# A new faster way to solve 5x5 edges in Hoya5/Yau5?

#### DXPower

##### Member
So I've been thinking about how I can improve the first 4 non-cross edge pairs you do in Hoya5. So, after you finish your cross edges and final two centers, you have to do the top four edges. Normally, you would just use free slicing, which can take up to 3 slices an edge. That can take over 12 slice moves in all, not even counting possible flips and insertion moves. EDIT: NEVER MIND ABOUT 12 SLICE MOVES I AM BAD AT COUNTING

So I made a slight alteration to this method. It works in a similar way to final edge pairing on 4x4, in which you slice multiple edges in a row to solve multiple at the same time. I've been using it for a few weeks now and here's what I've made:

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The first step is to look at the edge on the front left and look at the uppermost edge piece (I'm going to call this tedge). When you slice a u', you want to form a tedge and center edge (cedge) pair (The tedge + cedge pair I'll call ctedge). So before you slice, insert into the front right edge the correct cedge with a standard R U' R type insertion. Rotate the cube y and then repeat for the next ctedge. Do this one more time.

When you're done, do a u' and you will have 3 completed ctedges in the middle layer, all on the top. This means that you can now do a 3u' and complete each pair successively with minimal look ahead and super small move count!

To make the completed edges, use the empty slot without a ctedge to insert bottom edges (bedge) that will form the ctedge when you do a 3u'. So you insert one bedge, slice, and immediately insert the next bedge. This puts the completed edge pair into the top layer while simultaneously readying the next bedge for pairing. You continue doing this until you run out of ctedges.

Once you have 3 completed edges (don't put the last one in the top layer JUST yet), look for an easy free style edge for your fourth and last edge. Try to insert an edge piece and and put the completed edge in the top layer in the same motion. Once you finish these 4 edges you go into the L4E stage of 5x5.

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One of the best things about this method is that, if your bedge is in the middle layer, it is 75% chance to already be in the correct orientation, so you can just slice across and make an insertion-less edge pair.

Also, look ahead is incredibly easy on this method, as it eliminates most of the middle layer for searching, and you already know what edge colors you're looking for. If you remember what ctedges you made in what order (it's super easy, it's just 3), it's extremely easy to look ahead. Orientation of the color specifically almost doesn't matter because you just have to ensure that the bedge gets into the bottom middle layer, so you don't need to remember the orientation.

If you happen to get into a cycle that only allows you to make two ctedges, just complete it and make two edges and then free style the rest. It is still much more efficient than standard free styling.

Also, sometimes when you slice over you complete either multiple edges or one accidentally. This happens very frequently, surprisingly.

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There's only a few downsides I can think of to this method: a bit restricted and a bad first cycle can be confusing (but that is easily fixed with a y rotation and starting a new one). Also, switching from this method to the final edge as freestyle does get a bit confusing at first, but with enough practice it can be pretty smooth.

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What do you guys think? Could it be better than actual freestyle? What do you think can improve? I'm thinking that maybe I could fit the freestyle edge in before the slicing, to remove the awkward transition between the two.

What should I call it? I kinda want to call it Tophats because you're working with a bunch of tall blocks that sit on top of the bottom edge piece.

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#### Dom

##### Member
Make an instructional video. This seems interesting.

What kind of times have you gotten with this method?

#### DXPower

##### Member
I already not a very fast 5x5 solver (2:30 average last time I did it a week ago), but I definitely adopted this method quickly after I developed it. The biggest thing for me is the reduced move count of the method, and my TPS isn't that great so it dropped my times by maybe 15-25 seconds or so for the edge pairing stage, but I never really practiced the normal edge pairing so it's not really a good metric.

I'll make a video of it later today, perhaps.

#### One Wheel

##### Member
I had a roughly similar idea, I think, for 6x6 edge pairing, where I essentially did 3-2-3 style edge pairing like for 4x4 to pair inner and outer wings, then to straight 3-2-3 edge pairing with those pairs. I ended up giving up on that plan pretty quickly once I actually got 6x6, but I don't know if it might work if I ignored the last 4 edges at that stage, but it was just too many pieces and orientations to worry about, and much easier to just go for the easiest freestyle case. the only other drawback I see to your plan is that at least on my good solves I end up with at least two edges that have two pieces paired without trying, and it sounds like it would be extra work to preserve them . I'll give it a shot later today, and maybe see if I can't resurrect my 6x6 edge pairing method as well.

