Method hierachy

Advanced methods and approaches for solving Sudoku puzzles
I was going to post the number of solved puzzles and forgot and should have posted the solving order. I will also combine box/line and box/box results in the future. As far as the number of puzzles, you are right, only 92.3% of the puzzles were actually solved, but I did include the results from unsolved puzzles in the statistics. The solving order is as follows:
L_NAKED1
L_NAKED2
L_HIDDEN1
L_LOCKED1
L_LOCKED2
L_NAKED3
L_HIDDEN2
L_HIDDEN3
L_NAKED4
L_HIDDEN4
L_XWING 'includes basic and finned
L_SWORDFISH 'includes basic and finned
L_XY
L_XYZ 'generalized (allows 2-3 cell pilots)
L_WXYZ 'generalized (allows 2-4 cell pilots)
L_VWXYZ 'generalized (allows 2-5 cell pilots)
L_XYRING4
L_XYCHAIN4
L_XYRING5
L_XYCHAIN5
L_SUEDECOQ
L_ALS1 'xz only, same as xy-wing, xyz-wing, etc
L_ALS2 'xz only
L_TURBOT4 'same as locked candidates
L_TURBOT5 'includes basic and grouped
L_ALS3 'xz only
L_ALS4 'xz only
L_JELLYFISH 'includes basic and finned
L_SQUIRMBAG 'includes basic and finned
L_TURBOT6 'includes basic, finned, and grouped
L_TURBOT7 'includes basic and grouped
L_COLOR1 'type 1 includes basic and some grouped
L_COLOR2 'type 2 includes basic and some grouped
L_COLOR3 'type 3 includes basic and some grouped
L_UNIQUE1 'type 1
L_UNIQUE2 'includes types 2 and 2B
L_UNIQUE3 'includes types 3 and 3B
L_UNIQUE4 'includes types 4 and 4B
The initial clues for one of the jellyfish was:
..24...............91.56....3....6.9...6.1..41.6.35..2........1..92...3.38.....47
which proceeded to:
..24....3..3..2....91356.2853..2461992.6.1354146935..22.45.3..1.1924..3.385169247
with candidates (* are the jellyfish, x are the deletions):
Code: Select all
`+-------------+----------+--------------+| 678*  56  2 |  4 19 78*| 1579* 679* 3 ||4678x 567  3 | 78 19  2 |14579x 679x 56||  47*   9  1 |  3  5  6 |   47*   2  8 |+-------------+----------+--------------+|    5   3 78 | 78  2  4 |     6   1  9 ||    9   2 78 |  6 78  1 |     3   5  4 ||    1   4  6 |  9  3  5 |   78*  78* 2 |+-------------+----------+--------------+|    2  67  4 |  5 78  3 |    89 689  1 ||  67*   1  9 |  2  4 78*|    58   3 56 ||    3   8  5 |  1  6  9 |     2   4  7 |+-------------+----------+--------------+`

For the finned squirmbag:
........82.713..6.46...7.1..7.....42....64...8..........3.....9..53..1....25..8.7
........82.7138.6.468..7.1..768...42....64.8.8.4........3..2.59..53..12...25..837
Code: Select all
`+---------------+---------------+---------------+| 1359  1359 19 |  46 2459x 569x|  2579 79    8 ||    2    59* 7 |   1    3    8 |   459* 6   45 ||    4     6  8 |  29* 259*   7 |  2359* 1   35 |+---------------+---------------+---------------+| 1359*    7  6 |   8 159* 1359*|   359* 4    2 || 1359 12359 19 | 279    6    4 |  3579  8  135 ||    8 12359  4 | 279 1259 1359 | 35679 79 1356 |+---------------+---------------+---------------+|   17    18  3 |  46   78    2 |    46  5    9 ||  679*  489* 5 |   3   78   69*|     1  2   46 ||   69*   49* 2 |   5  149* 169*|     8  3    7 |+---------------+---------------+---------------+`

