I see. Pretty cool.
HTR is half turn reduction. In FMC terms, it’s DR on all axes. It’s just a fancy way of saying that the cube is solvable using only half turns.
2-gen methods
- Thread starter Devagio
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HTR is half turn reduction. In FMC terms, it’s DR on all axes. It’s just a fancy way of saying that the cube is solvable using only half turns.
Technically, DR on all axes isn't enough to guarantee it's half-turn-solvable. Consider for example an N perm, which definitely can't be solved with only half turns, but is DR on all axes (if you AUF it to be 2c2e).
AlphaCuber is awesome
Veteran
square In back -> 1llsll only ~7000 algs
imo it’s the only reason to bother doing a cp method such as Briggs
imo it’s the only reason to bother doing a cp method such as Briggs
True, I stand corrected.
By the way, while we are coming up with methods, another interesting exercise is to find the god’s number for RU-gen scrambles using R and U moves only.
There are 17 move 2GLLs with no more efficient solutions without involving other faces, so that is a lower bound. Simple F2L>2GLL ensures we can solve it in 2+12+12+20 = 46 moves, so that is a nice weak upper bound. Let’s see if we can narrow this further.
Though, it’s a very restricted set, I guess a fairly well written code should run in under a day on a laptop.
It’s 1900 algs afaik. Mentioned it in the OP.
It's already known, actually! There's less than 100 million states, so even crummy old computers didn't have too much trouble with that.
Source: http://forum.cubeman.org/text/fullcube.txt
Code:
Analysis of the 3x3x3 <U, R> group
----------------------------------
ML's Conjecture: The < U, R > group is >=20 turns deep in qt metric
Now confirmed, Sept 1, 1994
branching
Moves Deep arrangements (q only) factor
0 1 --
1 4 4
2 10 2.5
3 24 2.4
4 58 2.416
5 140 2.413
6 338 2.414
7 816 2.414
8 1,970 2.414
9 4,756 2.414
10 11,448 2.407
11 27,448 2.401
12 65,260 2.378
13 154,192 2.363
14 360,692 2.339
15 827,540 2.294
16 1,851,345 2.237
17 3,968,840 2.144
18 7,891,990 1.988
19 13,659,821 1.755
20 18,471,682 1.352
21 16,586,822 0.898
22 8,039,455 0.485
23 1,511,110 0.188
24 47,351 0.031
25 87 0.002
----------
73,483,200
Moves Deep arrangements (q+h) total
0 1 1
1 6 7
2 18 25
3 54 79
4 162 241
5 486 727
6 1,457 2,184
7 4,360 6,544
8 13,016 19,560
9 38,482 58,042
10 113,094 171,136
11 328,920 500,056
12 942,351 1,442,407
13 2,616,973 4,059,380
14 6,774,848 10,834,228
15 15,105,592 25,939,820
16 24,231,019 50,170,839
17 19,421,274 69,592,113
18 3,843,568 73,435,681
19 47,465 73,483,146
20 54 73,483,200AlphaCuber is awesome
Veteran
i was told it was 7k but that might be an upper bound so adding in auf things I can see it being around there, in that case it might make cp methods viable.
This is legit the coolest method so far!
Yep, you’re right; it’s 7k. I initially miscalculated.
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WoowyBaby
Veteran
How about this method?
