For returning visitors: I've simplified this article even further by replacing some of the steps with shorter and easier moves, thus eliminating the need for entire steps that I had previously posted.
Solving the Rubik's Cube Is Easier Than You Think!
Many people give up on the Rubik's Cube after playing it for only a few minutes and never pick it up again.
Here is the secret:
It's almost impossible to solve the cube without knowing the basic solution method. The solution pamphlet that comes with a store-bought cube can be very confusing, so I've arranged this article to make it simple, and I've included pictures and videos.
You do not have to memorize long complicated algorithms to solve the cube using this article.
For beginners, the layer-by-layer method is the easiest.
The first step in this method starts with picking a color to build the 1st layer. A layer is 8 cubies, has 9 stickers on the face, and 12 stickers around the outside edges of the face.
For the purposes of this article, I will pick the white side as my first color to start solving the cube.
Get to Know Your Cube
Before getting started on the layer-by-layer method, it's important to go over the basics.
On each of the 6 faces, the cube has 3 kinds of stickers:
- The center dot
- The 4 corner stickers
- The 4 edge stickers
In total, there are:
- 6 center dots, 1 color each, at the center of each face.
- 12 edges, which have 2 colors each, and are in-between the center and corner dots.
- 8 corners, which have 3 colors each, and are on the left & right, and top & bottom of each edge cubie.
There are 20 "cubies" that can be moved around, while the 6 center dots always remain in place.
A cubie is an edge or corner.
A "face" is a side of the cube (9 stickers only). In the picture above you can see the white face. It is the side of the cube that is always facing you on the front, no matter what color it is. Its opposite is the back face.
The rules for the faces are the same as the colors:
- Face (F) & back (B) are on opposite sides of the cube, the front and the back.
- Left (L) & right (R) are on the left and right sides of the cube.
- Up (U) & down (D) are on the top and bottom of the cube.
The standard notation for the cube is up, down, left, right, face, and back, or U, D, L, R, F, B for short.
Helpful Hint: Cube Color Schemes
In American models, the following colors are always opposite of each other.
- Green and Blue
- Orange and Red
- White and Yellow
Take the following quiz to see if you can use your knowledge of color scheme to figure out the hidden colors of the cube in the above diagram.
For each question, choose the best answer. The answer key is below.
- In the above diagram, the LEFT side would be _______.
- In the above diagram, the DOWN side would be _______.
- In the above diagram, the BACK side would be ______.
How to Read Rubik's Cube Notations
Rubik's Cube instructions will tell you to rotate to different sides. So, when the instructions tell you to move up, it means to turn the up side clockwise 90 degrees (1/4 the way around the top of the cube).
Another way to look at it is to imagine you are looking at the top of the cube and you want to turn a hand on a clock from 12 o'clock to 3 o'clock, so you would turn the top layer to the right one time.
The short video below shows the basic cube notation and solves the checkerboard pattern at the end.
NOTE: For all the videos in this article, be sure you have the annotations turned on to see the instructions.
Watch full-screen & high quality to see the instructions better. Slow the video down if necessary. Pause the video at anytime. The settings for the videos can be found in the lower right hand corner of the video.
Basic Cube Notation Chart
Solving the First Layer
Step 1: The Daisy Flower
Find the yellow center dot and you're ready to start solving the 1st layer.
- To start solving, make the "Daisy Flower" on the yellow face.
- The yellow face has the yellow center dot.
- Move the 4 white edges to the yellow face as shown below.
- The color of the corner stickers do not matter.
- Watch the video below the picture for an example solve of the Daisy Flower.
Step 2: The White Cross
Now you just need to move those four white edges to the white face, and line them up with the blue, red, green, and orange center dots.
That will complete the "White Cross." The video below the picture shows an example.
Step 3: Corners With White Stickers
- To finish the 1st layer, the corners with the white stickers need to be put into place.
- For this, and from this point on, you can keep the white face on the left side of the cube.
- There are 4 corners with white stickers, and they can be put into place 1 of 3 ways.
- The 3 pictures below each show one way. Below each picture is an example video.
Solving the Second Layer
To complete the second layer, the 4 edges that do not have a yellow sticker need to be put in-between the center dots in the 2nd layer (blue, red, green, and orange).
They can be put into place 1 of 3 ways. The 3 pictures below show each one. Below each picture is a video example.
