2*2 Rubik 39;s Cube Solution Pdf
Aila Gilb
The method presented here divides the cube into layers and you can solve each layer applying a given algorithm not messing up the pieces already in place. You can find a separate page for each one of the seven stages if the description on this page needs further explanation and examples.
Watch the cube being solved layer-by-layer with this method:
It fixes the white edges, corners then flips the cube to solve the second layer and finally completes the yellow face.
Press the Play button to start the animation
If you get stuck or you don't understand something, the online Rubik's Cube solver program will help you quickly fix your puzzle. All you have to do is input your scramble and the program will calculate the steps leading to the solution.
Use this stage to familiarize yourself with the puzzle and see how far you can get without help. This step is relatively intuitive because there are no solved pieces to watch out for. Just practice and don't give up easily. Try move the white edges to their places not messing up the ones already fixed.
In this step we have to arrange the white corner pieces to finish the first face. If you are very persistent and you managed to do the white cross without help then you can try to do this one as well. If you don't have patience I'll give you some clue.
Twist the bottom layer so that one of the white corners is directly under the spot where it's supposed to go on the top layer. Now, do one of the three algorithms according to the orientation of the piece, aka. in which direction the white sticker is facing. If the white corner piece is where it belongs but turned wrong then first you have to pop it out.
Until this point the procedure was pretty straight forward but from now on we have to use algorithms. We can forget the completed white face so let's turn the cube upside down to focus on the unsolved side.
In this step we are completing the first two layers (F2L). There are two symmetric algorithms we have to use in this step. They're called the Right and Left algorithms. These algorithms insert the Up-Front edge piece from the top layer to the middle layer while not messing up the solved white face.
If none of the pieces in the top layer are already lined up like in the images below, then turn the top layer until one of the edge pieces in the top layer matches one of the images below. Then follow the matching algorithm for that orientation.
After making the yellow cross on the top of the cube you have to put the yellow edge pieces on their final places to match the colors of the side center pieces. Switch the front and left yellow edges with the following algorithm:
All pieces are on their right places you just have to orient the yellow corners to finish the puzzle. This proved to be the most confusing step so read the instructions and follow the steps carefully.
Turn the top layer only to move another unsolved yellow piece to the front-right-top corner of the cube and do the same R' D' R D again until this specific piece is ok. Be careful not to move the two bottom layers between the algorithms and never rotate the whole cube!
A common misconception is that the cube is solved one colour at a time. This is simply not possible because of the nature of the pieces and the design of the cube. Instead, we approach the cube layer by layer. The bottom layer is solved first, the middle layer next and the last layer towards the end, building the layer up on the previous one.
The yellow cross can be divided into three cases. The algorithm used for each case is the same, however, the initial positions vary. Identify the case on your cube and position it according to the corresponding position in the image. Simply repeat the algorithm until the cross is solved.
Now to match all the corner pieces in the top layer, find a corner that is already matched and keep it towards the front-right of the cube. If none of the corner pieces is in the right place, you can hold the cube in any orientation with the unmatched pieces on top and apply the algorithm.
Now, keeping the yellow side on top and the corner which is not aligned on the front right corner, use the above algorithm till the corner is aligned, then rotate the top layer and bring the unaligned corner to the front right corner and then again apply the same algorithm till the corner is solved. Repeat the process until all the corners are solved.
Congratulations on completing the cube! While the first-time solving is confusing, remember that you get better with each solve. It typically takes at least 5-10 solves to get comfortable with a new method, so keep practising.
Avani Sood from Bengaluru has won 12 female national records overall and has been competing for the past 4 years. She started cubing when she was 11. Her main event is Megaminx. Apart from cubing, she loves to cook and read. She has participated in 10 competitions and won 1 podium.
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My solution is to generate a minimal perfect hash. This involves keeping ALL of the cubes in memory until I have discovered the entire pattern database then generating a minimal perfect hash based off of that. The MPH takes a couple hours to run depending on the pattern database size, but I only need to do it once since I save it to disk. In the end, I can throw away the cubes themselves storing only the MPH. That way I can take a randomized rubik's cube, apply the pattern, then look up the array index in the MPH to get an estimated solution length.
This paper describes an algorithm to generate an index based off of the lexicographical ordering of a permutation. Basically you can take the permutation 1, 2, 3 and figure that it is the smallest with an index of 0. 1, 3, 2 is next up with an index of 1 and so on.
The corners only pattern database for instance contains all rubik's cubes that have had their edge stickers taken off. There are exactly 88,179,840 cubes in this set. Any corner cubie on a rubiks cube can be in one of 24 different states. The state of the 8th corner cubie can be calculated based on the other 7 so cubes in the corners only pattern database each have 7 values between 0 and 23
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I ordered a Rubik's Cube a few days back, and it finally came in the mail today. I've never quite mastered the algorithms necessary to solve a cube, so seeing expert solvers speed through the task has always felt a little bit mystical to me.
Six sides to the cube, and all of them red. It's practically impossible to lose! But it also raises questions about what winning really looks like. Here's a challenge: think of one way to rearrange this cube in a way that most people would agree is "losing". I'll share a few answers at the end of the article.
With a standard Rubik's Cube, there are a number of different algorithms that can take you to the end, but you'll definitely know when you reach the "solution"...it's when each side only has one color showing. But that's only because of your perspective.
Since every side of a Rubik's Cube is typically a solid color, it doesn't matter which way each cube is positioned...but there are variants of the standard Rubik's Cube like the Picture Cube where orientation matters - you can have every color matching without "solving" the puzzle. In the below video, you can see a cube that would be considered solved for most purposes, but fails for the intended use at the 1:23 mark.
Can I consider my all red Rubik's Cube "solved" because each side has only one color on it, or is it now unsolvable since I can never tell if I returned it to the original state? And does the introduction of orientation mean that some solutions are better than others?
Most of the time, puzzles are solvable because they've been designed to have that concrete and recognizable end...that's something that's much more of a rarity in real life. But even seemingly solvable puzzles can hide unexpected complexities.
But back to my all red Rubik's Cube. There are all sorts of ways to render the presumably solved puzzle unresolved. Write on the sides with a permanent marker, and all of a sudden you have new information that wasn't there before. Peel off a few stickers, and you could break things even more. If you're feeling particularly violent, pry the pieces apart and you no longer even have something recognizable as a cube.
I am trying to figure out how to measure the relative success level of a given (but unsolved!) Rubik's Cube state. My first idea was to calculate the number of overlapping "cells" in the destination (solved) state and the given (unsolved) state, and present this as the following:
But I have the feeling that this ratio doesn't necessarily correlate with the actual success level (so you're not necessarily closer to the full solution with a relatively high level of correct cell positions). Is there a more elegant (and calculable) way to measure this?
If you could measure the distance from any state to the solved state, you'd have a trivial solution algorithm: simply make any move that reduces the distance! Therefore, a distance measure cannot be simpler than a cube-solving algorithm.
If you for whatever reason cannot use one of the existing solver implementations, you can improve the estimation heuristic by not just counting how many cells are incorrectly positioned but rather summing the distance(whatever that might be) from their correct positions.
You can represent position of a cell by 3D vector(=array) of 3 values in range that is from -1 left/bottom, to 0 for center to right/top for +1. For example the [1,1,0] is for upper-right cell of front face. Center of cube is the origin. Note: face center cells are fixed so the position is orientation invariant as long as you always orient face centers the same way.