5x5 Cube Solution

[Zulema Estabrooks]

Possible Problem:
The corner you are looking for is in the top layer, but in the wrong position or turned the wrong way around. Turn the cube so that the corner is in the front right top corner then move the corner to the bottom layer by following the following steps.

You will now have 4 or 2 edge pieces in the correct place. Matching with the center colors. Ensure the correct edge pieces are at the back and right face. Use the algorithm below to put the edge pieces in the correct position.

STEP 5 - COMPLETE THE THIRD LAYER CORNERS

(1) First we will put the corners in the correct position (A).
You will now have either 0, 1 or ALL the corners pieces will be in their correct positions, either the right way up or reversed.
If one corner piece is in the correct corner turn the cube to that this correct corner is in the front top right position. The piece is in the correct position, BUT may not be turned the correct way around.

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!

The Mensa cube is a puzzle in which a solid cube has been partitioned into $N=11$ rigid parts. The goal of the puzzle is to re-assemble the cube from its parts and place it back in its rigid box. See pictures below.

I've found some formulae like Kasteleyn's 1961 count of domino tilings of checker boards, but nothing that would address the more general shapes of the Mensa puzzle. My personal suspicion is that there is only one way to solve it because of the lack of symmetries, but I have no idea how I would prove something like that.

We have an internal cube we've developed where, over time, the solution file has gone out of date with the production cube. Updates have been made to the production cube directly from BIDS as opposed to being made to the off line solution, then deployed.

Is there a way to create a current solution file from the production cube? If you open the cube on the production server from BIDS, it asks if you want to create a solution file, but that only creates the file, it does not populate the entire project file with all the elements (dimensions, cubes etc) of the cube.

Open up BIDS (VS) and instead of connecting to the SSAS DB/Cube, select New Projct. In the project type, select 'Import Analysis Services 9.0 Database' (in 2008 it replaces '9.0' with '2008'), run through the wizard which basically requires an AS server and DB, voila, you have a project based on the server copy.

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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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Happy Cubing!

Rubik's Cube partially disassembled next to a hammer19201080 173 KB
One of my first 3D renders years ago was this basic scene. I remodeled and rendered it Blender this weekend. I also changed it up a bit and added a tiny bit more humor than just giving it a funny title.

This is the only texture map image I used for the cube, a plain black and white mask. I probably could have used transparency if I had given it more thought, but this worked Ok.
Texture map20002000 17.8 KB

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.

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