First Two Layers: Inserting the Edges (Case 1)
In this picture, below, the green/orange edge is on top, lined up with the green center dot. It needs to be moved toward you and to your left.
First Two Layers: Inserting the Edges (Case 2)
In this picture, below, the blue/orange edge is on the front, lined up with the blue center dot. It needs to be moved up and to your left.
First Two Layers: Inserting the Edges (Case 3)
Shown in the picture below, this is a case that does not happen as often as the others, and takes a few more moves to solve. The green/red edge is already in place, and it needs to be flipped.
Solving the Third (Last) Layer
Step 1: The Yellow Cross
The "Yellow Cross" is the first thing to make for the 3rd layer, which is the 1st of the 4 pictures below.
You're only looking at the yellow stickers on the yellow face, specifically the edges only. The colors on the 4 corners do not matter, and neither does the 2nd color of the yellow edges.
Case 1: You Got the Yellow Cross! A Skip!
This happens, if you have the yellow cross already, awesome! This is called a "skip" and you can skip on down to "Align the Yellow Cross."
If you have one of the 3 cases below you will have to flip the yellow edges to make the yellow cross before you can continue.
1 short algorithm fixes all 3 of the following cases. Watch the video for your case number to see it in action.
- (U F R) (F' R' U') === (Up, Face, Right) (Face invert, Right invert, Up invert)
Note: "invert" means to do the move counter-clockwise. Remember lefty loosey . . . imagine it like opening a soda bottle.
Case 2: The Yellow Dot
This is when none of the 4 yellow edges are visible on the yellow face. Thankfully, this almost never happens.
Solve it like this:
- Do the algorithm once to get the yellow "L".
- Put that "L" in the lower back corner with an R2 (right twice)
- Do the algorithm again to get the yellow "line".
- Then, make sure the "line" is horizontal, and do the algorithm once more to get the "Yellow Cross".
Case 3: The Yellow "L"
This is by far the most common case. It's when 2 of the 4 yellow edges are visible on the yellow face, making it look like an "L".
- Put that "L" in the lower back corner
- Do the algorithm once to get the yellow "line"
- Then, make sure the "line" is horizontal
- Then, do the algorithm once more to get the "Yellow Cross"
Case 4: The Yellow "Line"
This happens once in a while. It's when 2 of the 4 yellow edges are visible on the yellow face, making it look like a line.
- Make sure the "line" is horizontal
- Then, do the algorithm once to get the "Yellow Cross"
Once you have the Yellow Cross, it's time to line it up with the center dots in the 2nd layer.
Step 2: Align the Yellow Cross
In the following picture, the yellow cross is complete, but it is not correctly lined up with the center dots (the blue, red, green, and orange center dots in the 2nd layer).
Note: If all 4 yellow edges are already lined up correctly, you can skip down to "Moving the Corners".
1 algorithm will fix this.
- (U R U') (R U R2 U') === (Up, Right, Up invert) (Right, Up, Right twice, Up invert)
I have an easy way of setting up the cube before doing the algorithm to make this work.
First line up 1 of the yellow edges with the same color as the center dot on the top of the cube, like in the picture below. Blue, in this case.
Now look at the yellow edge on the front of the cube. In this case it is green, and it needs to be red.
So, move that green sticker to the top of the cube, and do the algorithm one time, and then put the blue sticker back on top of the cube like it was before and see if the sticker on the front has changed to red.
Watch this video below to see it.
Now all you have to fix are the corners.
Moving the Corners (If Necessary)
- The algorithm: (R' U' R D) (R' U R D')
If all 4 yellow corners are already in place, you can skip down to "Twisting the Corners."
In the following picture, everything is solved except the 4 remaining corners, and 3 of them are not in their correct positions.
(This step moves them to their correct spots, and they may still be twisted afterwards).
Watch the video below the picture to see the algorithm.
Last Step: Twisting the Corners (If Necessary)
- The algorithm: (U L U' L') (U L U' L')
Continuing from the previous video, this step will twist the corners and solve the cube.
- Place one of the twisted corners at the top-front position and do the algorithm one time.
- The corner will either be solved afterwards, or not.
- If not, then do the algorithm one more time and it will be.
- Important: After that, rotate the 3rd layer to put another twisted corner in the top-front position, and do the algorithm again.