#### DXPower

##### Member
I had a roughly similar idea, I think, for 6x6 edge pairing, where I essentially did 3-2-3 style edge pairing like for 4x4 to pair inner and outer wings, then to straight 3-2-3 edge pairing with those pairs. I ended up giving up on that plan pretty quickly once I actually got 6x6, but I don't know if it might work if I ignored the last 4 edges at that stage, but it was just too many pieces and orientations to worry about, and much easier to just go for the easiest freestyle case. the only other drawback I see to your plan is that at least on my good solves I end up with at least two edges that have two pieces paired without trying, and it sounds like it would be extra work to preserve them . I'll give it a shot later today, and maybe see if I can't resurrect my 6x6 edge pairing method as well.
It's much easier on 5x5 because you're looking for cedges in the first step, which are super easy to find and orient correctly. In the second part, it's only going to be bedges so you instantly know how to insert it to get out correctly oriented.

#### Chree

##### Member
I want to start by saying this ideal is very cool, and I like where your head's at. But I would also like to challenge the idea that this method "is much more efficient than [Freeslice]". First: Your "12 slice moves in all" figure for Freeslice edge pairing is incorrect. It takes at most 2 slices to solve any one edge. So solving 4 edges would take 8 slices. Plus, Tophats only concerns itself with the first 3 edges, so we're only talking about 6 slices now.

I'll sum it up with a very rough idea of what Tophats would look like side-by-side with Freeslice. Let's forget for the moment that bad cases would force a Tophats user to use Freeslice anyway, and just look at an ideal case: where everything you need is already in the U layer with no AUF necessary, so every insertion is only 3 moves (like R U R', etc). I'm only going to look at the first 3 edges, since that's all that Tophats covers before defaulting back to Freeslice. I've also ignored rotations, because Tophats only really requires 1 rotation, and any good Freeslice-r can avoid them almost altogether during the first 3 edges.

Freeslice:
See Tedge#1. Insert Cedge#1 and slice. 4 moves.
Insert Bedge#1 and slice. 4 moves.
See Tedge#2 in adjacent slot. Replace TCBedge#1 with Cedge#2 and slice. 4 moves.
Insert Bedge#2 and slice. 4 moves.
See Tedge#3 in adjacent slot. Replace TCBedge#2 with Cedge#3 and slice. 4 moves.
Insert Bedge#3 and slice. 4 moves.
24 moves total. (6 are slices)

Tophats:
See Tedge#1. Insert Cedge#1. 3 moves.
See Tedge#2. Insert Cedge#2. 3 moves.
See Tedge#3. Insert Cedge#3 and slice. 4 moves.
Insert Bedge#3 in empty slot and slice. 4 moves.
Replace TCBedge#3 with Bedge#2 and slice. 4 moves.
Replace TCBedge#2 with Bedge#1 and slice. 4 moves.
22 moves total. (4 are slices)

Total moves saved: 2 (slices).

While Tophats may save a couple slice moves, on average, I don't think it's enough to be considered very advantageous.

I have a couple other criticisms of the method which I feel wipe out the potential advantage of saving 2 moves, but I'll hold off on those for now and see if I've somehow missed an important point in regards to move counts.

#### One Wheel

##### Member
After trying it I think this has potential, but it's not drastically better. I might be doing it wrong, but for comparison here are the times for the last 12 solves I did prior to this morning, using freeslice:
3:51.45
3:53.90
3:47.02
3:56.78
3:27.65
3:36.10
3:35.49
3:30.91
3:49.89
3:28.84
3:56.39
3:47.20
Ao12: 3:43.72

Now 12 solves this morning, using this method:
4:07.73
4:08.58
4:23.13+
4:33.71
3:22.91
3:41.94
3:29.48
4:15.56
3:40.68
3:48.42
3:45.50
3:51.39
Ao12: 3:55.25

The takeaway here is, first and foremost, I'm not an elite 5x5 solver. I grant that these were the first 12 solves I did using this method, and obviously my times got better as I got more familiar with it, but nevertheless I don't think that the (potentially) reduced move count makes up for the added difficulty of taking advantage of easy cases that you get in freeslice. Especially the case with a wing and a cedge connected, but the wing is backwards. That is extremely quick and easy using freeslice, and it is also pretty common, but it messes this system up, at least as I was using it. It is entirely possible that this is an objectively better system, but until somebody shows that it is, and maybe comes up with an explanation showing how I was doing it wrong, I'll stick with freeslice.

