In my final blog entry, I will be going over solving my most challenging puzzle, the ghost cube. Just looking at the puzzle can be confusing: every side is the same color so how do you solve it, or mix it up? In practice, the ghost cube is actually just a standard 3×3, but the axes by which you turn on are offset. Essentially, you have to line up the layers correctly to be able to turn the puzzle, as then you can see the standard lines in between the pieces.

Axes by which you turn the puzzle are highlighted

Now, we will scramble the cube!

As usual, the first step is to solve the cross, but it is difficult to figure out how to start that on the ghost cube. I find it easiest to start with matching the edge that has the logo for the puzzle onto its appropriate center and then solving the other edges from there. From here, it should look like:

Next, we will fill in the corner pieces to finish the first layer. Essentially, just try slotting in corners that seem like they are the correct shape, and if it isn’t then you can just substitute another piece until the layer solidifies. Again, it is easiest to start by matching the pieces with the logo.

After the first layer, we have to solve the middle layer by orienting the centers and middle edges. Again, because the pieces have similar shapes you just have to try each combination until the full shape of the layer is formed.

Now, only the last layer has to be solved. We start by making the cross with the center and edges.

The last step is to solve and orientate the last corners, which brings the puzzle back to a solved, cubic state!

The reason this puzzle is so difficult is that is is very hard to keep track of pieces and figure out where they go because you have to rely on examining the shape of each piece, which is harder to track than a color. If anything, the ghost cube would be much easier to solve if each side was a different color, as it would be much simpler to figure out where to slot each piece.

That wraps up the final blog entry, thanks for reading about me solve all different kinds of Rubik’s Cubes!

In this blog entry, we will go over solving my favorite puzzle, the 2×2, and then my second favorite the Pyraminx!

The 2×2 is unique since it is the only standard cubic puzzle without any center pieces; it is composed of 8 corner blocks! Now, we will scramble the cube!

Normally, the first step of a cube is to solve the center cross, but since the puzzle is all centers we simply have to orientate the centers in one layer, and then flip the puzzle upside dow. When starting with the white face, the puzzle should look as follows:

Next, we make the face that is opposite from the layer that we started a solid color. Since we started on the white face, we now solve the opposite yellow side:

Finally, the last step is to orientate the last two corners that are out of position with a single algorithm, which finishes the 2×2!

The pieces on the Pyraminx will be referred to as follows:

Now, let’s scramble the puzzle!

First, we rotate the outer pieces of the pyramid to match all the pieces it is adjacent to; this is extremely simple to do, as rotating these pieces does not move any other pieces.

Next, we choose a color and rotate all of the inner pieces of that color onto one face; in this case, we use the green pieces.

Now, we slot in the edge pieces of the chosen color to finish the side and put the completed side at the bottom.

After that layer is completed, we have to solve the upper half using a single algorithm to rotate the edge pieces, and then the Pyraminx is solved!

The reason that these two are my favorite puzzles is because of how quick and simple they are to solve! For example, using the methods that I describe here, I can solve each of them in under 10 seconds pretty consistently. Also, because there are so few pieces in each, you can often get lucky and skip steps, which can lead to some impressive times, such as my record of 0.69 seconds on the 2×2! In the next and (final?) entry we will go over my most difficult puzzle, the shapeshifting Ghost Cube!

The megaminx is a 12 sided dodecahedron puzzle with pentagon sides. The pieces still follow a similar pattern to a standard 3×3, but it is not exactly the same. The biggest similarity is that the center pieces on the megaminx also do not rotate relative to each other, which allows for each face to be referenced by the color of the center. The megaminx also has corner and edge pieces on each face, but it has 5 of each while a standard 3×3 has 4 of each. Now that the fundamental similarities of the puzzle have been established, we will mix it up and go through solving it!

We start by picking a face and matching the edges of its color to it. For this, we will start with the silver side. Matching all the edges to the face results in a star pattern on the face, and each edge must be properly aligned with each center face as well so that the colors still match. This is the equivalent of solving the cross on a 3×3.

After solving the star, we must solve the next two layers: the corners on the top face and edges next to them. This, again, mirrors that of solving the middle layers on a 3×3 puzzle, as the process is exactly the same. When the first two layers are correctly solved, the puzzle should look like this:

Next, we solve all the faces adjacent to the first face that was chosen for the star. Essentially, we are making a solid color on all the sides that we partially solved in the previous step. The megaminx should look like, from both a top and down perspective.

At this point, the only unsolved faces are ones adjacent to the face opposite from the one that we initially solved the star on, and the opposite face itself. Since we started with the silver face, the black face is our opposite side. We fill in the middle layers, similarly to how we did in with pairing the edges with the corners in the second step. This leaves us with just the last layer to solve.