This one actually contained 2 7-node Grouped Turbot Chains (p-group elements, g-guards) with a broken wing
.5.....6.2..1..........3519...7...95...6.....7....2..3.9.27.1.4.........53....2..
.5.9.7.622.91563......23519...7...959.563.7217..592..3.9.275134...3..95.53...92..
Code: Select all
`+---------------+-------------+-------------+|   13   5   13 |  9   48   7 |  48   6   2 ||    2  48*   9 |  1    5   6 |   3 478  78 ||  468p 67 4678p| 48*   2   3 |   5   1   9 |+---------------+-------------+-------------+| 3468  26 2348 |  7 148x 148g|  68   9   5 ||    9  48x   5 |  6    3  48x|   7   2   1 ||    7  16  168 |  5    9   2 | 468  48   3 |+---------------+-------------+-------------+|   68   9   68 |  2    7   5 |   1   3   4 ||   14 127 1247 |  3  168 148x|   9   5 678 ||    5   3  147 |48* 1468g  9 |   2  78 678 |+---------------+-------------+-------------+`

There are 24997 more. I'd be happy to share them all as well as my solver if you need it
Mike Barker

Posts: 458
Joined: 22 January 2006

Just noticed that the last two puzzles weren't completely solved. Here's a 7-node Grouped Turbot Fish for a solved puzzle:

..35.82...1.6..3...59.3...6.........4...6.82..6..41..3...7.....728....5...4......
6435.82.781762.3.5259.37.8638..7....47..6.82.962841573..67.....728....5...4...7..
Code: Select all
`+----------+-------------+---------------+|  6  4  3 |   5  19*  8 |    2  19    7 ||  8  1  7 |   6   2  49 |    3  49    5 ||  2  5  9 |  14*  3   7 |   14*  8    6 |+----------+-------------+---------------+|  3  8 15g|  29   7 259 |1469x 146g 149p||  4  7 15 |  39   6 359 |    8   2   19p||  9  6  2 |   8   4   1 |    5   7    3 |+----------+-------------+---------------+| 15 39  6 |   7  58 249 | 149g 134   28 ||  7  2  8 | 134g 19*346 |  469   5  149*|| 15 39  4 | 129  58  26 |    7 136   28 |+----------+-------------+---------------+`

And for the finned squirmbag:
..1..2....5...7.4.....9..7.......8.....94.6..49..5....5.......23..2.15...7....9..
7.14.2359953.1724...439.17.1.572.894..794.61549.15.72351..794323492.15.7.725349.1

Code: Select all
`+------------+----------+---------+|   7  68* 1 |  4 68  2 | 3  5  9 ||   9   5  3 | 68* 1  7 | 2  4 68*||268x 268* 4 |  3  9  5 | 1  7 68*|+------------+----------+---------+|   1  36* 5 |  7  2 36*| 8  9  4 ||  28 238  7 |  9  4 38 | 6  1  5 ||   4   9 68*|  1  5 68*| 7  2  3 |+------------+----------+---------+|   5   1 68*| 68* 7  9 | 4  3  2 ||   3   4  9 |  2 68  1 | 5 68  7 ||  68   7  2 |  5  3  4 | 9 68  1 |+------------+----------+---------+`

I'll go ahead and modify my solver only to count completed puzzles and rerun (should take a day or so).
Mike Barker

Posts: 458
Joined: 22 January 2006

hi there mike,

Thanx for the interesting puzzles.......

I just went through the first 3, interesting remarks:

