sequence 9 to finish. In possibility 3
doing either sequence 11a or 11b will work, this one is easy enough
to calculate if a solution is possible for example if your front face
is Red and the left and right bottom are orange and red, simply do
11a if the Red is on the left, and 11b if the Red is on the right,
this would then finish the solution.
Note: You can manipulate pieces in sequence 9 since sequence 9 does
rotate the left right and back pieces, but it's risky because it
flips them too, so I decided not to document trying to manipulate
pieces using sequence 9 because the time spent trying to figure out
these predictions would take longer to solve anyway.
b. Place sides in right area (1 sequence)
sequence 12 makes it to where the bottom sides of the front left
and back get rotated all to the left to where front=left
left=back and back=front.
sequence 13a swaps front with right and back with left and sequence
13b swaps front with left and back with right Once again, you can
either do a or b depending on which front face you select
Sequence 12: Md B2 Mu (RoR) Br Md B2 Mu Bl Md (Rol) Md Bl Mu (Ror) Mu Br
Sequence 13a: Md Bl M2 Bl M2 Bl Mu Bl M2 B2 M2 B2
Sequence 13b: Md Br M2 Br M2 Br Mu Br M2 B2 M2 B2
Both 12 and 13 keep the flipping status preserved so if they are
flipped correctly the cube should be solved!
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