- Then it's the same as before. The corner will either be solved afterwards, or not.
- If not, then do the algorithm one more time and it will be.
Watch this last video to see it in action. (It looks like it is really messing up the cube a lot, but have no fear, it will solve itself in the end!).
The Cube Should Now Be Solved!
If not, you may have a situation where the cube has been taken apart at some time or another, and did not get put back together properly.
The way you can tell if this is the case is if:
- There is only 1 cubie that is twisted or flipped...
- There are colors on two or more of the cubies that need to be swapped with each other.
- In the case of that happening, you will have to pop out the cubies and put them where they go or twist or flip them. This is not cheating in any way at all.
RainbowGirl891010 on January 12, 2020:
The last step completely messed up my cube especially the white bit, and I redid it and tried that step again and it still failed. I’ve spent days working this out and it’s really annoying. My cube is brand new so I don’t get it. Please help
Eiden bruff on November 17, 2019:
It was really greater than most other jerks.It is so much clearer than any other rules...Now I can solve a cube in a minute.thank you so much
Mark Wipfler (author) from USA on March 06, 2019:
"I" Hey, mark here.. I'm not going to do CFOP because that is 78 Algorithms.. lol.. that would take months to make all the pictures and all.. but you can watch this video for that:
and look in the description box for all the details for all the algorithms. :)
2 hours ago
I don't get it so I know how to solve it can you post a method called the CFOP please cause i'm not good at it.
I on March 06, 2019:
I don't get it so I know how to solve it can you post a method called the CFOP please cause i'm not good at it.
Name on November 18, 2018:
Tried the videos. Didn’t work! Couldn’t get past the second layer.
Pushkar jat on November 18, 2018:
Umang on September 21, 2018:
Thanks mark. Lovely algorithm and very well made videos. Thanks was able to get it through.
Angry REbiks on September 05, 2018:
it is to hard make the vidios withpeople talking to explain!!!
Rose on July 08, 2018:
Allen Sam on June 24, 2018:
Mark Wipfler (author) from USA on June 23, 2018:
K Skinner.. Try this from one of my other websites: http://markwipfler2.wixsite.com/solvethecube/easy_...
KSkinner on June 22, 2018:
Hi, years ago I bought a cube and followed the instructions and learned how to solve it. Once you got the first layer, you basically had 5 moves. I have forgotten one of the last moves. I can get two layers and all the corners set on the third layer. At this point my old solution had two moves. I remember one not the other. This solution didn't involve flipping the cube over or anything to do with a yellow cross. You solved the four corners of the third layer first, then there were two moves left. Can you please help me find that last move? I have been searching all over for that technique. But, everything I've found involves a bunch of moves depending on the yellow pattern. This other solution didn't care what the yellow looked like. Please help!
Pooja Haribhakti on May 28, 2018:
I solved the whole cube .........yaaaaay.
M.R.SHARVESHWAR on May 26, 2018:
wooooww...i solved thanks for all videos and procedures
A cuber on May 09, 2018:
Makes no sense
? on February 25, 2018:
Hanif Hizan on February 23, 2018:
Before i watch this video i just cant solve and easy to get mad!
But after i watch all of your vid i already know how to slve it thanks mark by the way i am 10 years old
GRRRRRRR on December 20, 2017:
ITS TO CONFUSING
nathan on November 19, 2017:
couldn't get the first layer done
Georgia on July 18, 2017:
Plz can u guide me that how do I have to hold the cube while performing the algorithm to move the corners of the last layer(the 2nd last step). Plz tel as I want to solve this rubix cube! :)
Nay Af on June 29, 2017:
I got severe headache while trying to understand these steps. Seems like rubik cube is not my cup of tea. Very sad :(
Alden Leonard on June 11, 2017:
WAY to confusing. Just give me the frigging formula and I will be happy.
hanif yousafzai on May 29, 2017:
thanks mark. even i did not ever ever touch Rubik's cube before,for the first time i tried from your tutorial and i am done.salute to your effort (Y).
