Some more efficient methods.

The methods I described in my previous posts can solve a cube, however they are not close to being very efficient. Therefore, I am outlining a few more efficient methods for each cube in this post, starting with the 2×2.


A good method for 2×2 is the Ortega method. It is a very useful method and can easily take your times down to less than 5 seconds. This method is done by first solving a face, then solving the opposite face, and finally permuting both layers. There are 13 algorithms to learn in total, some of which you will already know, to solve using Ortega.

A good place to learn this method is Cyotheking’s website.

Pros- Easy to learn, can get quite fast.

Cons-To get world class, this method isn’t sufficient.

Another good method for 2×2 is called CLL. It is a very simple method used by world class solvers. It is done by solving a layer, and then using one algorithm to solve the last layer. There are many extensions of this method which can be used along with CLL to get better times.

A good place to learn this is  Cyotheking’s website, which also has the extensions I mentioned earlier.

Pros- World class times are possible

Cons- Lots of algorithms are needed, particularly if you want to learn the extensions.


Moving on to 3×3, there are lots of methods available for use in advanced solving. The most popular is the CFOP method, also known as the Fridrich method as it was proposed in the 1980’s by Jessica Fridrich. This method can be called a more efficient form of the beginners method. The steps to it are (1) Solving the cross, (2) Solving the first two layers, (3) Orienting the last layer and (4) Permuting the last layer to solve the cube.

A good place to learn this method is Bob Burton’s website 

Pros- Simple, somewhat intuitive

Cons- Lots of algorithms to learn

Another method for 3×3 is the Roux method, proposed by Frenchman Gilles Roux. His method is where you build two 1x1x2 blocks on opposite sides, solve the last layer corners, orient the last 6 edges, and finally solve the rest with one algorithm.

A good place to learn this is Waffo’s cube Thngy

Pros- Very intuitive, few algorithms

Cons- Hard to understand at first


For Pyraminx, the method I have described earlier is quite good, if the top 3 edges can be done efficiently. Another method is LBL, or Layer by Layer. It is a very fast method and can be used to achieve times of 5-6 seconds. It is done by building the bottom layer, then finishing the top with one algorithm. There are 5 algorithms to learn.

A good place to learn this is Legoboyz3 ‘s video

Pros- Simple, few algorithms

Cons- Not sufficient for world class times


A bottom first method for solving Pyraminx

Pyraminx is a pyramid-shaped twisty puzzle that is a World Cube Association event. I have developed a method for Pyraminx. A Pyraminx looks like this.


I do not know if this method has already been developed or if it is original, so I am just saying what I discovered.  The breakdown of this method is that you first solve the bottom part of the Pyraminx, (shown below left), and then you solve the rest (shown below right).


I have developed my notation to go with this method. It consists of the letters R, R’, L, L’, B, B’, D and D’, which are explained below. The cube has to be held with one vertex pointing down, as shown in the pictures.

The letter R represents a clockwise turn around the right-most vertex, as shown below.


The letter R’ represents a counterclockwise turn around the right-most vertex, as shown below.


The letter L represents a clockwise turn around the left-most vertex, as shown below.


The letter L’ represents a counterclockwise turn around the left-most vertex, as shown below.


The letter B represents a clockwise turn around the back-most vertex, as shown below.


The letter B’ represents a counterclockwise turn around the back-most vertex, as shown below.


The letter D represents a clockwise turn around the bottom-most vertex, as shown below.


The letter D’ represents a counterclockwise turn around the bottom-most vertex, as shown below.


Now for the breakdown of Pyraminx. It is made up of three main types of pieces: Center Pieces, (shown below)


Edge pieces,(shown below)


And tips,(shown below)


The first thing you do to solve is find the  red-green-blue tip and position it on the bottom, as shown below.


Once you do that, you need to solve the three edge pieces around the red, blue, and green centers. This step is intuitive, and there’s not much I can explain here. Once you’re done, your cube should look like this, with the bottom part solved.:


You can practice the above step to get a better understanding of the Pyraminx. The next step, solving the yellow layer, is broken into two parts: getting the yellow centers on the top face and solving the last three edges.

For the first part,  the first thing you have to do is check if there is a yellow center on the front face. If there is, it should look something like this:




If you don’t have any yellow centers on the front face, you should rotate the cube so that at least one yellow center is on the front face. if you can’t get any yellow centers on the front face, then you can move on to the next step.

However, if you do have at least one yellow center on the front face, identify if it is on the left or right. If it is on the left, your cube should look like this:


If it is on the right, your cube should look like this:


If the center piece is on the left, do the algorithm L B L’ B’ L’.

If the center piece is on the right, do the algorithm R’ B’ R B R .

