All these puzzles with a handful of easy algorithms??? Absolutely!

Sunday, January 10, 2010

Step 3: The Remaining Edge Pieces

By this stage, you should have placed all 4 bottom edge pieces and 3 middle edge pieces. When this is done, four possibilities exist for the top edge pieces:

All three are in the correct position relative to each other

Two of the three are correct relative to each other, and these two are opposite each other

Two of the three are correct relative to each other, and these two are next to each other

None of the three are in the correct position relative to each other

Let's look at all 4 cases separately.

Case 1: All three are relatively correct

In this case, carry out an edge piece series using the 4th top edge currently in the middle, the central top edge, and either of the other top edges. Make sure you finish with three top edges facing the top. When you're done, you will have the situation in either case 3 or case 4.

Here's a video detailing Case 1.

Case 2: Two out of three are relatively correct, and these two are opposite each other

No edge piece series is required here. The 4th middle edge piece belongs where the 4th edge piece is currently. So, to fix this:

Rotate the top face until a turn of the front or right face will move the 4th top edge from the middle to its correct position in the top face.

Turn the front or right face so this happens. (This will also push the out-of-position top edge piece into the middle layer.)

Rotate the top face 2 turns.

Rotate the front or right face in the opposite direction.

You will now find that all edge pieces are correctly placed.

Here's a video detailing Case 2.

Case 3: Two out of three are relatively correct, and these two are next to each other

In this case, carry out an edge piece series using the 4th top edge currently in the middle, the out-of-position top edge, and the 4th middle edge piece. Make sure you finish with all four top edges facing the top.

You will now find that all edge pieces are correctly placed.

Here's a video detailing Case 3.

Case 4: None of the top edge pieces are correct relative to each other

In this case, carry out an edge piece series using the 4th top edge currently in the middle, the central top edge, and either of the other top edges. Make sure you finish with three top edges facing the top. When you're done, you will have two of the top three correct relative to each other, and can go to Case 2 or 3.

Here's a video detailing Case 4.

When you have correctly placed and oriented all edge pieces, you are ready to move onto the corners.

Very nice explained. I would like you to explain how to proceed when you have none, one or two yellow edges on top. I find this situation very often. You can check two edges on top, on right position, easily, just running this procedure on a solved cube.

Ok. So that took awhile. I need practice, obviously. I did solve it, but only after I focused on my cube and experimented. Initially I believe I focused on the instructions too much. Next...

Seems simple, but on several attempts I have completed the all 4 middle edge pieces and all 4 top edge pieces. But while all 4 middle edge pieces are in the correct position, the top 4 edge are out of position. The bottom edge colors of all 4 are the same, but their corresponding side colors are wrong. What am I doing wrong? Any suggestions?

I think your problem is that you're not aiming to only complete 3 middle edge pieces. Even if you complete 4 middle edge pieces by accident, just do an edge piece series to take the 4th one out, so that you have 3 middle edges only, and 3 yellows only on top. Once you're at this point, you're nearly there. Let me know if this helps.

Great videos, but I found some inconsistence between the video and the explainations in text in case 1 and case 4. Shouldn't we move the 4th top edge currently in the middle and either two adjacent top edges currently in the top? Please check again:)

Thanks. I don't think it's an inconsistency. I think you've not quite understood what I mean, or else I haven't explained it well enough!

When you say "either two adjacent top edges currently in the top", that's true. But that's just what I mean by saying "the middle top edge, and either of the other top edges".

To be honest, I think Marhsall's method here is needlessly complicated and I'm going to re-do this page to make it simpler. I don't like things where there are 4 cases to remember when only two will be enough. Stay tuned.

Now, if I've completely misunderstood what you're saying, please accept my apology and let me know how.

Yeah, I think I misunderstood the "the middle top edge, and either of the other top edges" part in earlier time. My apology:)

Also, I totally agree with the idea of the simplification of 4 cases. From my point of view, at least case 1 and case4 are more or less the same, because they both need to be converted into case 2 or case 3.

