Monday, January 11, 2010

Step 5: The End Game

Philip Marshall calls this last stage the End Game, so I'll do that too.


For me, the explanation of the End Game was close to the most difficult part of the original site to grasp. However, it's actually quite straightforward. At this point, we have a cube which is almost solved - only 3 corner pieces remain unplaced.


Here's the method:
  1. Find any corner piece which will roll over along a cube edge into position. Call this piece 1.
  2. Look at the 2nd corner piece. This is the one currently in the position where piece 1 will end up. When it moves into position, one of the the three colours will end up on the top face. Note what colour this is.
  3. Now look at that sticker colour. The 3rd piece will be somewhere in the face of that colour. Whatever colour is on the sticker of that face, needs to be on the top face in the position where piece 2 will end up.
  4. Use setup moves to move the 3rd piece until it is in position on the top face with the required sticker colour.
  5. Carry out a Corner Piece Series.
  6. Reverse any setup moves done in step 4.
I am aware that this description is still not the easiest to understand. The video below will convince you that the end game is fairly easy to do.









And that's it! Your Rubik's Cube is now solved. I hope this site has been helpful. If you have any questions or want some clarifications, please use the comments to do so.



49 comments:

  1. Good work. How about other sizes like 2*2 and 4*4? Can same mothod be used...please show!

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    1. The process works similarly for other sizes. I have in my possession a 4*4, 5*5 and a 3*3 soduko. All of them work beautifully using this method. There's one or two extra things to note with the 4*4, but the 5*5 is definitely my favourite.

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  2. Hey, I came across this page after I spent a few hours scratching my head on Philip Marshall's page. Good job, but is it normal that I can't see the videos? They're crucial for the understanding...

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    1. No it's not normal that you can't see the videos. They work fine on FF and IE8. Which browser are you using? PErhaps there's some plugin needed - the videos were just uploaded to this blog site using the tools provided. I'm fairly sure they're now flash videos. Perhaps you don't have flash?

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  3. Congratulations for your work. I came to this blog after spending some days searching in different sites about Marshall's method, and mis-learning some algorithms. I was unable to find these videos through Google, so I would suggest you to tag these videos with all words related (Utimate Rubik's, Philip Marshall, etc.) so new people interested on this method can come here directly without wasting time in other sites. Thanks!!!

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  4. Hi. I have a question.

    While solving my cube, I sometimes encounter two cases in the End Game that I'm not sure how to solve using this method. One of these is that I will have two corner pieces in their correct locations but they are twisted incorrectly. The other situation is that I will have three corner pieces that are placed correctly but twisted incorrectly. What am I supposed to do in these situations?

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  5. Hey Timothy,

    These are easy fixed.

    When you have two corners only in their correct locations but twisted, just do a corner piece series involving those two corners and any other corner. Then you'll have 3 corners remaining and you can do the endgame.

    When you have 3 corner piece placed but twisted, just do a corner piece series using those three. Since they are all in position initially, when you do a CPS, they'll all be out of position, and then you'll be ready for the endgame.

    Let me know if you need more explanation.

    Cheers

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    1. Hello Chareaves,

      I just have the same problem as Timothy with the 3 corner piece placed but twisted, except my 3 corners can't be solved in 1 CPS inclueding them all because they are on 2 different faces.

      What shall I do ?

      Thanks for answer,
      Rebecca

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    2. Hi Rebecca

      Look at the same answer to Timothy's case. It doesn't matter if your corners are not on the same face. For instance, if you have 2 corners on the up-left edge and the 3rd on the down-front-right corner, just turn the down face until it's on the down-front-left corner. That way, all 3 corners will be on the left face. Now turn the whole cube so that the left face becomes the up face and do the CPS to move the corners out of position.

      Post back if this doesn't help.

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    3. Thanks a lot ! I didn't thought about it that way...

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    4. Hmmm, I'm still mastering this method (I've got a few solves under my belt) and I've just encountered this scenario - two corner pieces in the right position but wrong orientation. I tried doing a corner piece series with the two affected corners and a random third corner, but as I recall there wasn't a move available in which one of the corners could be moved into place by rolling over along an edge.