Shane on April 20, 2017:
Still do not get it urggghhhhh
Monisha on March 31, 2017:
The third layer doing a yellow cross just won't work
I need some help with it
hassan on December 18, 2016:
great tutorial Thks Mr
deep on May 24, 2016:
nithin on October 22, 2015:
what is that it is very very difficult my cube is used one so hw will i shuffle it you do it with a fresh cube and even if it is shuffled all cubes will not have the same right sooooooo please try another one
daphne on June 02, 2015:
Can anyone please help me solve yellow, green, blue, and orange please.
daphne on June 02, 2015:
I still can't do it I've gone on a bunch of websites to solve my RUBIK'S CUBE I've only gotten red and white no other colors.:(
DRB THE GR8 on May 23, 2015:
it was pleasing to learn the theory but can u suggest some more easy techniquw
Mark Wipfler (author) from USA on May 15, 2015:
Sudheerhr, that cube of yours is a 3x3x3, just like a regular rubik's cube, which is what this tutorial is about. :)
sudheerhr on May 12, 2015:
no,its not megaminx. . it's a OCTAGON BARREL CUBE.. please tell me how to solve it. Thank You..
Mark Wipfler (author) from USA on May 04, 2015:
Octagon cube? do you mean a Megaminx? If so, it is just like a 3x3x3, it even uses mostly the same algorithms as the 3x3x3, but there are more middle layers on the Megaminx. I do not have a tutorial set up for that, nor do I have a program than will animate it. But you can look up tutorials for it, there are some that I have found in the past.
sudheerhr on May 04, 2015:
please tell me how to solve an octagon cube
Mark Wipfler (author) from USA on April 19, 2015:
Thank you Min Xie!
Min Xie on April 19, 2015:
Thanks a lot Mark. First time for myself and my 2 boys to get the job done with your help! Great post!
Mark Wipfler (author) from USA on April 10, 2015:
Awesome Katrina. glad to hear it!
Katrina on April 10, 2015:
Great video! My ten year old son was able to follow along and finally solve his Rubik's cube.
Mark Wipfler (author) from USA on March 30, 2015:
Thank you Abhishek!
Abhishek on March 30, 2015:
Thank you Mark . It was the first time after a year's struggle that I managed to solve a cube . And I really, really appreciate your way of explaining . This is the best site which I found . Thanks again for your help.
Mark Wipfler (author) from USA on March 07, 2015:
Thank you Angel!
Angel on March 07, 2015:
These are the best instructions on how to solve the Rubik's cube I've found online. Thanks for the help, Mark; you are very good at teaching.
maggs224 from Sunny Spain on February 21, 2015:
I was in our garage a few days back and I saw our old cube on a shelf. Now I have read this I might go back to the garage and have a go at solving it lol...
rakesh on February 17, 2015:
I don't have any pattern on the top layer that u hv showed
Mark Wipfler (author) from USA on January 31, 2015:
Alex, I think you may have ran into that problem where you just need to turn the last layer 1 time in either direction, and then you will have one edge piece lined up, and the other 3 are not. Which is what you want, cause the last step of PLL shows how to solve that case.
I'm sorry it took me awhile to answer.
tejasvi, did you get yours going? Let me know if I can be of any help, I just need to know what it is you need help with.
Mark Wipfler (author) from USA on January 31, 2015:
Natalie, was the corner piece twisted? lol. That happens to me sometimes during a solve, it happens so quick that I don't know it at first. Then it quickly becomes un-solvable without twisting it back in place.
I've actually twisted the stem on the inside of a corner piece by trying to pop it back into place, and the cube still works!
natalie on December 29, 2014:
When I was done placing my corners, only one of my corners was messed up, but it was in the right place. The video is super helpful, and I can't believe how fast I was able to figure out the first two layers!!
tejasvi on December 25, 2014:
i don't understand the last layer tip could u help me
Alex on December 15, 2014:
What if you set up the cross but 2 sides are matched and 2 sides aren't?
Mark Wipfler (author) from USA on November 25, 2014:
Your Welcome Nik!
Nik on November 25, 2014:
I have been using this excellent site for about a week, trying to memorise solving the cube, so that I can do it without looking up the instructions. I agree that This site is the best! Thanks Mark!
Mark Wipfler (author) from USA on November 20, 2014:
Thank You Debjit!
Debjit Goswami on November 20, 2014:
very helpful tutorial...very nice illustrations...