I ended up with something like Case 3: Red Top edge is in position, Green Top edge is in position. The Orange Top edge is where the Blue Top edge is SUPPOSED to be, and the Blue Top edge is in the center (between Blue and Orange).

However, the Blue Top edge is in such a position that if I do a FR'F'R Edge Series, the Orange Top edge will be inverted. Basically, in the center cubelet, Yellow is pointed at the Orange face, and Blue is pointed at the Blue face.

When you do FR'F'R, you're using the orange-blue as piece 1, but the yellow-orange as piece 3. Therefore, the yellow-orange will invert, which is why it ends up in position but inverted.

You just need to figure out which piece will be piece 3, the one that flips. In your case, the orange-blue needs to come down from the top to the middle. And if it doesn't flip, then it will be inverted. So that needs to be piece 3. Since that's piece 3, and it's coming down from the top-left position into the middle, it means that the yellow-blue is piece 1 and the yellow-orange is piece 2. So you need to do R U' R' U.

This site has made the cube fun again rather than a permanently jumbled conversation piece.

I'll be sure to send a few bucks your way as soon as I remember or reset my paypal password.

I also sought out the Ultimate Solution (because I knew I wasn't going to commit a half-dozen or more algorithms to memory) and found the official page to be baffling. I'm glad the creator of the method figured it out and shared it, but it did me no good until I finally clicked on the SECOND Google search result and got here.

This particular page is going to be the one I'll have to work to commit to memory - what to do in each of the 4 cases - though I've already memorized what to do when you have two top edge pieces in the right relative order and are opposite each other. That's the one where no edge series is needed.

What I notice is that the steps to remediate case 1 and case 4 are actually identical! If these were combined into a single case (All are correct OR none are correct) that might make it simpler to remember.

Although the videos help, I think this page would be improved with the addition of a java animation for each case. Thanks.

Thanks for your kind words. The official page is rather baffling, isn't it?

As to the 4 cases, the reason I've done it like this is because Marshall does it like this. There's a much easier way though. Hold the cube with the not-done middle edge at the front. Now use it to solve the two opposite back upper edges. Once that's done there'll be 3 left. Solve them. That's how I would have set it up if I'd come up with the Ultimate Solution.

in case 1 you say in the video at the end that you want to make sure "you have two pieces remaining on top". it is a bit confusing because you actually want 3 total. might want to reword the video. just a thought

>> There's a much easier way though. Hold the cube with the not-done middle edge at the front. Now use it to solve the two opposite back upper edges. Once that's done there'll be 3 left. Solve them.

I would be most grateful if you could clarify the steps for your alternative method.

I've been thinking about revamping this whole method for some time now. In fact I was planning on making a brand new video for solving the Rubik's cube tomorrow, covering everything from the white cross to the last three corners, including this step of placing the edges. Would you be able to hang out until then? I think that will be much easier for you to see it in action on the video rather than me try and explain it. What do you say?

I've spent about seven years trying to understand PM's method. I've no intention of even considering any other algorithmic methods - I think you call them "cheating" :)

Well firstly thanks for your very kind words. I have put a ridiculous number of hours into this site, and into all the videos on these pages housed on my youtube channel. I think I'm currently up to about 750 videos. Crazy.

I do intend to preserve the current site, but one of the problems I've found is this: if someone knows about Marshall's method, all good and well. But if someone's never heard of it, and they stumble across a page on this site and start reading and watching, as soon as they hear things like 'edge piece series' and 'corner piece series', they get confused and give up.

The second problem is that I initially split my videos into smaller videos with multiple parts, to make it easier to find just what was needed. But I've found that people often seem to watch just the video they need, and because they haven't seen the earlier parts (which contain vital context etc) things don't always make sense to them and they get confused and/or annoyed.

So when I say 'revamp this method', it's more about the following: making one, or at most two videos on solving the cube, and also not being specifically an "ultimate solution" method, but rather the method which I think is best for solving the cube. It has the same basic structure of the method but leaves out some of the more confusing parts (eg. the issue you initially wrote about).