#1: Now I'm not sure if you use the same Finned-fish technique which I'm using, but as you emply finned x-wing prior to jellyfish:
There is a finned x-wing as follows before the Jellyfish.
Code: Select all
`*-----------------------------------------------------------------*|#678    56     2     | 4      19     78    | 1579   679    3     ||*4678  -567    3     | 78     19     2     | 14579  679   *56    || 47     9      1     | 3      5      6     | 47     2      8     ||---------------------+---------------------+---------------------|| 5      3      78    | 78     2      4     | 6      1      9     || 9      2      78    | 6      78     1     | 3      5      4     || 1      4      6     | 9      3      5     | 78     78     2     ||---------------------+---------------------+---------------------|| 2      67     4     | 5      78     3     | 89     689    1     ||*67     1      9     | 2      4      78    | 58     3     *56    || 3      8      5     | 1      6      9     | 2      4      7     |*-----------------------------------------------------------------*Eliminating 6 From r2c2 (Finned XWing in Columns 19)*-----------------------------------------------------------------*| 678    56     2     | 4      19     78    | 1579   679    3     || 4678   57     3     | 78     19     2     | 14579  679    56    || 47     9      1     | 3      5      6     | 47     2      8     ||---------------------+---------------------+---------------------|| 5      3      78    | 78     2      4     | 6      1      9     || 9      2      78    | 6      78     1     | 3      5      4     || 1      4      6     | 9      3      5     | 78     78     2     ||---------------------+---------------------+---------------------|| 2      67     4     | 5      78     3     | 89     689    1     || 67     1      9     | 2      4      78    | 58     3      56    || 3      8      5     | 1      6      9     | 2      4      7     |*-----------------------------------------------------------------*Eliminating 7 From r2c1 (2x2x2x2 Jellyfish in Columns 2345)Eliminating 7 From r2c7 (2x2x2x2 Jellyfish in Columns 2345)Eliminating 7 From r2c8 (2x2x2x2 Jellyfish in Columns 2345)`

#2: The same here, but after the double finned x-wing, there is a finned swordfish
Code: Select all
`*-----------------------------------------------------------------*| 1359   1359  *19    | 46     2459   569   | 2579  *79     8     || 2      59     7     | 1      3      8     | 459    6      45    || 4      6      8     | 29     259    7     | 2359   1      35    ||---------------------+---------------------+---------------------|| 1359   7      6     | 8      159    1359  | 359    4      2     || 1359   12359#*19    | 279    6      4     |-3579  *8      135   || 8     -12359 *4     | 279    1259   1359  | 35679#*79     1356  ||---------------------+---------------------+---------------------|| 17     18     3     | 46     78     2     | 46     5      9     || 679    489    5     | 3      78     69    | 1      2      46    || 69     49     2     | 5      149    169   | 8      3      7     |*-----------------------------------------------------------------*Eliminating 9 From r6c2 (Finned XWing in Columns 38)Eliminating 9 From r5c7 (Finned XWing in Columns 38)*-----------------------------------------------------------------*| 1359   1359  *19    |*46    -2459  -569   | 2579  *79     8     || 2      59     7     | 1      3      8     | 459    6      45    || 4      6      8     |#29     259    7     | 2359   1      35    ||---------------------+---------------------+---------------------|| 1359   7      6     | 8      159    1359  | 359    4      2     || 1359   12359 *19    |*279    6      4     | 357    8      135   || 8      1235   4     |*279    1259   1359  | 35679 *79     1356  ||---------------------+---------------------+---------------------|| 17     18     3     | 46     78     2     | 46     5      9     || 679    489    5     | 3      78     69    | 1      2      46    || 69     49     2     | 5      149    169   | 8      3      7     |*-----------------------------------------------------------------*Eliminating 9 From r1c5 (Finned Swordfish in Columns 348)Eliminating 9 From r1c6 (Finned Swordfish in Columns 348)`

which means that the above eliminations can be achieved by the same finned swordfish

#3: This was a nice surprise, a finned jellyfish
Code: Select all
`*--------------------------------------------------------*| 13    5     13   | 9     48    7    | 48    6     2    || 2     48    9    | 1     5     6    | 3     478   78   ||*468   67   *4678 |*48    2     3    | 5     1     9    ||------------------+------------------+------------------||*3468  26   *2348 | 7    -148  *148  | 68    9     5    || 9     48    5    | 6     3    #48   | 7     2     1    || 7     16    168  | 5     9     2    | 468   48    3    ||------------------+------------------+------------------|| 68    9     68   | 2     7     5    | 1     3     4    ||*14    127  *1247 | 3     168  *148  | 9     5     678  || 5     3    *147  |*48    1468  9    | 2     78    678  |*--------------------------------------------------------*Eliminating 4 From r4c5 (Finned Jellyfish in Columns 1346)`

I will have a look at the next 2........