      Has anyone solved in this situation? Are there any videos or more detailed instructions?

      Delete
    5. Hi Alex

      As you've seen, Timothy and Rebecca posted about this above. You've done exactly the right thing: doing a CPS to move them out of position. Now, once you've done that, you're at the endgame.

      To be honest, you don't need one corner to roll along an edge. If I remember correctly, Marshall says that if you can't find one, then turn a face to create one. But it's just as easy to find a piece that will go across a diagonal, and call this piece 1.

      All that really matters is that you find one piece that will roll along an edge or go across a diagonal into its spot. That's piece 1. Once you've figured that out, you think where piece 2 will go, and put the 3rd piece in its correct orientation before doing the CPS.

      I hope this explains things. If it doesn't, let me know and I'll make a video to show it.

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    6. This comment has been removed by the author.

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    7. @Hearts
      I didn't delete your comment. But blogger, in its wisdom, did.

      You asked for a video where 3 corners are in position but twisted. OK. I'll make one and upload it soon.

      Delete
    8. @Hearts and others

      I have just uploaded two new videos dealing with this type of situation, of two or three corners being in position but not oriented correctly. I hope they help.

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    9. I forgot to say they're above as examples 4 and 5...

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  6. aweeeeesomeeeeeeee methood

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  7. @Anonymous

    Thanks! Spread the word...

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  8. Hi, thanks. I had confusion but later figured it out so I deleted my comments.
    Your tutorial is great. But I found that I still have confusion on step 5. I sometimes can't see the video, so I have to read your method description. My confusions are as follows.


    1. Find any corner piece which will roll over along a cube edge into position. Call this piece 1. (I think piece 1 cannot be always found, but we need to use some setup move to make piece 1 there, am I correct?)

    2. Look at the 2nd corner piece. This is the one currently in the position where piece 1 will end up.

    When it moves into position, one of the the three colours will end up on the top face. Note what colour this is.

    ("When it moves into position", "it" actually means piece 2, right? So here it means, find the top color of piece 2 after piece 2 is move by CPS, right?)

    3. Now look at that sticker colour.

    (So you mean piece 2's top color after CPS, right? To make description better, say that color is YELLOW in my following questions.)

    The 3rd piece will be somewhere in the face of that colour.

    (So you mean piece 3's current location, not after CPS, right?

    You mean at piece 3's current location, piece 3 occupies 3 faces, one of the faces MUST be YELLOW, am I right?)

    Whatever colour is on the sticker of that face, needs to be on the top face in the position where piece 2 will end up.

    (Do you mean that on the YELLOW face, piece 3's current position also has a color, say it's BLUE. We need to try to make BLUE on top face BEFORE the CPS, right?)


    4. Use setup moves to move the 3rd piece until it is in position on the top face with the required sticker colour.

    (Do you mean that, when you try to use setup move for piece 3, you have to try to keep piece 1 & 2 not moved?

    If my understanding is right (keeping piece 1&2 not moved), during the above steps, when you try find BLUE color for piece 3, you can also try to look at piece 1's position directly, and figure out what color shall be on top for piece 3, such that after CPS, piece 3 will be at the correct position at piece 1's current position.

    If my understanding is right (keeping piece 1&2 not moved), you can also try to keep piece 1&3 not changed, try to use setup moves to move piece 2, such that after CPS, piece 2 will be at correct position. Am I right?
    )

    5. Carry out a Corner Piece Series.

    6. Reverse any setup moves done in step 4.

    (I guess we need also to reverse step 1? And do you actually have any tips to remember how to reverse? Especially after a very long setup sequence. I often screw up everything at this step.)

    Thanks a lot. I know it's a long question but I think may ppl especially newbies like me will have similar confusion.

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    1. @Hearts,
      First, if you can't see the videos, go to my youtube channel (user is chareaves) and search for the appropriate video there.

      Now, to your questions.

      "I think piece 1 cannot be always found, but we need to use some setup move to make piece 1 there, am I correct?"
      Yes, this is correct. Normally, you shouldn't need any more than 1 or 2 setups to make a piece 1.

      "When it moves into position", "it" actually means piece 2, right? So here it means, find the top color of piece 2 after piece 2 is move by CPS, right?"
      Correct.