Now that we just have the last layer to solve, we start by creating a star on the face with the black center and aligning the edges with the centers adjacent to the face.

After creating the star, we make the top face a solid color by rotating the corners so the black color faces upward.

The last step to solve the megaminx is to move the corners to their corresponding positions. At this point, any color that is not aligned with any of the center pieces needs to be moved so that its colors match the surrounding pieces. Completing this step solves the puzzle.

Overall, solving the megaminx is fairly similar to the process for solving a standard 3×3, but some steps need to be repeated due to the larger number of sides. You solve the star and first two layers first, which is exactly the same process as the 3×3, Next, the next two middle layers need to be solved, following a process that is similar to solving the original middle two layers of the puzzle. After solving all the middle layers, it is just the last layer that needs to be solved, again like the 3×3. In the next blog entry, we will discuss two of my personal favorite puzzles, that are much quicker to solve: the 2×2 and the pyraminx.

In this blog entry, we can finally look at solving the 5×5 Rubik’s Cube! Surprisingly enough, despite having more pieces the 5×5 is actually simpler to solve than the 4×4 due to being an odd-numbered puzzle. Let’s start by scrambling the puzzle!

Similarly to the 4×4, we start by building the inner square of the puzzle on each side. The main difference, however, is that the 5×5 has designated center pieces, like the 3×3. This means that no matter how we rotate the puzzle, the center pieces will always be in the same position relative to each other. This makes solving the inner center easier than the 4×4 because we know where to build the inner squares, whereas in the 4×4 we had to remember the correct orientation of the standard centers to build the inner blocks.

After solving the inner centers, we have to complete edge pairing. The process is exactly the same as the 4×4 but has to be repeated twice because on the 4×4 each edge is 2×1 blocks, whereas on the 5×5 each edge is 3×1 blocks due to the inner center being 3×3 blocks. After completing edge pairing, the puzzle should look like this:

The next steps are again similar to the 4×4: solve the puzzle exactly like a 3×3! The paired edge blocks can be treated as a standard 3×3 edge piece, and the inner 3×3 center blocks can be treated as a normal center piece. Like normal, we start with the cross

And next we solve the corners and middle edges:

Finally, we are at the last layer. If you remember with the 4×4, parity was possible, where an edge piece has to be flipped or rotated using a special algorithm that does not exist on the 3×3. However, because this is a 5×5 which has designated centers, this cannot occur. This means solving the last layer is exactly the same as the 3×3 with nothing extra required! 

Because the 5×5 does not need you to memorize where each center should be positioned, as well as not needing parity, it is considered simpler than the 4×4. The set of rules for solving a 4×4 and 5×5 can be used to solve ANY cubic puzzle, no matter how large. You always start by solving the inner centers, then pair the edges, and from there solve it like a 3×3. The only caveat is on the even-numbered puzzles you can get parity, so an additional two algorithms are required. Because the pattern is the same for any cubic puzzle, for the next blog we will shift to a new type of puzzle: the megaminx, a twelve-sided puzzle with hexagon sides.

Now that the basics of solving a 3×3 Rubik’s Cube were covered in the previous blog post, we can now examine the general method for solving a 4×4!

When trying to apply the method for solving the standard Rubik’s Cube to a fully scrambled 4×4, we immediately encounter difficulty. Because this is a cube with an even number of pieces on each side, there is no specific center piece to build a cross off of as we previously did. We have to introduce a new step of creating 2×2 centers on each face of the cube. This step is necessary for all even-numbered puzzles because there is not a specific center like there is with any odd-numbered cube. When completed correctly, the 4×4 should have a solid 2×2 on the inner part of each face, as shown below.

There is still another step that we must complete before we can start with the cross: edge paring. Because our “centers” that we created are 2×2 blocks, our edges must also be two pieces each to be able to properly form a cross. This means we have to pair all the edges with their respective colors. After edge pairing is properly performed, as shown below, we can start to use the same method we used with solving the 3×3.

We start with the white cross:

And solve the corners and middle edges:

However, when starting to solve the last layer, a few more differences occur with the 4×4. There is a chance that no matter how you rotate the outer layers you cannot get a cross on the yellow face; this error is called “edge flip parity.” Essentially, because the centers are not fixed, an edge can get flipped during edge pairing and it is not evident until this point. If this occurs, a specific algorithm is needed to flip the edge, and complete the cross.

Next, we continue solving the last layer as normal, but in the last step of permuting the last layer, another potential parity can occur. This time, two of the edge pieces are swapped, leading to another state that is impossible on a standard Rubik’s Cube. This is called “edge rotation parity,” and similar to the previous parity a specific algorithm is necessary to solve the puzzle.