And in the new video, I won't even refer to the edge piece series as an edge piece series. I'm still pondering whether to retain the corner piece series.

Anyway, if there's anyway I can improve things after the new video (hoping to make it today), by all means let me know!

>> 7 years? That's dedication! So has my site helped or not?

Absolutely! Within minutes, you clarified two of the steps that I never understood from PM's method.

Previously, I could only solve a cube whose solution did not involve any of those two steps. That meant that I had to randomly apply an EPS or CPS to force a different configuration, which I could then solve.

BTW: "7 years" refers to "elapsed time". I only do the cube once or twice per year to impress and help youngsters such as my own daughters.

Before each demonstration, I was forced to spend a week trying to decrypt PM's description.

Now, I'm having to do the same again in order to impress my grandchildren. Luckily I came across your site a couple of days ago when I was just about to bring down PM's site in frustration :)

I have no intention of inflicting 25-step algorithms on any youngster. But I'm careful to mention that they exist for speed-cubing.

Ah, right. OK. Well I should mention that i made those videos. I ended up making one showing an edge solve, and that video solves them beginning as Marshall does, the white cross, then 3 middle edges. But then instead of the whole "3 yellow stickered pieces on top" etc, I solve the 2 edges opposite the last middle edge. Once that's done, there are 5 possible cases for the final 3 edges. (One of those cases is "solved", so really only 4). Anyway, all of that is in the video, so I hope it can provide an easier method for you.

I then made 2 other videos for the corners. The first is what I call the mindless method, which just uses an edge piece series over and over until all corners are solved. The 2nd video is a corner piece series solve, including a couple of extra endgame scenarios.

And if none of them help at all, then please feel completely free to let me know exactly what you need clarifying, and I'm happy to make a private video for you to show you.

I also encountered another situation whereby in the end game scenario, 2 corners are rotated and swapped such that when you turned the right face up, the upper corner will be in place, and when you turned the right face down, the lower corner will be in place.

oK, well on a 3x3 cube it's impossible to end up with only one edge flipped. There will always be 2 (or a multiple of 2) flipped. If your cube genuinely has only one flipped, then somebody has previously physically removed the edge and replaced it flipped.

Thanks. That makes sense. I dropped the cube once and had randomly placed back the edges and corners. I will put them back in the right order before trying.

I really appreciate this site. This is the only method I could find for solving a Rubik's cube that is both intuitive and intelligible.

I'm frustrated, though, because I use your "revamped" version of this step--placing 3 middle edges and 2 top edges before finishing the last 3--and almost every single time, I get Case 5 from your video with 2 edges swapped, which takes a lot more moves to get out of. Sometimes, I get Case 4, but pretty much never Case 1, 2, or 3. Is there a strategy to placing the previous edges to avoid this, or is this just the way the combinatorics work out?

It's pure coincidence that you're getting case 5. I'm not sure if it's a totally even split among the cases, but I would expect over the long haul there would be a relatively even spread. There's no real strategy to avoid it.

Okay, I investigated different strategies over several dozen solves, and I found that there does appear to be a pattern. The key is in placing the middle layer edges.

I initially tried a "greedy method" of matching each middle layer edge in the top layer to its matching center so that I could correctly place it with either FR'F'R or R'FRF'. When I did this, I got Case 5 on 13 out of 20 solves.

However, when I used a strategy where whenever possible in placing a middle layer edge, I made sure the yellow stickers landed on the top face, I only got Case 5 on 6 out of 20 solves. In fact, I got Case 1 or 2 on 9 out of 20 solves, making for a significantly faster average time.

Very nice explained. I would like you to explain how to proceed when you have none, one or two yellow edges on top. I find this situation very often. You can check two edges on top, on right position, easily, just running this procedure on a solved cube.

ReplyDeleteJaime

ReplyDeleteYou need to look at Step 2. That will tell you how to do what you need...

In Case 3, is it correct when you write "Make sure you finish with three top edges facing the top."? Shouldn't it be all four?