Tarek

tarek

Posts: 2735
Joined: 05 January 2006

To continue:

#4: My solver couldn't spot the grouped turbot

#5: Again there is simpler fish:
Code: Select all
`*-----------------------------------------------*| 7    68   1   | 4    68   2   | 3    5    9   || 9    5    3   |*68   1    7   | 2    4   *68  ||*268  268  4   | 3    9    5   | 1    7   *68  ||---------------+---------------+---------------|| 1    36   5   | 7    2    36  | 8    9    4   || 28   238  7   | 9    4    38  | 6    1    5   || 4    9    68  | 1    5    68  | 7    2    3   ||---------------+---------------+---------------||*5    1   -68  |*68   7    9   | 4    3    2   || 3    4    9   | 2    68   1   | 5    68   7   ||#68   7    2   | 5    3    4   | 9    68   1   |*-----------------------------------------------*Eliminating 6 From r7c3 (Finned Swordfish in Columns 149)`

I'm not sure if that means that there is a difference in our perspective to seeing things or is it just a programming issue.

Tarek

tarek

Posts: 2735
Joined: 05 January 2006

Thanks for the feedback. Looking at the results, my solver is missing the sashimi fillets. I'll fix that. Not, sure about the Turbot fish. Can you send me the steps your solver takes and I'll look at the differences.
Mike Barker

Posts: 458
Joined: 22 January 2006

Mike Barker wrote:I went ahead and reran my solver with 25000 random puzzles first moving colors after grouped turbot fish (so there are now no color eliminations) and changing it so it records the number of times a technique is used not just the number of puzzles it is used in.

Are those 25000 random puzzles available to others in any forum? If "yes", where?

If "no", I suggest using Gordon Royle's library of 36,628 puzzles available at http://www.csse.uwa.edu.au/~gordon/sudoku17. Then others can run the same puzzles through their solvers and compare results.

Ron
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Hi Mike! Thanks for providing those puzzles!

As you know, I will now do anything I can to try and prove that you don't need such complicated techniques to solve them! Nothing personal!

..24...............91.56....3....6.9...6.1..41.6.35..2........1..92...3.38.....47

Now, first I am a bit puzzled that your turbot fish did not already kill off this one:

and then to take out the other two, you can add one more strong link to that pattern:

No need to involve 10 7's when 6 does the job!

Ok, onto the finned squirmbag:
..1..2....5...7.4.....9..7.......8.....94.6..49..5....5.......23..2.15...7....9..

Again that elimination can be done with three strong links:

and just for fun, look at the patterns of the 6's... A completly identical pattern... I have never seen anything like this before!

this reduction also solves the puzzle! (the one in the 8's don't)

Now for the grouped Turbot with 7 nodes:
..35.82...1.6..3...59.3...6.........4...6.82..6..41..3...7.....728....5...4......

If I understand your list correctly, you are allowed to apply ALS xz for up to 4 cells before you use the Turbot 7.

Now if you first identify this one:
(suprise, suprise... three strong links! )

and now this als:

Code: Select all
`+----------+-------------+---------------+ |  6  4  3 |   5  19   8 |    2  19    7 | |  8  1  7 |   6   2  49+|    3  49    5 | |  2  5  9 |  14   3   7 |   14   8    6 | +----------+-------------+---------------+ |  3  8 15#|  29   7 259+|1469  16#  149 | |  4  7 15 |  39   6 359 |    8   2   19 | |  9  6  2 |   8   4   1 |    5   7    3 | +----------+-------------+---------------+ | 15 39  6 |   7  58 249+| 149  134   28 | |  7  2  8 | 134  19 346 |  469   5  149 | | 15 39  4 | 129  58  26+|    7 136*  28 | +----------+-------------+---------------+x=5, z=6# marks one set, + the other * cell to eliminate 6 from`

and then you can use this little one:

Agreed it is on the line of what is "simpler" but maybe a little...?