#### DXPower

##### Member
I want to start by saying this ideal is very cool, and I like where your head's at. But I would also like to challenge the idea that this method "is much more efficient than [Freeslice]". First: Your "12 slice moves in all" figure for Freeslice edge pairing is incorrect. It takes at most 2 slices to solve any one edge. So solving 4 edges would take 8 slices. Plus, Tophats only concerns itself with the first 3 edges, so we're only talking about 6 slices now.

I'll sum it up with a very rough idea of what Tophats would look like side-by-side with Freeslice. Let's forget for the moment that bad cases would force a Tophats user to use Freeslice anyway, and just look at an ideal case: where everything you need is already in the U layer with no AUF necessary, so every insertion is only 3 moves (like R U R', etc). I'm only going to look at the first 3 edges, since that's all that Tophats covers before defaulting back to Freeslice. I've also ignored rotations, because Tophats only really requires 1 rotation, and any good Freeslice-r can avoid them almost altogether during the first 3 edges.

Freeslice:
See Tedge#1. Insert Cedge#1 and slice. 4 moves.
Insert Bedge#1 and slice. 4 moves.
See Tedge#2 in adjacent slot. Replace TCBedge#1 with Cedge#2 and slice. 4 moves.
Insert Bedge#2 and slice. 4 moves.
See Tedge#3 in adjacent slot. Replace TCBedge#2 with Cedge#3 and slice. 4 moves.
Insert Bedge#3 and slice. 4 moves.
24 moves total. (6 are slices)

Tophats:
See Tedge#1. Insert Cedge#1. 3 moves.
See Tedge#2. Insert Cedge#2. 3 moves.
See Tedge#3. Insert Cedge#3 and slice. 4 moves.
Insert Bedge#3 in empty slot and slice. 4 moves.
Replace TCBedge#3 with Bedge#2 and slice. 4 moves.
Replace TCBedge#2 with Bedge#1 and slice. 4 moves.
22 moves total. (4 are slices)

Total moves saved: 2 (slices).

While Tophats may save a couple slice moves, on average, I don't think it's enough to be considered very advantageous.

I have a couple other criticisms of the method which I feel wipe out the potential advantage of saving 2 moves, but I'll hold off on those for now and see if I've somehow missed an important point in regards to move counts.
Good points. Didn't realize I messed up the slice counts, it was 12am when I wrote that, lol.

anyway, how do you feel about look ahead with Tophats? Knowing which edges you're going to be solving in advance is certainly beneficially to that.

One more note, I just thought of a solution to using free slice for one edge anyway: just do Tophats twice, each with only two edges. However I haven't really analysed it so I don't know if that's any better.

#### One Wheel

##### Member
anyway, how do you feel about look ahead with Tophats? Knowing which edges you're going to be solving in advance is certainly beneficially to that.
I suspect that the reason that 3-2-3 and similar edge pairing styles work so well on 4x4 is that there are relatively few pieces to look at. On 5x5+ there are more pieces to look for, so lookahead has more to do with recognizing patterns or groups of pieces than it does with finding any specific piece. I remember watching a video of a presentation by Kevin Hayes on how to get fast at big cubes. The two things I remember are forcing edge parity on 6x6 to your last layer, and his statement regarding edge pairing something to the effect of "you should always feel like you're getting lucky."

#### DXPower

##### Member
Yeah I see what you mean. However, with Tophats you're basically limiting look ahead to center edges in the first part, and bottom edges in the second part. Look ahead for cedges is super easy because it's the same on 3x3 (8 places to look). Bedges would be about the same, but would probably still be beneficial because you have less places to look (3/4 middle layer edges will be taken up). Plus, if it's in the middle layer, it's 4/5 chance to be oriented correctly (I recalculated it from 3/4, as it can also be in the buffer), only needing a 3u slice to pair it up. However as you solve the edges and put them in the top, it becomes more likely that they are in the middle and not oriented correctly (as with free slicing).