ReplyDeleteThanks anonymous. I've fixed it now.

ReplyDeleteThis comment has been removed by a blog administrator.

ReplyDeleteOk. So that took awhile. I need practice, obviously. I did solve it, but only after I focused on my cube and experimented. Initially I believe I focused on the instructions too much.

ReplyDeleteNext...

this is the only rubiks cube solution i havent mastered, and i dont think i will anytime soon

ReplyDeleteAnonymous...

ReplyDeleteWhy on earth not??? It's a simple solution.

Are you the person in the video?

ReplyDelete@zachary,

ReplyDeleteYes.

I will try this. I can LBL average 40secs... I think this will be even faster.

ReplyDeleteSeems simple, but on several attempts I have completed the all 4 middle edge pieces and all 4 top edge pieces. But while all 4 middle edge pieces are in the correct position, the top 4 edge are out of position. The bottom edge colors of all 4 are the same, but their corresponding side colors are wrong. What am I doing wrong? Any suggestions?

ReplyDeleteJoe

@Joe

ReplyDeleteI think your problem is that you're not aiming to only complete 3 middle edge pieces. Even if you complete 4 middle edge pieces by accident, just do an edge piece series to take the 4th one out, so that you have 3 middle edges only, and 3 yellows only on top. Once you're at this point, you're nearly there. Let me know if this helps.

Thanks Chareaves,

ReplyDeleteThat was my problem. Pretty easy once I got the hang of it. Now on to solving Five Corners!

Joe

Great! Glad to hear you're progressing. If you get stuck with the corners, just post another comment...

ReplyDeleteGreat videos, but I found some inconsistence between the video and the explainations in text in case 1 and case 4. Shouldn't we move the 4th top edge currently in the middle and either two adjacent top edges currently in the top? Please check again:)

ReplyDelete@Anonymous

ReplyDeleteThanks. I don't think it's an inconsistency. I think you've not quite understood what I mean, or else I haven't explained it well enough!

When you say "either two adjacent top edges currently in the top", that's true. But that's just what I mean by saying "the middle top edge, and either of the other top edges".

To be honest, I think Marhsall's method here is needlessly complicated and I'm going to re-do this page to make it simpler. I don't like things where there are 4 cases to remember when only two will be enough. Stay tuned.

Now, if I've completely misunderstood what you're saying, please accept my apology and let me know how.

Yeah, I think I misunderstood the "the middle top edge, and either of the other top edges" part in earlier time. My apology:)

ReplyDeleteAlso, I totally agree with the idea of the simplification of 4 cases. From my point of view, at least case 1 and case4 are more or less the same, because they both need to be converted into case 2 or case 3.

I ended up with something like Case 3: Red Top edge is in position, Green Top edge is in position. The Orange Top edge is where the Blue Top edge is SUPPOSED to be, and the Blue Top edge is in the center (between Blue and Orange).

ReplyDeleteHowever, the Blue Top edge is in such a position that if I do a FR'F'R Edge Series, the Orange Top edge will be inverted. Basically, in the center cubelet, Yellow is pointed at the Orange face, and Blue is pointed at the Blue face.

I hope that made sense. Any suggestions?

@Anonymous

ReplyDeleteWhen you do FR'F'R, you're using the orange-blue as piece 1, but the yellow-orange as piece 3. Therefore, the yellow-orange will invert, which is why it ends up in position but inverted.

You just need to figure out which piece will be piece 3, the one that flips. In your case, the orange-blue needs to come down from the top to the middle. And if it doesn't flip, then it will be inverted. So that needs to be piece 3. Since that's piece 3, and it's coming down from the top-left position into the middle, it means that the yellow-blue is piece 1 and the yellow-orange is piece 2. So you need to do R U' R' U.

This'll take care of things!

This site has made the cube fun again rather than a permanently jumbled conversation piece.

ReplyDeleteI'll be sure to send a few bucks your way as soon as I remember or reset my paypal password.