R2 U' R' U2 R2 U2 R2 U R' U' R2 U2 R U R' U' R U2 R' U' R' U R' U2 R
U R U2 R2 U R' //
U' R2 U' R2 //
U R U2 R2 U2 R2 U2 R //
R U R U R' U' R' U' R' //
// 27
R' U2 R U R2 U R2 U2 R2 U2 R U' R' U R2 U R2 U2 R2 U' R2 U R2 U R'
R U2 R2 U' R U' R' //
U R2 U R2 //
U' R U R' U' R' U' R' U //
S' U2 S U2 R U2 //
// 26
R' U R U R U R' U R' U R2 U R' U2 R U R2 U R2 U' R U2 R' U2 R
U2 R U2 R' U2 R //
U' R2 U R2 //
U' R' U2 R U2 R2 U2 R2 U2 R U2 R //
U R' U' R U R U R U' R' U' //
// 33
U' R U' R2 U2 R' U2 R' U2 R2 U2 R2 U R' U2 R' U2 R' U' R U' R' U R2 U2
U' R U R' U R U2 R' //
R U2 R2 U2 R2 U2 R //
U2 R U R' U R2 U2 R2 U2 R2 U R U' R' U' //
// 30 (25 with cancels)
Number of algs: Few
Number of moves: Few
Number of issues: Few
Number of how-cool-it-is: High
R2 U' R' U2 R2 U2 R2 U R' U' R2 U2 R U R' U' R U2 R' U' R' U R' U2 R
U R U2 R2 U R' //
U' R2 U' R2 //
U R U2 R2 U2 R2 U2 R //
R U R U R' U' R' U' R' //
// 27
R' U2 R U R2 U R2 U2 R2 U2 R U' R' U R2 U R2 U2 R2 U' R2 U R2 U R'
R U2 R2 U' R U' R' //
U R2 U R2 //
U' R U R' U' R' U' R' U //
S' U2 S U2 R U2 //
// 26
R' U R U R U R' U R' U R2 U R' U2 R U R2 U R2 U' R U2 R' U2 R
U2 R U2 R' U2 R //
U' R2 U R2 //
U' R' U2 R U2 R2 U2 R2 U2 R U2 R //
U R' U' R U R U R U' R' U' //
// 33
U' R U' R2 U2 R' U2 R' U2 R2 U2 R2 U R' U2 R' U2 R' U' R U' R' U R2 U2
U' R U R' U R U2 R' //
R U2 R2 U2 R2 U2 R //
U2 R U R' U R2 U2 R2 U2 R2 U R U' R' U' //
// 30 (25 with cancels)
Number of algs: Few
Number of moves: Few
Number of issues: Few
Number of how-cool-it-is: High
Imam Alam
Member
- Joined
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yes!
this is what I was talking about in my original reply (except for using S moves as you did in one of your example solve)
also, check out this method where I use 2-gen CO, then DR and then HTO reduction (and it has variants where CP and EO are done first/early)
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This is definitely not few algs! XD
RU comms are certainly unintuitive enough to call them algs; especially when I’m considering even 3style as an algorithmic approach.
Really cool method though!
CO>absoluteCP>2-3EPalgs
I assume this is why it has "few" issues and not "no" issues.
WoowyBaby
Veteran
Oh no, there are actually not very many algorithms, I'm serious! (Definitely less than 20 are needed!)
Well, S' moves are actually incredibly fast OH (for me, about as fast or even faster than a U2 spin), which I think Devagio is trying to make this for(?)
Plus, it's not bad that I go out of the 2-gen moveset for literally 2-3 moves. It's not like there's a rule that says you can't do this, and as I said, S' moves are speedy (try it!). And, the biggest thing is, doing R U R2 U' R' U' R' U2 R U' instead of simply S' U2 S is just kind of stupid lol
--------------------
The method steps, by the way, are:
Step 1: Orient all corners (preferably in a way that orients the most edges on the second axis).
Step 2: Solve all corners (preferably in a way that solves some edges)
Step 3: Use one edge algorithm to reduce down to 3e, or rarely, only if significantly easier, 2e2e.
Step 4: Apply one last sequence to finish that cube!
The number of algorithms for the first two steps is 0. Orienting corners is intuitive and only requires recognizing a few different cases.
Solving the corners from there takes only 4-5 moves on average and is super fast to execute because you know what to do instantly!
The third step sometimes relies on your arsenal of (R, U) 3e edge algorithms, which honestly doesn't have to be very big at all, I would say you can use this method with proficiency knowing a total of less than 15 algorithms. If you choose to use 2e2e algorithms in this third step, this solving/reduction step, then you're in luck! You don't have to memorize any algorithms, because (R, U) 2e2e algs basically don't exist! What I mean by this is that the optimal solution to any given 2e2e in 2-gen is almost always a set-up to R2 U2 R2 U2 R2 U2. Setting up to that simple 6-mover is legitimately, and when I say this I'm being real, all three- intuitive, fast (because the setups are easy to see), and optimal. So that's nice.
The fourth step is much of the same of the third, except here it is a lot less thinking and intuition, which is a drawback to step 3, but it is pretty easy to see where pieces need to go, so it's really only barely a drawback. anyway, in this fourth and final step, you simply just solve the case that you see. It's just like solving OLL or something, you simply look and spam your algorithm. If you only know a couple of 2-gen 3e algs then you may have to do one premove beforehand, but this is both much slower, because more thinking is involved, and a little bit more inefficient movecount wise, so just learn a few more 3e algs (again, not that many) and you'll be much better. You'll just spam your 10 move algorithm to finish.
