From Jayden Mcneill's newsletter. Very useful for Square1, just wanted to get this info out there. Subscribe to his newsletter on his website for some top tier content https://jaydenmcneill.com/homepage

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I'm not exactly much of a Square-1 solver anymore, but if you're into the event and aren't doing this already, you're missing out

Note that what I'm going to talk about in this email isn't new by any stretch of the imagination. Andrew Nelson has been talking about this stuff for years

https://www.speedsolving.com/threads/forcing-good-us-in-square-1-speedsolving.34147/

https://www.speedsolving.com/threads/square-1-1-look-permutation.15855/

Anyways, here's two concepts I wanna throw your way

The first one is the idea that you can force PBL skips more often than you think. All you need is a PLL case on U that can be solved with two Jperms, two Nperms, or one of each, and a PLL case on D with the same property

By understanding how to intuitively solve these cases using two CP algorithms (since all Square-1 CP algs are simply J and N perm combos), you can solve a lot of PBL cases using 2 CP algs!!!

The PLL cases you need to learn are as follows

Aperms (use J followed by J to solve)

Gperms (for the cases with an opposite sticker between the headlights, you use Jperm then Nperm. vise versa for the other Gperms)

Hperm (two N perms)

Jperms (one Jperm, or two Jperms, or Jperm into Nperm or Nperm into Jperm! lots of versatility here so pay attention to the other PLL on the puzzle as well as the E layers position so that you make the best choice)

Nperms (one Nperm or two Jperms, usually two Jperms is more efficient in the context of these PBL cases though)

Tperm (two Jperms)

Uperms (two Jperms)

Yperm (two Jperms)

If you have a PBL case that's made up of two PLL's from anywhere in the above list, then you can always solve PBL by using two CP algorithms

Setup: /-3,0/3,3/0,-3/4,0/3,0/-3,0/3,0/-3,0/5,6

Normally in this position, you would likely see someone either do J/J with no misalignment and get Zperm with an E flip, or by misaligning the top to get Uperm with E flip (worse than Z), or mayyybe if they're smart, double misalign into U/U with E flip (half the time this will be good, but in this case you get "matching" Uperms so it's not so nice...)

Using what I described earlier however, you could just apply an Nperm to the Gperm, which will give a Jperm on the top

Doing just a direct Nperm however isn't very efficient, and also leaves the E layer flipped which isn't great for double Jperm

Since the Jperm on bottom allows us a bit of freedom in what CP algorithm we do, we could try applying a Jperm to the bottom at the same time, which is a 5 slice 2gen CP instead of a 6 slice 3gen CP

This would then give us Jperm Jperm to finish while also flipping the E slice

The BEST way to get Jperm Jperm while flipping the E slice however would be by doing Nperm on both layers, which is a 3 slice CP that also flipped the E slice :)

Note that you can also do N/N in 4 slices while preserving the E slice by using /3,3/-6,0/-3,-3/, meaning that N/N would be the optimal choice here regardless of how the E slice was flipped

However, in this case we're going to use the more traditional N/N and solve PBL with 1,0/-3,3/3,-3/-4,3/-3,0/3,3/0,-3/0,3

As you can see, this kind of knowledge can really pay off

That being said, there are definitely times where even if you CAN do PBL with 2 CP algs, you don't necessarily want to

There are also cases where it's impossible to do 2 CP algs and solve PBL, but it's still possible to make your overall PBL better, which brings us to...

Forcing good U/U

Again, whether or not you can even force U/U is going to come down to what PLL cases you have on each side

PLL cases that go into Uperm

Aperms

Fperm

Gperms

Jperms

Rperms

Tperms

Uperms

Vperms

Yperms

PLL cases where you can CHOOSE whether or not you get CW or CCW Uperm

Fperm

Tperm

Vperm

Yperm

PLL cases where the Uperm is predetermined

Aperms

Gperms

Jperms

Rperms

Uperms

Basically, if you have a PBL case where one side has F T V or Y, and the other has ANYTHING that can go into Uperm, you can ALWAYS force good U/U, which is a 5 slice EP (much better than bad U/U). These are the cases you want to learn

If you DON'T have F T V or Y, but instead just have a combination of anything that can go into Uperm, then you best bet is going to be either doing CP into whatever U/U you get, or if at all possible, two CP algs to force an EP skip

Scramble: 1,0/-3,0/3,3/0,-3/2,2/-3,0/3,3/0,3/0,6/3,-2

Here's an interesting example of a case where you could actually do CP twice and force an EP skip

However, the ONLY way you can do it in this case is by using J/J twice and then cancelling into an E flip

The above scramble is effectively an inverse of that approach (so it's 9 slices long)

However, if your Sq1 IQ is high enough, you may have noticed that we have different Aperms on each side, meaning if we do J/J once to solve CP, we'll also get different U perms AKA one of the good U/U cases

/-3,0/3,3/0,-3/1,-3/5,-1/-3,0/1,1/-3,0/-4,6

This also adds up to 9 slices

So, which is better?

Well, in my opinion doing CP>EP is a LOT more simple than CP>CP>cancelling an E-flip in terms of recognition and execution

Whatever you think is better, the point remains that PBL with 2 CP's isn't exactly always king if it's possible

If you haven't already, look into these PBL methods and adopt them

Also start using 0,-1/-2,1/2,2/0,-3/ and 1,0/-4,2/4,-2/ as CP algs sometimes when they force good EPs

I like using the first one for R/R or J/R combos to give me adj adj sometimes (other times I'll just force pure Z or Z/Z if I can cancel it)

The second one is nice for V/V, gives adj/adj instead of good or bad U/U which is mainly nice when you get E-flip using the CP alg

And that's about it

You could also just learn full algorithmic PBL which I think a few people are currently attempting

I'm not one of those people because I like 3x3

Any questions let me know

Keep on cubing

Talk soon

-J

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