I also sought out the Ultimate Solution (because I knew I wasn't going to commit a half-dozen or more algorithms to memory) and found the official page to be baffling. I'm glad the creator of the method figured it out and shared it, but it did me no good until I finally clicked on the SECOND Google search result and got here.

This particular page is going to be the one I'll have to work to commit to memory - what to do in each of the 4 cases - though I've already memorized what to do when you have two top edge pieces in the right relative order and are opposite each other. That's the one where no edge series is needed.

What I notice is that the steps to remediate case 1 and case 4 are actually identical! If these were combined into a single case (All are correct OR none are correct) that might make it simpler to remember.

Although the videos help, I think this page would be improved with the addition of a java animation for each case. Thanks.

Thanks for your kind words. The official page is rather baffling, isn't it?

DeleteAs to the 4 cases, the reason I've done it like this is because Marshall does it like this. There's a much easier way though. Hold the cube with the not-done middle edge at the front. Now use it to solve the two opposite back upper edges. Once that's done there'll be 3 left. Solve them. That's how I would have set it up if I'd come up with the Ultimate Solution.

in case 1 you say in the video at the end that you want to make sure "you have two pieces remaining on top". it is a bit confusing because you actually want 3 total. might want to reword the video. just a thought

ReplyDeletechareaves said, April 11, 2012 5:18 PM

ReplyDelete>> There's a much easier way though. Hold the cube with the not-done middle edge at the front. Now use it to solve the two opposite back upper edges. Once that's done there'll be 3 left. Solve them.

I would be most grateful if you could clarify the steps for your alternative method.

Thanks.

Hi OldGrantonian

DeleteI've been thinking about revamping this whole method for some time now. In fact I was planning on making a brand new video for solving the Rubik's cube tomorrow, covering everything from the white cross to the last three corners, including this step of placing the edges. Would you be able to hang out until then? I think that will be much easier for you to see it in action on the video rather than me try and explain it. What do you say?

Hi Chareaves,

ReplyDeleteMany thanks for your prompt response.

I've spent about seven years trying to understand PM's method. I've no intention of even considering any other algorithmic methods - I think you call them "cheating" :)

So a few more hours won't make any difference.

7 years? That's dedication! So has my site helped or not?

Deletechareaves said, January 7, 2013 10:48 PM

ReplyDelete>> I've been thinking about revamping this whole method for some time now.

I hope you intend to preserve the current site, while introducing a new site (or a new section).

Your efforts to date deserve to become part of the folklore and culture of PM's original method. It would be a shame to lose these.

Hi again

DeleteWell firstly thanks for your very kind words. I have put a ridiculous number of hours into this site, and into all the videos on these pages housed on my youtube channel. I think I'm currently up to about 750 videos. Crazy.

I do intend to preserve the current site, but one of the problems I've found is this: if someone knows about Marshall's method, all good and well. But if someone's never heard of it, and they stumble across a page on this site and start reading and watching, as soon as they hear things like 'edge piece series' and 'corner piece series', they get confused and give up.

The second problem is that I initially split my videos into smaller videos with multiple parts, to make it easier to find just what was needed. But I've found that people often seem to watch just the video they need, and because they haven't seen the earlier parts (which contain vital context etc) things don't always make sense to them and they get confused and/or annoyed.

So when I say 'revamp this method', it's more about the following: making one, or at most two videos on solving the cube, and also not being specifically an "ultimate solution" method, but rather the method which I think is best for solving the cube. It has the same basic structure of the method but leaves out some of the more confusing parts (eg. the issue you initially wrote about).

And in the new video, I won't even refer to the edge piece series as an edge piece series. I'm still pondering whether to retain the corner piece series.

Anyway, if there's anyway I can improve things after the new video (hoping to make it today), by all means let me know!

chareaves said, January 8, 2013 8:25 AM

ReplyDelete>> 7 years? That's dedication! So has my site helped or not?

Absolutely! Within minutes, you clarified two of the steps that I never understood from PM's method.