      "So you mean piece 2's top color after CPS, right?"
      Correct.

      "So you mean piece 3's current location, not after CPS, right?"
      Correct.

      "You mean at piece 3's current location, piece 3 occupies 3 faces, one of the faces MUST be YELLOW, am I right?"
      Correct.

      "Do you mean that on the YELLOW face, piece 3's current position also has a color, say it's BLUE. We need to try to make BLUE on top face BEFORE the CPS, right?"
      Correct.

      "Do you mean that, when you try to use setup move for piece 3, you have to try to keep piece 1 & 2 not moved?"
      Correct. But I don't mean that you can't move them at all. I mean that you need to get piece 3 into its correct position with the correct colour on the top face, while piece 1 and 2 are also in position. this normally means you'll move piece 1 and/or 2 out of the way, put piece 3 in position and then move piece 1 and/or 2 back.

      "If my understanding is right (keeping piece 1&2 not moved), you can also try to keep piece 1&3 not changed, try to use setup moves to move piece 2, such that after CPS, piece 2 will be at correct position. Am I right?"
      Hmmm. Possibly. I'm not exactly sure what you mean. I think this might be over-complicating things.

      "I guess we need also to reverse step 1?"
      Correct. But almost always you can avoid step 1. If you can't find a corner which will roll, then you can always simply carry out any CPS with those three pieces. This will create a different configuration of the pieces. The only time this won't work is when the three piece are all diagonally opposite each other. If this doesn't make sense, ignore it.

      "And do you actually have any tips to remember how to reverse?"
      Yes. Practice this whole thing many times. I found that initially I had trouble remembering my setups. After you do it lots, you discover that there are only really a few variants of setups. You get to know exactly what's needed when and you can pretty much carry it out without even thinking about it.

      "I often screw up everything at this step."
      Been there, done that!

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  9. Hi, as a complete newbie, may I know that whether my understanding on the End Game step is correct?

    My understanding is that: you firstly find piece 1 that after CPS it will be at correct position. After here, fix piece 1 location. Then you fix piece 2 location too. Then you find what piece 3's color shall be after CPS, try to use setup moves only moves piece 3, such that after CPS piece 3 will be at piece 1's current location with correct colors.

    Since piece 1 & 2 not moved, after CPS, piece 1 & 3 will be at pice 1&2's original position with correct color. So during reverse setup, piece 3 & piece 1 will not be moved and they will be correct. Though after CPS, piece 2 is not right, but it will be "magically" corrected after reversing setup moves (because setup moves only moves piece 3, so during reverse, piece 2 will be at piece 3's position, so reverse will only move piece 2).

    Is my understanding correct? Thanks.

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    1. "My understanding is that: you firstly find piece 1 that after CPS it will be at correct position. After here, fix piece 1 location. Then you fix piece 2 location too. Then you find what piece 3's color shall be after CPS, try to use setup moves only moves piece 3, such that after CPS piece 3 will be at piece 1's current location with correct colors."
      Yes. This is exactly right.

      "So during reverse setup, piece 3 & piece 1 will not be moved and they will be correct."
      Yes. Correct.

      "Though after CPS, piece 2 is not right, but it will be "magically" corrected after reversing setup moves (because setup moves only moves piece 3, so during reverse, piece 2 will be at piece 3's position, so reverse will only move piece 2)."
      Once again, absolutely right. I'd say you have an excellent understanding of how things work here.

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  10. Thanks a lot! After several days practicing I believe that I've completely mastered this method. This is the first time that I feel I can solve it and knowing why it's solved. Memorizing formulas made me feel sick about the cube before.

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    1. You're very welcome. I'm glad you've mastered it. That's also what I felt when I got it: I felt like I'd actually *solved* it.

      Now, onto some other ones for you. 4x4x4?

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  11. Hey thanks !
    Now I can solve the cube in about 15-20 mins always. I had a little difficulty understanding end game, but the videos cleared the confusion.

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  12. i can solve pretty quickly but this was my first exposure to this method. played with the steps a bit, but got right the first time round eventually. felt pretty good. i love the end game. looking forward to practicing it. thanks.

