• Welcome to the Speedsolving.com, home of the web's largest puzzle community!
    You are currently viewing our forum as a guest which gives you limited access to join discussions and access our other features.

    Registration is fast, simple and absolutely free so please, join our community of 35,000+ people from around the world today!

    If you are already a member, simply login to hide this message and begin participating in the community!

2gen Square-1 Solver (by ben1996123)

qqwref

Member
Joined
Dec 18, 2007
Messages
7,830
Location
a <script> tag near you
WCA
2006GOTT01
YouTube
qqwref2
God's number is 43 ignoring the middle layer, or 44 including the middle layer in turn metric (/ = 1 move, (x,0) = 1 move).

Ignoring middle layer:
Code:
depth   positions
0       1
1       8
2       10
3       39
4       40
5       142
6       144
7       460
8       426
9       1304
10      1186
11      3544
12      3375
13      9878
14      9769
15      29002
16      29573
17      88309
18      90465
19      271282
20      277449
21      827415
22      843048
23      2460655
24      2431730
25      6697884
26      6019635
27      14389848
28      10693709
29      21423501
30      15307424
31      30447214
32      21390049
33      32266820
34      14093340
35      12748845
36      4583014
37      5464277
38      2351079
39      1413334
40      148940
41      23142
42      290
43      1

Including middle layer:
Code:
depth   positions
0       1
1       8
2       10
3       40
4       50
5       184
6       227
7       584
8       700
9       1680
10      2017
11      4560
12      5670
13      12736
14      16000
15      37272
16      47451
17      112968
18      145182
19      346648
20      446528
21      1058968
22      1364842
23      3168264
24      4045811
25      8800688
26      10802822
27      19927400
28      22620870
29      31615032
30      34929938
31      44881008
32      49595709
33      54070720
34      50129617
35      28152160
36      21500086
37      10339048
38      8838395
39      4092704
40      2301502
41      218304
42      48159
43      624
44      13

Solver download link here

Input format: letters a-l and (if you are using the solver with the middle layer) a 1 to indicate that the middle layer is flipped. Solved state is abcdefghijkl

example: F perm + edge parity on D + middle layer flip: gfcdebahkjil1

When you run the solver it will generate a 457mb file if you ignore the middle layer, or 914mb if you include it, then ask for a position to solve. It will give you a list of all of the optimal solutions.

Some stuff I've found so far:
adjacent parity: 4/3/2/3/-3/-2/-4/-2/-3/-2/3/2/5/2/2/5/3/3/
adj-adj CP parity: /3/3/-2/-2/4/-4/-2/5/-3/
corner-edge swap: -2/-4/3/-5/-4/-2/-5/-4/2/4/-3/4/2/-4/-5/-2/-1/-5/-3
j perm: 1/3/5/3/1/4/-1/2/3/-2/1/4/-4/4/2/6/5/-3/-3
u perm: /3/1/4/5/6/2/4/1/2/-3/-1/-3/3/
 

Wilhelm

Member
Joined
Aug 26, 2013
Messages
267
Location
Bruchsal, Germany
WCA
2010KILD02
YouTube
WilhelmKilders
This is really nice. I considered bandaging a Square-1 that I have laying around and now I might end up doing it cause I can solve it. I already tried to solve it but couldn't really find any algs and I had to stop at EO.
 

Lucas Garron

Member
Joined
Jul 6, 2007
Messages
3,557
Location
California
WCA
2006GARR01
YouTube
LucasGarron
Some stuff I've found so far:
adjacent parity: 4/3/2/3/-3/-2/-4/-2/-3/-2/3/2/5/2/2/5/3/3/
adj-adj CP parity: /3/3/-2/-2/4/-4/-2/5/-3/
corner-edge swap: -2/-4/3/-5/-4/-2/-5/-4/2/4/-3/4/2/-4/-5/-2/-1/-5/-3
j perm: 1/3/5/3/1/4/-1/2/3/-2/1/4/-4/4/2/6/5/-3/-3
u perm: /3/1/4/5/6/2/4/1/2/-3/-1/-3/3/
These are cool. I would have expected them to be quite longer.

Do you have any data on whether a typical position takes about the same number of U turns + D turns compared to a normal alg?
 
Last edited:

Stefan

Member
Joined
May 7, 2006
Messages
7,287
WCA
2003POCH01
YouTube
StefanPochmann
Yay, 2gen Square-1! I wrote one almost ten years ago as well and checked all possible swaps, this one was the shortest:
UFR<=>DBR: / 3 / -5 / -4 / 4 / 4 / -4 / 4 / 4 / -4 / 4 / -3 / -3 / (or backwards)
Ben's solver finds the same alg(s) for that case (it's abcdeflhijkg). Mine also found the same for qqwref's "adjacent parity". Looks like both solvers are correct :)

Would be good to write the sum of the numbers as well (i.e., the total number of 30 degree U-turns), and sort the optimal algs for a case by this number.
 
Last edited:

Stefan

Member
Joined
May 7, 2006
Messages
7,287
WCA
2003POCH01
YouTube
StefanPochmann
Oh... I thought he had just written the solver. It's a bit confusing, wish he were back...

Compared my favorite case as well, the solvers again found the same alg(s):
DRF<=>DBR: /3/1/2/-4/4/-4/-4/4/-4/-4/-2/5/-3/ (or backwards)
 
Last edited:

Stefan

Member
Joined
May 7, 2006
Messages
7,287
WCA
2003POCH01
YouTube
StefanPochmann
I realized our solvers don't fully match, because I went the other direction on the D layer. So for example abcdelghijkf ("swapping f and l) is invalid for mine, while for yours it results in the shortest "swap" alg:
4/2/5/-2/-3/2/3/-3/4/-3/3/-1
Though I can't execute it, I get stuck at the 5. What's going on?
 

Stefan

Member
Joined
May 7, 2006
Messages
7,287
WCA
2003POCH01
YouTube
StefanPochmann
Hmm, that opposite corner parity is much shorter than the opposite edge parities. I wonder whether that's the case in general, and what the average move counts are for "CP, EP" vs "EP, CP". Has this been compared already? What do the top solvers do?
 
Last edited:

blade740

Mack Daddy
Joined
May 29, 2006
Messages
853
WCA
2007NELS01
YouTube
blade740
Hmm, that opposite corner parity is much shorter than the opposite edge parities. I wonder whether that's the case in general, and what the average move counts are for "CP, EP" vs "EP, CP". Has this been compared already? What do the top solvers do?
CP, EP is the generally accepted norm. However, I solve parity along with CP, partially to take advantage of the lower movecount algorithms.
 

qqwref

Member
Joined
Dec 18, 2007
Messages
7,830
Location
a <script> tag near you
WCA
2006GOTT01
YouTube
qqwref2
I realized our solvers don't fully match, because I went the other direction on the D layer. So for example abcdelghijkf ("swapping f and l) is invalid for mine, while for yours it results in the shortest "swap" alg:
4/2/5/-2/-3/2/3/-3/4/-3/3/-1
Though I can't execute it, I get stuck at the 5. What's going on?
Ben says that the reason it doesn't work is because the position isn't cubeshape. So you have to do the inverse to set it up.
 
Top