Summed up, I think the power of three strong links is not something one should underestimate! They can be hard to find, but only using 6 cells, they are by definition easier to find than anything that requires more cells... (like the 11 of a finned squirmbag...)

(and they are really easy to program too... I don't even want to think about how to program finned squirmbags or grouped turbot fishes...)

havard

edit: did not comment on the right elimination...
Havard

Posts: 377
Joined: 25 December 2005

[Edit: updated to include advanced BUG techniques and longer XY-chains]

I thought it might be worthwhile to update my list of solving techniques and their relative frequency. In this case, I've used a set of 10000 randomly generated puzzles (using suexg). My solver has been expanded to include most of the non-advanced techniques listed in the Collection of Solving Techniques including locked sets (except for remote pairs which get picked up in XY-chains), Fishy cycles (including the latest Frakenfish), X-cycles (which I implement by finding disjoint strong links and grouped strong links rather than Turbot Fish, etc), ALS techniques, all of the latest UR techniques, BUG-lite techniques including strong link varieties, as well as simple and grouped nice loops (without AUR and almost-X-cycles). I never implemented a full BUG. For processing time reasons I've limited ALS to no more than 6 cells (fewer when part of grouped nice loops) and nice loops to no more than 9 bivalued cells or strong links. BUG-lites are also limited in size. I've chosen the following solving order working from easier to harder, but keeping similar techniques together:
L_NAKED1
L_HIDDEN1
L_LOCKED1 'include line/box and box/box eliminations
L_NAKED2
L_NAKED3
L_HIDDEN2
L_HIDDEN3
L_NAKED4
L_HIDDEN4
L_XWING 'includes basic, finned, big fin, and franken
L_SWORDFISH 'includes basic, finned, big fin, and franken
L_JELLYFISH 'includes basic, finned, big fin, and franken
L_SQUIRMBAG 'includes basic, finned, big fin, and franken
L_EMPTY 'empty rectangle
L_STRONG2 'two strong links (basic and grouped)
L_STRONG3 'three strong links (basic and grouped)
L_STRONG4 'four strong links (basic and grouped)
L_XY 'XY-wing
L_XYZ 'generalized (allows 2-3 candidate pilots)
L_WXYZ 'generalized (allows 2-4 candidate pilots)
L_VWXYZ 'generalized (allows 2-5 candidate pilots)
L_UVWXYZ 'generalized (allows 2-6 candidate pilots)
L_TUVWXYZ 'generalized (allows 2-7 candidate pilots)
L_XYRING4 '4-node XY-ring
L_XYCHAIN5 '5-node XY-chain
L_XYRING5 '5-node XY-ring
L_XYCHAIN6 '6-node XY-chain
L_XYRING6 '6-node XY-ring
L_XYCHAIN7 '7-node XY-chain
L_XYRING7 '7-node XY-ring
L_XYCHAIN8 '8-node XY-chain
L_XYRING8 '8-node XY-ring
L_XYCHAIN9 '9-node XY-chain
L_ALS1xz 'xz rule (set A is a bivalue cell)
L_SUEDECOQ 'SueDeCoq
L_UNIQUE1 'UR+1 (type 1)
L_UNIQUE2 'UR+2x (types 2/2B)
L_UNIQUE5 'UR+2d, UR+3x (types 5/5B,...)
L_UNIQUE3 'UR+2X (types 3/3B)
L_UNIQUE6 'UR+2r(x,d)
L_UNIQUE9 'UR+2k(x,d)
L_UNIQUE4 'UR+2(X,D,B)/1SL (types 4/4B,...)
L_UNIQUE7 'UR+3(X,C,N,U,E)/2SL
L_UNIQUE8 'UR+4(X,C)/3SL
L_UNIQUE11 'UR+2D, UR+3(x,X)/1SL
L_UNIQUE10 'UR+2K(X,D), UR+3K(X,D)
L_UNIQUE12 'UR+4(x,X)/2SL, UR+4(x,X)/1SL
L_BUG2 '2 row or columns (all types including advanced)
L_BUG3 '3 row or columns (all types including advanced)
L_BUG4 '4 row or columns (all types including advanced)
L_BUG5 '5 row or columns (all types including advanced)
L_ALS2xz 'xz rule (A=2 cell ALS)
L_ALS3xz 'xz rule (A=3 cell ALS)
L_ALS4xz 'xz rule (A=4 cell ALS)
L_ALS5xz 'xz rule (A=5 cell ALS)
L_ALS6xz 'xz rule (A=6 cell ALS)
L_ALS1xy 'xy rule (B=1 cell ALS)
L_ALS2xy 'xy rule (B=2 cell ALS)
L_ALS3xy 'xy rule (B=3 cell ALS)
L_ALS4xy 'xy rule (B=4 cell ALS)
L_ALS5xy 'xy rule (B=5 cell ALS)
L_ALS6xy 'xy rule (B=6 cell ALS)