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  13. Thanks for these videos chareaves, this method is great fun to use.

    Jez

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  14. The end game is indeed the most difficult. Setting up the corner pieces, so that they would roll into their position righly oriented.

    My kids are also very interested in solving cubes. (7 and 8 years) and I learned them both the Fridrich method a year ago. I feel l need to teach them this universal as well. However I think the last step for the corners would be to difficult for them. I think I will just teach them to roll de corner pieces in position and than orient the last pieces.

    To be honest, I do not see the very great need to avoid this step, since this last step is also very understandable. You bring the corners in one layer and you just get a corner out and bring it in rightly oriented. Turn the top layer (it won't hurt the chaos in the other layers) and undo the chaos in the other 2 layers by reversing your moves.

    And that is what it is all about, understanding what happens, so you won't have to memorize tons of algs.

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    1. Hey Bart

      First, your comments seem to be double-posting. This is the 2nd one where 2 identical comments have appeared, posted at the same time. It's no big deal, just letting you know.

      I understand the end game myself well now, but only after a lot of practice at it. Just keep in mind that this page was about making Marshall's method possible. If I was teaching someone to do the last 3 corners myself, I would do what you've said: put them in position, and then orient them. Where the understanding of this comes into its own is when I try and figure out corners on the dayan gem 7 (as an example), and I see that in order for a particular corner to place properly, I need to have it oriented in a certain way to begin with. I'd be super-interested to see whether Marshall would do things differently now with all these new puzzles!

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  15. Strange that it was twice publsihed twice. Don;t know what happened, but I'll make sure I push the publish button once.

    Yes, I understood that you wanted to let's say bring alive his method, because it can be used on many cubes. (I spend quite some time here lately) I just mentioned it, because if people got a cube for christmas and they begin from scratch and they hopefully find this place (simple solutions), that they might be a bit disencouraged, because of the difficulty of the end game.

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  16. Hey thanks, this is an awesome tutorial! I wondered if the concepts of the EPS and CPS translate well for bigger cubes, like the 4x4 or 5x5? And can we apply these techniques for other puzzles, like the Rex Cube, for example?

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    1. Thankyou Marc,
      The EPS and CPS translate everywhere! Have a look around this blog and my youtube channel (youtube.com/chareaves) and you'll see that almost every puzzle uses just the EPs and CPS. The only kinds of puzzles which require something more are some bandaged puzzles, which need sune. Other than that, yep, rex is just EPS all the way. Same with Master Skewb, prof pyraminx, almost all of them.

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  17. This method is so much fun once you've mastered it - every solve is different. I haven't been able to put my 3x3x3 down since I came across this site. Many, many thanks - I feel I understand the cube far more than I ever did learning the "Beginner Method".

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    1. Mate, you're welcome. Very glad to have helped!

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  18. Hi, I have an issue in the end-game, where the last three pieces are in "position" to roll over, but all three already have the top-face-color on top, i.e. the top face is already complete. Is that weird? Was I supposed to follow some step to make sure that the top face does not complete before the end-game?

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    1. That's not weird at all. Totally normal. Just use one of them as piece 1 which rolls into piece 2's position, and then setup the 3rd piece so that it correctly lands on piece 1. Exactly as described.

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  19. Hi I wanted to make some comments.

    1) First of all, I wanted to thank you (and in so doing, Marshall as well) for bringing this method to the world in such a clear way. I think to fully understand this method, one has to read your site, then go through Marshall's page, then come back here and go over it again. I have an engineering background and always felt frustrated why it was that young kids could solve the cube in a matter of moments whereas I could not. I found that memorizing tons of algorithms without visualizing what they are doing are just solving for the sake of records, nothing else. People like you and us are doing it for the fun and satisfaction we get every time we solve a puzzle. I find no big deal in someone blindfolding themselves and then solving a cube. Its like a robot. No fun! When I found this site and went through Marshall's and this site's methods, it was truly a "Eureka" moment for me. I have no wish to memorize So thanks again.

    2) I am amazed at some of the negative comments about how bad this site's tutorials were. I fully agree with you that it was from people who did not want a method that makes them understand what they are doing but just provide another quick process. I was further amazed at how courteous you were in your replies. I would have lost my cool a long time ago. Show a true teacher.