One more thing to note it that you really shouldn't be doing any awkward d moves (I find them awkward on big cubes, at least). However, Tophats probably does have more rotations (at least how I do it) than freestyle. How I do it: Insert cedge, rotate, insert cedge, rotate, insert cedge, slice + rotate. I don't do any more rotations after that, so the total is 3 rotations, but I find it really smooth since you're keeping the same grip position.

I just got home so I am going to try and get my webcam working so I can possibly record a video on it.

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#### mark49152

##### Super Moderator
Staff member
AvG edge pairing is also good on 5x5 and only requires looking for midges. Yes it requires more slices, but that's not a problem as long as you are looking ahead and keeping moving. Lookahead is way more important than fine-tuning move efficiency, until you are fast, IMHO.

#### Chree

##### Member
anyway, how do you feel about look ahead with Tophats? Knowing which edges you're going to be solving in advance is certainly beneficially to that.
I can see why one might begin to think Tophats has a lookahead advantage over Freeslice. Looking for cedges is easy, and feels a bit like 4x4 edge pairing. But something only provides a Lookahead advantage when it eliminates possible locations of pieces, especially in locations where you can't immediately see (ie, B and D faces).

Does this do that? Well, not really. If I'm looking for the next tedge, if could be in a bedge slot on the B face. Or, like in your example video, the bedge I'm looking for might be in a different bedge slot and I didn't notice while pairing ctedges. This makes the solving method less straight forward than 3-2-3 edge pairing on 4x4, where you're constantly eliminating possibilities all around the cube.

Meanwhile, the attempt at greater Lookahead comes at the cost of restrictions to "What you're allowed to look for". Freeslice is, of course, NOT restricted to a Tedge->Cedge->Bedge solving order (even though that's what I used in my example above). You can go C>T>B, or even B>T>C (at the cost of an extra slice unless you got dem gud fingertricks). Freeslice lets you solve them in the order that you see them, or in an order that prevents rotations, or in an order that preserves or builds other tredges, or in an order that takes advantage of lucky cases. For Tophats, you sorta get what you get, like in 3-2-3.

The first time I tried this method I ran into a bad case: Tedge#1 was BO. Tedge #2 was YO, it was in place, but flipped, so I did a flipping alg. And then, Tedge #3 was the other BO piece, but the BO cedge was already locked in place with Tedge#2. So here are my choices at this point:

1. Continue with Tophats: I could have rotated and built off of the cedge that was paired with Tedge#1, essentially creating Tedge#0 in the Open Slot. But this is a bit more difficult than Tophats intends to be, because now I have to make sure I don't accidently bring down the bedge instead of the tedge, even if I notice the bedge first.
2. Switch to Freeslice: I already knew where all 3 BO pieces were. The problem is that I already used a flipping alg to fix that YO cedge, so I'd have to do another flipping alg just to build the pair Freeslice. This all amounts to wasted time.

It wouldn't have been a problem if I had noticed that BO bedge before doing that flipping alg, of course, but then I would just be doing Freeslice. So it seems to me that every time you run into a bad case that requires you to fall back on Freeslice, the time you spent attempting Tophats in the first place was a waste. With that as a possibility, it makes me less inclined to ever begin with Tophats at all, especially if it doesn't actually save a significant number of moves, nor provide any significant boost to Lookahead.

It is a cool idea, and I think it is a starting place to something useful, but it's not there yet. So definitely keep playing around. I'll also play with this a bit and let you know if I notice anything cool.

#### Y2k1

##### Member
IMO I believe it is like 6-2-6 on 4x4, when it works, it works really well but when it doesn't, it flops pretty badly

#### DXPower

##### Member
The first time I tried this method I ran into a bad case: Tedge#1 was BO. Tedge #2 was YO, it was in place, but flipped, so I did a flipping alg. And then, Tedge #3 was the other BO piece, but the BO cedge was already locked in place with Tedge#2. So here are my choices at this point:

1. Continue with Tophats: I could have rotated and built off of the cedge that was paired with Tedge#1, essentially creating Tedge#0 in the Open Slot. But this is a bit more difficult than Tophats intends to be, because now I have to make sure I don't accidently bring down the bedge instead of the tedge, even if I notice the bedge first.
Yeah I see your point. But, like in my video, I've just been doing a rotation to enter into a new "cycle". I just thought of this while typing this response, you could also do a u and then use the new piece that you bring in, perhaps, to start a new cycle, instead of doing a rotation.