Mark Wipfler (author) from USA on September 07, 2014:
Thank you all .. I really appreciate your comments, I work on new ways to sovle the cube on a constant basis, and I just started a new domain of my own. it is fix my cube, no spaces, with the www thang at front, com at the end, it's live right now, but I need to add some content, and it's all new stuffz that I will be adding to it. :)
Sabrina on September 04, 2014:
I tried again and I managed to solve the cube omg! thanks so much to your video! I was just bored when I was young so I kinda jumble the cube and I couldn't solve it so I left it in the cabinet. and years have passed and I got bored today so I took it out and tried solving it. thanks to your video, the messed up cube has returned to its original form!
sabrina on September 04, 2014:
hi! thanks to your video, I managed to solve the first layer! i followed exactly with the colour green. however for example, you used orange for the next one , saying that the edges should have any blue. but what if I actually have blue edges instead? how do I solve it? ):
Johnd800 on August 19, 2014:
You are a really persuasive writer. I can see this in your writeup. You've a way of writing compelling info that sparks significantly interest. dcgkkgkdbfcg
Mark Wipfler (author) from USA on August 14, 2014:
Thank you all so much, I have a lot of fun with this stuff!
Alicia Summers from Brooklyn, New York on July 31, 2014:
I have mastered solving Rubiks cube when I was a kid but now I can't remember the trick. Thanks for this, I can learn it again.
Alan from West Georgia on July 14, 2014:
This is the coolest, I remember when I was a kid messing with the cube for hours. Back then the one I had used stickers to color the sections, so of course I pulled them off and replaced them to cheat and solve the puzzle.
Apriljax from Florida on July 01, 2014:
omg..Now I want to go buy one and try it! I have never been able to do it!..lol. Thanks for this!;)
jayesh from kerala on June 28, 2014:
jayesh on June 28, 2014:
Its very simple.I solve the cube in two mints
noa on June 25, 2014:
well in my rubiks cube 3x3 , the bottom layer has only 3 edges... the 4th edge though in place is not in order....
Hezekiah from Japan on June 24, 2014:
This is excellent, I've never been able to solve one of these and I'd never seen a guide around neither. I will probably try to give it a go, not sure how long it will take me though.
S on June 19, 2014:
jammingj on June 19, 2014:
My cube is a different colour scheme.red is where blue shud b and you know the rest.i just cnt solve this thing and its annoying.help anyone?
Bschihl on June 11, 2014:
Mark, Good instructions. Just turned 66 and the cube can be crossed off My bucket list. Thank You
mark on June 08, 2014:
I don't get how you go from having a daisy to having the cross with no moves.... Your explain how to line up the edges after the daisy move and the next move you say "now that you have your white cross"
Rusty on June 04, 2014:
Just peel the stickers off or pull the cube apart it will take the same time as sloving it if it is done neatly
Frienderal from Singapore on May 31, 2014:
Thanks Mark Wipfler. Now I finally solve a Rubik's cube and I enjoy doing so! :)
SolveMyMaze on May 30, 2014:
I've just purchased a new Rubiks Cube after my first one met an untimely demise in that it came lost a fight against a hammer.
Regardless, I'll be using this hub to master my new one. Thanks for posting this!
Mark Wipfler (author) from USA on May 21, 2014:
CK Towles, yeah.. that Void Parity is annoying, I had to look it up on youtube to figure it out. I'm not sure if I still have the algo to fix that, I stopped playing with the void after I ran into that Parity Error a few times.
You can see how to fix it by searching youtube with this search term: How to Solve the Void Cube (Just Parity), this video is by MeMyselfandPi.
CK Towles from Pfafftown, North Carolina on May 21, 2014:
Above someone else wrote their name was "CK Towels" after my comment. I'm not sure why. My issue was the two pieces that would not fit. If I remember, I was using a Void at the time, so I think that is where the problem came in. Essentially the center squares (which are missing) on the Void puzzle must have been in the wrong location. It would be impossible to tell this while doing the puzzle. So that makes it a little challenging because the puzzle has to be shifted once we've figured out that it won't solve. I'm not sure if you responded to my comment. All I saw was that you said you misspelled my name because of the person who posted after me "Thi is the bomb you rock".
Kalaichelvi Panchalingam from PETALING JAYA on May 20, 2014:
this is definitely toooo difficult for the dreamer in me. I lost you after the first paragraph.