    3) Now on to some questions for you. Now that I have mastered the 3x3, what would you recommend for me next? Just curious.

    4) How long on average do you spend daily or weekly solving puzzles just to keep your skills sharp. Since every puzzle has a slightly different method, I am sure you rotate them on a frequent basis to make sure you can still solve all of them, correct? How long did it take you to master all the puzzles you have done?

    5) Was the solving of each different puzzle a trial-and-error method? How did you figure out the differences in each puzzles solution methods?

    6) I have had a sudoku sitting on my desk for a long time and I believe I read on this site somewhere that you had used this method on a Sudoku as well. Do you have the method of solution for it? I was unable to find it myself.

    Again, brilliant website. A breath of fresh air. Thanks!

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    1. Hi Kamran

      Sorry I've taken a while to answer, I've been away on holidays.

      Thanks for your kind words.

      now, after the 3x3, I would definitely do the 4x4 and 5x5. Both of these are a bit harder again. After that, do the 2x2. Then, do a cuboid like the 3x3x2 or 3x3x4.

      at the moment, I spend almost no time on puzzles. As I said I've been away but before that, I spent a crazy amount of time at work. I have some time off now though so maybe I'll get back into it. Generally, with puzzles, I spend time mastering a particular puzzle, and then often don't go back and play with it for ages, or maybe even not at all. I just don't have the time to spend on them these days. I used to spend a lot more time than I do now.

      generally, when starting with a new puzzle, I try and use the 2 basic algs to do the whole thing. The challenge for me is not getting them done quickly, or with some new alg, the challenge is to get them done "sensibly", using things I already know. as you've alluded, some people don't like that. They want a quick alg. I don't care.

      I do have a sudoku puzzle but haven't really had a good look at it yet.

      Many thanks for your comment!

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  20. This has been incredible. But I'm so flummoxed at the very final stage! I have got all my corners in the right spot, but only 2 are in the right orientation. I thought I could do the corner twist algorithm like I do with the 3x3, but it doesn't work since when I'm doing a 3x3, I go layer by layer so I have 4 bottom corners done already and just need to fix the last four. How on earth does flipping corners work on a 7x7?!

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    1. You're still trying to approach the cube from a layer by layer approach. The ultimate solution method is definitely not a layer by layer approach. You need to put the corners into position correctly oriented as you go. The worst case you should have is the final 3 corners needing to be cycled. Read through this stage again and see if what I'm saying makes sense. Perhaps go back to the overview as well.

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  21. Hi, Thank you so much for this technique. I'm down to 3 corner pieces to solve. None of them will roll into the correct position with a corner piece series. I am at a loss as to how to start the end game. Do I need to undo ones that are already solved and try again? Or should I try set up moves to place piece 1?

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  22. Generally, what you do is to use setup moves to get the piece into a position where you can roll it. If you want to tell me the position and orientation of your 3 pieces, I'll recreate it on my cube and send back what I'd do for setups.

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  23. All of them are in the correct position, wrong orientation.

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    1. Yes, but which positions? Where they are will make a difference as to the setups you can use. I'm assuming each piece needs to be rotated in the same direction? So either show me a picture, or else tell me which colour piece is in which position. Eg. the white-red-blue piece is in the UFR position, etc.

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    2. I figured it out and solved my cube, now I'm trying to do it again! Practice makes perfect 😊 Thanks so much again. I will teach my kids to use this method rather than memorizing dozens of algorithms.

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  24. Hi,
    What is the 'top face' that you mention?
    The end game requires everything but 3 corners to be solved.
    3 corners could be anywhere, so I don't understand what you mean with top face.
    Thanks in advance for your answer! :)

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    1. OK, I think I got it.
      piece 1 will roll into place as part of CPS.
      There are two different CPS moves that we can choose from.
      We choose one, and the top face is the top face for this CPS - the face where the 3 corner pieces will be moved.
      Please ignore my previous post.
      Your video is very helpful
      Thanks again

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    2. Yeah, basically I meant that once you've done your setup moves, you want all 3 corners on one face, which will be the top face, as far as the CPS goes. It sounds like you're good with it now...

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