However I don't really agree with you on it being harder to look ahead, as in the second part of Tophats there is a limited amount of places for a bedge to be, and the areas it can be just so happen to be the easiest to see (top layer), or insertionless (bottom layer). In freesclies, every edge makes it more and more likely to not be in the top layer, meaning the edge can be misoriented and require a flip.

The method might definitely be worth it if we can get around the freeslice last step or freeslice fallback. I think that with work I could possibly get around that.

#### Chree

##### Member
Yeah I see your point. But, like in my video, I've just been doing a rotation to enter into a new "cycle". I just thought of this while typing this response, you could also do a u and then use the new piece that you bring in, perhaps, to start a new cycle, instead of doing a rotation.

However I don't really agree with you on it being harder to look ahead, as in the second part of Tophats there is a limited amount of places for a bedge to be, and the areas it can be just so happen to be the easiest to see (top layer), or insertionless (bottom layer). In freesclies, every edge makes it more and more likely to not be in the top layer, meaning the edge can be misoriented and require a flip.

The method might definitely be worth it if we can get around the freeslice last step or freeslice fallback. I think that with work I could possibly get around that.
I didn't mean to imply it makes lookahead harder. I only meant to say it doesn't provide an advantage. At the very least, not a significant enough advantage to restrict myself for 3 of the Last 8 Edges, especially in light of the Freeslice Fallback problem. Once you get around that, I think you'll be on to something good. In the meantime, Freeslice seems to be better options, imho. Or if you're a Yau5/Hodder solver and the back slots are already solved, AvG.

#### DXPower

##### Member
IMO I believe it is like 6-2-6 on 4x4, when it works, it works really well but when it doesn't, it flops pretty badly
Yeah that's something I'm trying to work on, reducing the amount of bad cases in Tophats... I'm think possibly by doing 1 freeslice edge first, or by doing Tophats 2 edges at a time instead of 3 + 1...

I didn't mean to imply it makes lookahead harder. I only meant to say it doesn't provide an advantage. At the very least, not a significant enough advantage to restrict myself for 3 of the Last 8 Edges, especially in light of the Freeslice Fallback problem. Once you get around that, I think you'll be on to something good. In the meantime, Freeslice seems to be better options, imho. Or if you're a Yau5/Hodder solver and the back slots are already solved, AvG.
OK I think I just figured out a way to do the fourth edge using Tophat (still haven't fixed freeslice fallback, but the fourth edge is definitely an advancement).

So basically, after you make your first complete edge , you have that 1 completed edge in your FR slot, and 2 top hats in the FL and BL slots. So instead of inserting the edge for the next top hat, look at the bedge BELOW the FL top hat, and insert the matching cedge into the FR slot. If you do a d move, it matches up a bottom hat (?). So now you have 2 top hats (FL and BL), one bottom hat (FR), and an empty slot in BR. Then, you put in the corresponding tedge for the bottom hat in the empty slot and slice it over, completing the pair. Insert the bedge for the next top hat and fix the top hats with a u'. You can then continue with Tophats normally, and have all 4 edges solved in the end.

I was thinking that you could possibly turn the 3u in such a way that when you finish Tophats, you make a bottom hat, but I realized that you don't always do a u' to make a full edge pair so that wouldn't work. Doing it after the first top hat limits the possible cedge positions to the top layer and BR. If it's in BR you could leave it there and slice a d2 instead of a d (after removing the completed edge, ofc).

What do you think of this improvement?

Edit: After a bit of thinking, it is basically doing freeslice in the middle instead of the end, and making it a bit more efficient, too, because either the pieces are going to be on the bottom or on the top, making them just insertions. Small chance it's correctly oriented in BR, same chance it needs to be flipped in BR.

EditEdit: Also just realized my thinking above is wrong, it's either going to be in the d layer, making you need to flip the FR, u layer in the BR (slice) or FR (it's already solved lol), or in the top layer (insert). I wonder if you could simply make the cbedge pair, replace it with the bedge for the next tophat, and then just save that pair in the top layer for an easy freeslice at the end... it would remove the need to break the top hats temporarily, which is probably a plus.

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