And just a side note, I believe that no matter what your edge cycles are, you will only ever need to do 2 algorithms of 3e and 2e2e to solve all edges.
For example, if you have 4e2e, swap the 2e and any other 2 edges with a 2e2e to reduce to just 3e remaining. For 5e, two 3e's can be used.
And if you have all 7 edges messed up, which means you sadly didn't solve any of the edges during the corners stage, which you should be trying to do... But if your cycles are 3e2e2e, then it's pretty obvious you can still manage to solve it in 2 algs
The average movecount of this method is actually less than doing SQ->F2L->2GLL, so this method is pretty efficient.
Now this is all for now! I might, and probably will, make a little list of some useful 2-gen 3e algs later and edit it in, but for now this is it!
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I disagree at a couple of places tbh; but I wanna wait till you give a list of cases you think is exhaustive to make the method worth it. 7-cycles are the only places where I see you’d require 3 edge algs, and those I believe will be fairly rare, especially because you’ll almost always be able to influence edges really easily during corner solving.Oh no, there are actually not very many algorithms, I'm serious! (Definitely less than 20 are needed!)
Well, S' moves are actually incredibly fast OH (for me, about as fast or even faster than a U2 spin), which I think Devagio is trying to make this for(?)
Plus, it's not bad that I go out of the 2-gen moveset for literally 2-3 moves. It's not like there's a rule that says you can't do this, and as I said, S' moves are speedy (try it!). And, the biggest thing is, doing R U R2 U' R' U' R' U2 R U' instead of simply S' U2 S is just kind of stupid lol
--------------------
The method steps, by the way, are:
Step 1: Orient all corners (preferably in a way that orients the most edges on the second axis (which is just putting e-layer edges in the e-layer)).
Step 2: Solve all corners (preferably in a way that solves the most edges (for example, U2 R2 U R2 instead of R2 U2 R2 U' R2))
Step 3: Use one edge algorithm to reduce down to 3e, or rarely, only if significantly easier, 2e2e.
Step 4: Apply one last sequence to finish that cube!
The number of algorithms for the first two steps is 0. Orienting corners is intuitive and only requires recognizing a few different cases.
Solving the corners from there takes only 4 moves on average and is super fast to execute because you know what to do instantly!
The third step sometimes relies on your arsenal of (R, U) 3e edge algorithms, which honestly doesn't have to be very big at all, I would say you can use this method with proficiency knowing a total of less than 15 algorithms. If you choose to use 2e2e algorithms in this third step, this solving/reduction step, then you're in luck! You don't have to memorize any algorithms, because (R, U) 2e2e algs basically don't exist! What I mean by this is that the optimal solution to any given 2e2e in 2-gen is almost always a set-up to R2 U2 R2 U2 R2 U2. Setting up to that simple 6-mover is legitimately, and when I say this I'm being real, all three- intuitive, fast (because the setups are easy to see), and optimal. So that's nice.
The fourth step is much of the same of the third, except here it is a lot less thinking and intuition, which is a drawback to step 3, but it is pretty easy to see where pieces need to go, so it's really only barely a drawback. anyway, in this fourth and final step, you simply just solve the case that you see. It's just like solving OLL or something, you simply look and spam your algorithm. If you only know a couple of 2-gen 3e algs then you may have to do one premove beforehand, but this is both much slower, because more thinking is involved, and a little bit more inefficient movecount wise, so just learn a few more 3e algs (again, not that many) and you'll be much better. You'll just spam your 10 move algorithm to finish.
And just a side note, I believe that no matter what your edge cycles are, you will only ever need to do 2 algorithms of 3e and 2e2e to solve all edges.
For example, if you have 4e2e, swap the 2e and any other 2 edges with a 2e2e to reduce to just 3e remaining. For 5e, two 3e's can be used.
And if you have all 7 edges messed up, which means you sadly didn't solve any of the edges during the corners stage, which you should be trying to do... But if your cycles are 3e2e2e, then it's pretty obvious you can still manage to solve it in 2 algs
The average movecount of this method is actually less than doing SQ->F2L->2GLL, so this method is pretty efficient.
Now this is all for now! I might, and probably will, make a little list of some useful 2-gen 3e algs later and edit it in, but for now this is it!
In all, this looks really solid. Awesome!
There were five 2GLL cases I use S/S' moves for (I replaced two of them with RUL algs recently, but that's still three RUS cases left), so yeah, I already use S moves lol.
ThisNameIsAlreadyTaken
Regular
So you're basically saying what I said, but with more algorithms lol?
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