Below is summarized the number of times a technique is used in solving puzzles. Only the results from successful solutions are included (9953 out of 10000). Compared to the last listing the biggest change is the introduction of simple nice loops prior to most ALS techniques. The new UR techniques also show up fairly often as well (especially when compared to the original Types 1-4). After looking at a number of XYZ-wings where the ALS was not confined to a box, I decided to require the mYZ-wings be limited to be in a box otherwise the patterns could spread too far over the board. This explains the reduction in these types of eliminations and an increase in ALS. Empty rectangles show up much more frequently since I moved them prior to fish. Note, because almost all technique lists treat locked line/box and locked box/box eliminations as separate (although complementary) techniques, I've gone ahead and included them separately. If you prefer to treat them as one technique then simply sum the two corresponding values.
1) Naked Single (434258)
2) Hidden Single (133774)
3) Locked Line/Box (17735)
4) Locked Box/Box (4355)
5) Naked Pair (3764)
6) Finned X-wing (3526)
7) Naked Triple (2036)
8) XY-wing (1640)
9) Nice Loops with 4 Strong Links/Bivalue Cells (1406)
10) Nice Loops with 3 Strong Links/Bivalue Cells (1323)
11) ALS-xz rule with A=1 cell (991)
12) Generalized WXYZ-wing (977)
13) 6-node XY-chain (805)
14) Hidden Pair (756)
15) 5-node XY-chain (646)
16) FrankenFish (571)
17) Generalized VWXYZ-wing (563)
18) X-wing (561)
19) Generalized XYZ-wing (542)
21) Finned Swordfish (500)
22) UR+3(X,C,N,U,E)/2SL (468)
23) 7-node XY-chain (440)
24) UR+2K(X,D),UR+3K(X,D) (355)
25) Nice Loops with 5 Strong Links/Bivalue Cells (341)
26) UR+4(x,X)/2SL, UR+4(x,X)/1SL (288)
27) UR+2(X,D,B)/1SL (Type 4,...) (267)
28) 8-node XY-chain (229)
29) Generalized UVWXYZ-wing (212)
30) UR+2r(x,d) (190)
31) UR+4(X,C)/3SL (162)
32) Hidden Triple (155)
33) UR+2k(x,d) (155)
34) 6-node XY-ring (129)
35) Swordfish (122)
36) 9-node XY-chain (111)
37) Three Grouped Strong Links (107)
39) Big Finned Fish (102)
40) UR+1 (Type 1) (94)
41) Nice Loops with 6 Strong Links/Bivalue Cells (88)
42) ALS-xz rule with A=2 cells (78)
43) 7-node XY-ring (66)
44) 5-node XY-ring (65)
45) ALS-xz rule with A=3 cells (57)
46) Generalized TUVWXYZ-wing (51)
47) Grouped Nice Loops with 3 GSL/ALS (50)
48) UR+2D,UR+3(x,X)/1SL (49)
49) 8-node XY-ring (42)
50) ALS-xy rule with B=3 cells (35)
51) ALS-xy rule with B=1 cell (34)
52) UR+2X (Type 3) (31)
53) ALS-xy rule with B=2 cells (30)
54) UR+2x (Type 2) (29)
55) BUG-Lite with 2 buglets (26)
57) Grouped Nice Loops with 4 GSL/ALS (25)
58) Nice Loops with 7 Strong Links/Bivalue Cells (23)
59) ALS-xy rule with B=4 cells (21)
60) Finned Jellyfish (19)
61) 9-node XY-ring (18)
62) BUG-Lite with 3 buglets (12)
63) Two Grouped Strong Links (11)
64) ALS-xz rule with A=4 cells (10)
65) Four Grouped Strong Links (9)
66) Nice Loops with 8 Strong Links/Bivalue Cells (8)
67) Jellyfish (7)
68) ALS-xy rule with B=5 cells (7)
72) Grouped Nice Loops with 5 GSL/ALS (5)
73) UR+2d,UR+3x (Type 5,...) (3)
74) ALS-xy rule with B=6 cells (3)
75) Grouped Nice Loops with 6 GSL/ALS (3)
76) BUG-Lite with 4 buglets (1)
77) ALS-xz rule with A=5 cells (1)
78) Nice Loops with 9 Strong Links/Bivalue Cells (1)
79) Squirmbag (0)
80) Finned Squirmbag (0)
81) Empty Rectangle (0)
82) Grouped Empty Rectangle (0)
83) SueDeCoq (0)
84) BUG-Lite with 5 buglets (0)
86) ALS-xz rule with A=6 cells (0)
87) Nice Loops with 2 Strong Links/Bivalue Cells (0)
88) Grouped Nice Loops with 2 GSL/ALS (0)
89) Grouped Nice Loops with 7 GSL/ALS (0)
What does all this mean? Not surprisingly the first message is to search out locked sets (singles, pairs, and candidates) and empty rectangles. Based on these results, the next thing I'd look for are small nice loops (combinations of bivalued cells and strong links with make up a small continuous or discontinuous loop), followed by fish and small ALS (combinations of bivalued cells and an ALS with at least one restricted common candidate). In reality since finding a UR is easier, I might try to locate UR's in conjunction with strong links or ALS prior to the small nice loops and ALS, but the payoff is smaller. After maybe some bigger fish other techniques are less likely to result in advancing the puzzle. Of course these priorities change if the puzzle is of a know pedigree.