Johng753 on May 20, 2014:
I like this weblog so considerably, saved to my bookmarks. gkekdfkkekdd
Johnb838 on May 20, 2014:
I am now not certain the place you're getting your info, however good topic. I needs to spend some time learning more or figuring out more. Thank you for magnificent info I was on the lookout for this information for my mission. gaaeekfeeeec
Aaron Sparks on May 20, 2014:
Jeesh...i couldn't finish the article even with cube in my hands, i think i'll never solve that puzzle! :(
sai vamsi on March 26, 2014:
I don't like
Jane Arden on February 19, 2014:
What a cool hub
Mark Wipfler (author) from USA on February 14, 2014:
right on leoban, if you do a search on youtube for my channel, which is MountainScooter, you will find vidz, and links to other sites I have that are more in-depth to show you how to solve the cube :)
leoban-gray from Central Illinois on February 14, 2014:
Thanks for the hub. I'm a bit OCD, and rarely attempt a rubik's cube because I will be inclined to finish it. This hub will help! Thanks!
Hezekiah from Japan on December 25, 2013:
Very good explanation there, never really looked into it before. Never managed to solve one either.
rubiksgirl on December 19, 2013:
yow...how can you solve it faster? And i can't understand the move 3
Adith Varghese George from Kochi,Kerala on November 03, 2013:
Thanks for a great article and good presentation.Well solving a rubix cube is common.I can solve it in less than a minute.
sophia lee on October 26, 2013:
I got the yellow part done and I have 3 rows of orange, blue, green, and red. So I don't get it..!!
annam nimra on October 18, 2013:
i can't understand anything. i understood only till the first step - white cross. i am very confused. but i must know how to solve a rubik's cube. i can't find any other easier way in this. i must at least know how to solve two colors in the cube. maybe i will know how to solve it when i grow because i am only eight years old now.
vishal on August 07, 2013:
thank u for the information
Mark Wipfler on July 20, 2013:
Fareed on July 17, 2013:
Mark. this site is awesome. It helped me to solve the cube once in my life. The instructions could be a little more clearer. Otherwise, take my hats off to Mark. By far the best explanation and flow.
Mark Wipfler (author) from USA on April 25, 2013:
Hmm.. 4x4, basically the same as 3x3, only difference is that you have to solve the 4 dots on each center piece first (and get them in the correct place on the cube, Red Opposite Orange, Green Opposite Blue, Yellow Opposite White.
The way I remember how to get this correct (it is easy to get it wrong.. I learned the hard way) is to solve the white dot, then, as your holding the white dot on the face side, remember that the Blue dot belongs on the UP side, and solve it, then, again looking at it with white on the face (and blue up), the Red belongs on the right face.. solve that dot, then just do the opposites from there.
Once the dots are done, the edges have to be paired up. Not much explaining to do there, as long as you remember to move the center dots back where they belong after each time you pair up an edge.
Once the Edges are Paired, it becomes a 3x3 cube, and you solve it as that. the only real problem on big cubes is Parity. There is 2 parity cases that I run into a lot on big cubes.. the algos for them are on youtube.
I can help you more if you wanna talk to me, I cannot post the links that I would like to on this page, they do not allow it (well.. they do, but there is a risk of having the hub page shut down because of re-directing). hit me up at firstname.lastname@example.org
kruthika on April 24, 2013:
help me solve the 4 X 4 rubiks cube please. I very badly ant to do it within my vacations.
Mark Wipfler (author) from USA on April 06, 2013:
Awesome charan :) Glad to see that someone has made use of this page!
charan on April 06, 2013:
it was interseting i enjoyed doing it and i finished
Bharath on March 31, 2013:
I couldn't complete the last layer. Give me an definite algo.
ROME on March 30, 2013:
can i get 4x4 algorithn
siera on March 27, 2013:
i can't understand anything
Mark Wipfler (author) from USA on March 10, 2013:
Anna, I did... lol.. look at step 3, the first algo is counter clockwise, the second is clockwise.. Here is the counter-clockwise (edge piece needs to go up) :
Now look to see where that edge piece belongs.. in the picture below it belongs in the top layer. Do this to put it there:
RIGHT INVERT, UP INVERT, RIGHT, UP, then RIGHT, FACE, RIGHT INVERT, FACE INVERT.
Anna on March 09, 2013:
You write: "do the algorithm above for Counterclockwise".
If the algorithm above is for clockwise I don't understand what needs to be changed to go counter clockwise. Why not simply add what the "algorithm above for Counter Clockwise" is?