Previously, I could only solve a cube whose solution did not involve any of those two steps. That meant that I had to randomly apply an EPS or CPS to force a different configuration, which I could then solve.

BTW: "7 years" refers to "elapsed time". I only do the cube once or twice per year to impress and help youngsters such as my own daughters.

Before each demonstration, I was forced to spend a week trying to decrypt PM's description.

Now, I'm having to do the same again in order to impress my grandchildren. Luckily I came across your site a couple of days ago when I was just about to bring down PM's site in frustration :)

I have no intention of inflicting 25-step algorithms on any youngster. But I'm careful to mention that they exist for speed-cubing.

Good luck with your re-vamped methodology :)

Ah, right. OK. Well I should mention that i made those videos. I ended up making one showing an edge solve, and that video solves them beginning as Marshall does, the white cross, then 3 middle edges. But then instead of the whole "3 yellow stickered pieces on top" etc, I solve the 2 edges opposite the last middle edge. Once that's done, there are 5 possible cases for the final 3 edges. (One of those cases is "solved", so really only 4). Anyway, all of that is in the video, so I hope it can provide an easier method for you.

DeleteI then made 2 other videos for the corners. The first is what I call the mindless method, which just uses an edge piece series over and over until all corners are solved. The 2nd video is a corner piece series solve, including a couple of extra endgame scenarios.

In case they all help,

Edges: http://www.youtube.com/watch?v=daDS4GlO8BE

Corners (mindless): http://www.youtube.com/watch?v=LXo7HxSBDRI

Corners (CPS): http://www.youtube.com/watch?v=fT1iJGj61Bo

And if none of them help at all, then please feel completely free to let me know exactly what you need clarifying, and I'm happy to make a private video for you to show you.

I always get an edge flipped, no matter what I do. Any ideas how to resolve this? By the way, great method. Not much memorising required.

ReplyDeleteWell, I'd like to see exactly what you're doing. Are you following the method above? Which edge is flipped? At what stage?

ReplyDeleteImagine all the crosses are done, but one edge is flipped.

DeleteI also encountered another situation whereby in the end game scenario, 2 corners are rotated and swapped such that when you turned the right face up, the upper corner will be in place, and when you turned the right face down, the lower corner will be in place.

DeleteoK, well on a 3x3 cube it's impossible to end up with only one edge flipped. There will always be 2 (or a multiple of 2) flipped. If your cube genuinely has only one flipped, then somebody has previously physically removed the edge and replaced it flipped.

DeleteIt's also impossible to have 2 corners swapped on a 3x3 cube.

DeleteThanks. That makes sense. I dropped the cube once and had randomly placed back the edges and corners. I will put them back in the right order before trying.

DeleteI really appreciate this site. This is the only method I could find for solving a Rubik's cube that is both intuitive and intelligible.

ReplyDeleteI'm frustrated, though, because I use your "revamped" version of this step--placing 3 middle edges and 2 top edges before finishing the last 3--and almost every single time, I get Case 5 from your video with 2 edges swapped, which takes a lot more moves to get out of. Sometimes, I get Case 4, but pretty much never Case 1, 2, or 3. Is there a strategy to placing the previous edges to avoid this, or is this just the way the combinatorics work out?

It's pure coincidence that you're getting case 5. I'm not sure if it's a totally even split among the cases, but I would expect over the long haul there would be a relatively even spread. There's no real strategy to avoid it.

DeleteOkay, I investigated different strategies over several dozen solves, and I found that there does appear to be a pattern. The key is in placing the middle layer edges.

DeleteI initially tried a "greedy method" of matching each middle layer edge in the top layer to its matching center so that I could correctly place it with either FR'F'R or R'FRF'. When I did this, I got Case 5 on 13 out of 20 solves.

However, when I used a strategy where whenever possible in placing a middle layer edge, I made sure the yellow stickers landed on the top face, I only got Case 5 on 6 out of 20 solves. In fact, I got Case 1 or 2 on 9 out of 20 solves, making for a significantly faster average time.