Solving the 4×4 cube is essentially turning the 4×4 into a state that is solvable using the same method as the standard Rubik’s Cube. Creating centers and performing edge pairing makes the puzzle resemble a standard 3×3, and from there solving is the same except for the two easily recognizable and solvable parities that occur due to the nature of even-numbered puzzled cubes.

In the next blog entry, we will cover our last standard cubic puzzle, the 5x5x5.

This blog entry will discuss the basic steps of solving the Rubik’s Cube, but not explicitly explain every algorithm, or pattern of moves, needed for the later steps. If you wish to fully learn, you can use this guide, but this blog is intended to teach the general outline of solving the 3x3x3 cube so it can be compared to other puzzles in later posts.

The first step of solving the Rubik’s Cube is to choose a side, and construct a cross or plus sign on the face; it is most common to start solving the white face, so start orientating the cube so the side with the white center is on top. Remember that the centers of the cube are stationary, so the edge pieces must be rotated relative to each center to be correctly aligned with both colors. For example, the edge piece that is white and green must be aligned with both the white and green face of the cube, as pictured below:

Incorrect Cross Orientation & Placement

Correct Cross Orientation & Placement

After completing the cross, the corners in the same layer need to be filled in. Because we started with a white cross, we will now continue with the white corners. Similar to the edges in the previous step, the corners must be correctly aligned with all of the colors on the piece. For example, the white-green-orange corner piece must be placed so it is aligned with all three of the faces. Once the corners are all in place, the whole white layer will be complete, and the cube should be flipped vertically so the yellow face is on top.

Incorrect Corner Orientation

Correct White Corner Orientation

At this point, it is fairly difficult to solve the cube using only the intuition of pieces. Algorithms are required to continue solving the puzzles without messing up the progress that was already made. The next step is to fill in the four edges in the middle layer to fully solve the middle layer. Again, make sure to properly the edges are the proper orientation so each of the two colors is aligned with the respective center.

Incorrect Edge Orientation

Correct Edge Orientation

Now we have to make the top face a solid color, without worrying about the secondary or tertiary colors on each piece; this is called the orientation of the last layer. We first need to make another cross, but unlike the cross on the first face, where the edges were aligned with both the color on the first face and its secondary color as well, this cross only has to be aligned with the color of the last layer. There are three potential cases here: the top face will either have a line, an “L” shape, or just the center square of its color. Each of these cases has a specific algorithm to create the cross.

Yellow Cross

Next, we perform an algorithm to rotate all of the corners on the final layer to match the color of the top face. In the case of our cube, we should have the top face as solid yellow now, as shown below.

After the Orientation of the Last Layer

The last step is to shift the pieces in the last layer to fully solve the cube; this is called the permutation of the last layer. At this point, there are 21 possible states the puzzle can be in, each of which is solvable with a single algorithm. A list of cases and their respective algorithms can be found here.

After the Permutation of the Last Layer

Congratulations, now you know the basic steps of solving the standard Rubik’s Cube! In the next entry, we will cover how the procedure has to change for solving a 4x4x4 cube.

For those unfamiliar with the Rubik’s Cube, it is a 3x3x3 cubic puzzle created by Erno Rubik in 1974, where you have to twist and turn the sides until all the faces of the cube are a solid color. Solving the puzzle can seem to be a daunting task, especially considering there are over forty-three quintillion potential variations of pieces in the puzzle. In this blog, I will simplify the process of understanding the Rubik’s Cube, and in future entries teach the basics for solving the puzzle, as well as showcasing more complicated puzzles with similar properties.

The main concept required for understanding the Rubik’s Cube is the three types of pieces: corners, edges, and centers. Corner pieces are, quite simply, the pieces that are on the corners of the cube. There are a total of eight corner pieces, each with three colors on an individual block. Edge pieces are the remaining pieces on the outer edge of the Rubik’s Cube. There are twelve of them, each with two colors on a piece. Finally, there are center pieces, which are the single-colored pieces in the center of each of the six faces on the cube. Compared to the other piece types, centers are the most important because they are stationary. No matter how you rotate and turn the puzzle, the orientation of the centers relative to each other is always the same. The white center is always on the opposite face from the yellow center, the green is always opposite from the blue, and the red is always opposite from the orange. Because of this property, each face of the Rubik’s cube is defined by the color of the center; for example, the face with the green center will be referred to as the green face.

In the next blog entry, I will explain the basic steps of solving the Rubik’s Cube, and eventually talk about all the puzzles pictured below! For those who want to get a head start, I will be discussing a similar solving method to that of this guide, as well as covering a more advanced method that I personally use when solving my Rubik’s Cubes.