Now for the final step: Solving the last three edges.

For this step there are a few cases you need to memorize algorithms for.

The first case is where two edges need to be flipped in place, as shown below:


The algorithm for this case is L R’ L’ R B’ R B R’

The next case is where three edges need to cycle around, but they are all oriented correctly. There are two variants to this case:

1.  The three edges need to cycle counterclockwise-


The algorithm is B’ R B R’ R’ L R L’

2. The edges need to cycle clockwise-


The algorithm is B L’ B’ L L R’ L’ R

The third case is where two edges are flipped incorrectly and they need to cycle around counterclockwise-


The algorithm is L R’ L’ R

The fourth case is where two edges are flipped incorrectly and they need to cycle around clockwise-


The algorithm is R’ L R L’

After you are done with all of this, align the remaining three tips with their respective centers to solve the Pyraminx.

Now that we’re done solving, we should take a look at the move efficiency of this method.  I did fifteen solves using this method from computer generated scrambles, and I calculated the move average of this method to be about 25 moves, which if executed at 2-3 moves per second will take 8- 12 seconds. Of the 25 moves, 4 moves are required to build the bottom, 3 moves are needed to fix the tips, 12 are needed to solve the centers, and 6 are needed for the last 3 edges.

Based on the numbers that I got, one way to make this method faster is to solve the top face centers with one algorithm rather than 2-3 algorithms, more on that later…

This method isn’t as fast as Oka, LBL or Intuitive L4E, but it is a good starter method and you can get decent times with it.



A space racing video game in Scratch

Now that I have made a 3×3 scrambler in Scratch, I decided to do something a little more complicated. I created a video game, and you can see this video to get the basic idea. The game is about getting as many coins as possible before the countdown runs out, not a race to the finish line. Then, I will talk about how I made it.

game video

What I did was create a “Game Loop”, which is just one big loop that sends all the messages that tell every character (called sprite in Scratch) to do whatever they need to do. For instance, the scrolling scenery that repeats over and over again receives a message from the game loop when the game starts that moves it downward. Each sprite is programmed to react differently to the messages from the game loop, so that I can control every sprite with only a few messages.

This is an image of the game loop

Screen Shot 2016-09-02 at 8.15.50 PM.png

Where it says ” broadcast —- and wait ” or “broadcast —- “, it means that it is broadcasting a message to the other sprites to do whatever they need to do. When setup is broadcasted the scrolling scenery returns to its original position, the spaceships return to the centre, the screen is cleared of the asteroids in the middle and the screen is cleared of the coins.

The messages inside the “repeat until” block only repeat until a certain condition is met, in this case, until the “time left” variable is less than one. The “game over” message is sent when the “time left” variable is less than 1 to end the game.

Now I’ll go over the basics of each sprite.

The scrolling scenery is two sprites that fit seamlessly on top of each other and take turns filling the screen. The sprites are just the part with the asteroids. The stars are simply a backdrop.

The spaceships are exactly the same but programmed to move along the screen at a certain speed  when specific keys are pressed. They are also programmed to spin when they hit the asteroids or the other spaceship.

The asteroids are programmed to appear at the top of the screen, move down at the same speed as the scrolling scenery, and disappear when they hit the bottom of the screen. The original asteroid sprite is hidden and it creates clones of itself that move down the screen. This is a tedious long piece of code but routine.

This is the script used for making clones of the asteroids and the coins. Sprite 4 is the asteroid and sprite 3 is the coin.

Screen Shot 2016-09-03 at 1.53.01 PM.png

The coins are like the asteroids; they have clones that appear at the top of the screen and move down. However, they fall at a slower speed than the scenery, and they are more common than asteroids. Also, they are programmed to disappear when they touch spaceships and add one to that spaceship’s score. The code for the coins is below.

Screen Shot 2016-09-03 at 1.57.07 PM.png

And that’s all there is to my video game!

If you have any questions, leave a comment and I will reply. Happy Scratching!!!

A 3×3 scrambler in Scratch

According to WCA ( World Cube Association) regulations, your cube must be scrambled by a computer generated algorithm as to avoid some people getting easy scrambles because the person whose scrambling is biased.

So, I decided to make a scrambler using Scratch. Scratch, if you didn’t know, is a programming language that you can use to make simple video games and other programs. I used it for making a cube scrambler. Now, I’ll tell you about it.  My scrambler is for a 3×3 cube.

Screen Shot 2016-08-27 at 4.29.46 PM.png

The picture on top shows the scramble you get after you run my program. The picture on the bottom shows the script I used to run the scrambling algorithm. List is a way to store items in a Scramble program. I used two lists calles moves and scramble. Moves contains all the 18 possible moves, F, Fi, F2, B, …. . The idea is to pick a move at random from the list of moves and add it to the list called scramble. Scratch lets you pick an element at random.

Next, I explain the individual instructions.


Screen Shot 2016-08-27 at 4.30.33 PM.png

The top part of the picture, where it reads “when flag clicked” simply indicates that when the flag on the first picture is clicked, the program will start running.

The next part down, where it reads “hide list moves” means that the list of all possible moves is hidden so that you can’t see it.

The next part down, where it reads “delete all of scramble” means that the previous scramble from the program’s last use is deleted.

The yellow, C shaped part, that reads”repeat 25″ means the part within the C will be repeated 25 times. In this case, it means that the “add item random from moves to scramble” will be repeated 25 times.

The next part down, where it reads “add item random of moves to scramble” means that a random item of the list of possible moves will be added to the scramble.

The part at the bottom, which reads “show list scramble” means that the scramble will be displayed on the screen.

And thats an overview of my scramble generator!

Instructions for solving a 3×3 Rubik’s Cube.


A 3×3 Rubik’s cube is a three-dimensional object with 6 faces, 12 edges, and 8 corners. The cube has three types of pieces on each face.

33 pic 1.png

Pieces labeled 1- These are corner pieces. They have three colours on them. They move during the course of a solve.

Pieces labeled 2- These are edge pieces. They have two colours on them. They move during the course of a solve.

Piece labeled 3- This is a centre piece. This has only one colour on it. This does not move during the course of a solve.

IMPORTANT- An edge piece can only go to the spot of an edge piece and not a corner or centre. The same applies for corners and centres.

(in the illustrations, gray squares don’t matter)



In algorithms, we use letters to denote faces and which way they should turn. Each face can be turned clockwise or counterclockwise.

Front face= F/Fi

Back face=B/Bi

Top face=U/Ui

Bottom face=D/Di

Left face=L/Li

Right face=R/Ri

If there is an i next to the letter, the face is turned counterclockwise, and if there is no i, the face is turned clockwise.

Colour scheme


We are assuming the standard colour scheme, which means that white is opposite yellow, blue is opposite green, and red is opposite orange. If white is on the front face, then yellow is on the back face, green is on the top face, blue is on the bottom face, red is on the left face and orange is on the right face

Now let’s hurry up and get solving!

Step 0: scramble your cube


Step 1: solve the white cross

Hold the cube with the white centre piece on the top face.

Find an edge piece with white and some other colour on it.  I’ll take the white/red piece. Align the piece directly under its desired spot. Once you have done that, you can have one of two cases.

33 pic 2.png



If you have the case above, execute the algorithm Di, Li, F, L to put the edge piece into its desired spot. If you  have the case below, where the red side of the edge piece lines up with the red centre, do F, F.

33 pic 3

After solving the edge piece, make sure that both colours of the edge piece match up with the adjacent centres.

Repeat with all 4 edges of the white cross.


Step 2 : solve the white corners

After solving the cross, hold the cube with the cross on the top face and look for a white corner on the bottom layer. Once you find it, align it under its spot. Your cube should look like this  –

33 pic 4.png

Now that you are all set, execute the algorithm the algorithm Ri, Di, R, D as many times as needed to solve the corner.

If your corner is in the top face but in the wrong spot, execute the algorithm Ri, Di, R, D to get it into the bottom layer.

Repeat with all the white corners.

Step 3: solve the middle layer

Turn the cube over so that white is on the bottom face and then look for an edge piece that belongs in the middle layer that is in the top layer. Once you have found it, turn the top layer until that edge piece forms an upside down T shape. Once you have that, you can have one of two cases. I’ll use the red/green edge piece. In the figures below the green line on the top indicates that the other side of the edge piece is green. The green line on the side indicates that thet side has the green centre.  33 pic 5.png

If you have the case above, execute the algorithm U, R, Ui, Ri, Ui, Fi, U, F

If you have the case below, execute the algorithm Ui, Li, U, L, U, F, Ui, F

33 pic 6.png


If you have an edge piece that is in the middle layer and you want to take it out put it on the left side then execute the second algorithm.

Step 4 : Orient the yellow layer

Part one: get the yellow cross

At this point, you should have the white layer on the bottom, and the yellow face should be in one of these four states –

33 pic 7.png1

33 pic 8.png2

33 pic 9.png3

33 pic 10.png4


If you have case 1 or case 2, execute the algorithm F, U, R, Ui, Ri, Fi in the position shown with white on the bottom face. For case 1 you have to execute the algorithm twice.

For case 3 execute the algorithm F, R, U, Ri, Ui, Fi in the position shown with white on the bottom face.

For case 4, move on to part 2.


Part 2: get all the yellow on top

Now you can have one of these cases 33 pic 11.png



1 :one corner




33 pic 12.png




2 :2 corners




33 pic 13.png3  :no corners33 pic 14.png4 :all corners


For cases 1 and 2 execute the algorithm R, U, Ri, U, R, U, U, Ri in the position shown with white on the bottom.

For case 3 execute the algorithm mentioned above with red on the front face, yellow on the top face, and white on the bottom face.

For case 4, move on to step 5.


Step 5: permute the yellow layer

Now, you can either have the yellow layer solved, or it can be unsolved. If it is solved, turn the yellow layer until the whole cube is solved. If it is not solved, then you need to permute the last layer, or put all the pieces in their designated spot.

Part one: permute the corners

For this part, look at the corners of the last layer. You can have one of three cases.

33 pic 15.png


33 pic 16.png


33 pic 17.png

For case 1, hold the solved corners in the back and yellow on the top and execute the algorithm Ri, F, Ri, B, B, R, Fi, Ri, B, B, R, R, Ui.

For case 2, hold it with yellow on the top and do the algorithm above twice.

For case 3, move on to part two.


Part 2: permute the edges

Now you can have one of two cases –

33 pic 18.png33 pic 19.png

For case 1, execute the algorithm F, F, U, Ri, L, F, F,  Li, R, Ui, F, F to get case 2.

If you have case 2, there two possibilities you can have.


33 pic 20.png33 pic 21.png

If you have case 1, execute the algorithm F, F, U, Ri, L, F, F,  Li, R, Ui, F, F with the solved edge in the back and yellow on top.

If you have case 2, execute the algorithm F, F, Ui, Ri, L, F, F,  Li, R, U, F, F with the solved edge in the back and yellow on top.

If your cube is not solved then turn the top layer until the cube is solved.

If you followed my instructions correctly, CONGRATULATIONS!!!

Instructions for solving the 2×2 Rubik’s cube



A 2×2 cube is a three dimensional object with 6 faces, 8 corners and 12 edges. Each corner has three different colours. Each 2×2 cube is made from 8 pieces. The 6 faces are coloured differently.

Color scheme

We will assume the standard colour scheme which means that white is opposite yellow, blue is opposite green, and orange is opposite red. If you hold the cube with the white face facing you, then white is the front face. In other words the face that you’re looking at when the cube is at the eye level is the front face. Any face is made of four pieces. If white is the front face, yellow is the back face, red is the top face, orange is the bottom face, green is the left face, and blue is the right face.

Each face can be rotated either clockwise or counter clockwise. Following notation is used to describe the rotations of the faces.


  • right face – R/Ri                                                         
  • left face – L/Li
  • top face – U/Ui
  • bottom face – D/Di
  • front face – F/Fi
  • back face – B/Bi

The i means that a face is turned counterclockwise and if there is no i the face is turned clockwise. if there is a 2 after a letter than the face will be rotated twice.

Now lets hurry up and get solving!

Step Zero: Scramble your cube

Step One: The white layer

Pick a corner with white on it. This corner will not move in the solving of the first layer.The top face of your cube should look like this. The gray is any color . This means that the white corner square you picked is the top right corner of the top face.


Find another white corner with one of the other colours of the first corner.  Align the second corner so that it is below its designated spot. Hold the cube so that the first corner is on the top face and the second corner is on the right face. If the corner you want to correctly position is in the layer with the original white corner, do Ri Di R D to get it in the bottom layer and then put it in its designated spot.

Once you have that, do the algorithm Ri Di R D as many times as needed to align the two corners that you have chosen.

Repeat for every other white corner not in place. At this point, the white layer should be solved. 

Step Two: Orient the yellow layer

After you are done solving the white layer, turn the cube upside down so that the white layer is on the bottom face. Then reposition the cube so that it looks like one of the pictures below. If your cube does not match the pictures below then do the first algorithm, described below, starting in any position with white on the bottom face until you have one of the pictures below.


The yellow line indicates yellow on the top face of the corner. For the first case use the algorithm R U Ri U R U2 Ri. For the second case use the algorithm Li Ui L Ui Li U2 L.

If your cube is solved stop goofing with the cube and try to solve a 3×3 or read something interesting.

Step Three: Permute the yellow layer

When you have the face of the yellow layer solved, but not the whole cube, you can have one of two cases. 


For the adjacent corner swap, do the algorithm Ri U Ri D2 R Ui Ri D2 R2 with the solved corners at the back face and the white face being the front face.

For the opposite corner swap, do the algorithm mentioned above to get to the adjacent corner swap and then solve for adjacent corner swap. If your cube isn’t solved, turn the front face until it is solved. 

If you followed my instructions correctly, you’re done!