Given the relative frequency of small nice loops, has anyone looked at classifying the types of reductions that can occur with these and their relative frequency? It might make another nice step between beginning and intermediate techniques.

Also I still can't seem to find a Type 5 UR. Does anyone have an example or an explanation of why they are so rare?
Last edited by Mike Barker on Sun Jun 25, 2006 4:48 pm, edited 1 time in total.
Mike Barker

Posts: 458
Joined: 22 January 2006

It seems that one concern here is the order to apply the given techniques.

Why doesn't anyone look at the state of the puzzle and look at all possible reductions given all available techniques and then apply all of the resulting eliminations and count that as one step in the puzzle solution? This way no step will destroy any other valid step and maybe this will lead to a quicker solution.

Using an 'eliminated candidate' from one technique in an application of another technique should be perfectly valid, in my intuition that is.

Any thoughts?
doduff

Posts: 32
Joined: 29 May 2006

Doduff - I agree in principle that applying all techniques to the puzzle and then performing the eliminations will reduce the dependance on order. It will not eliminate the problem since an elimination may not be possible given the current state of the puzzle, but some current elimination will prevent a future elimination. For UR's this is addressed somewhat by dealing with missing candidates. I know when I am hand solving, my tendancy is to use my latest elimination as a starting point for determining the next step which is contrary to waiting until all eliminations are determined.

On a different subject Havard once asked what the order of techniques would be based on the highest order technique required to solve the puzzles. I used the same data set as my previous post. Obviously order here will also be important, but for the order used the results are listed below. Probably the result I found most striking was how seldom most of the UR techniques (with the exception of Type 1) actually crack a puzzle. A more advanced study would look at how elimination of some of these techniques increases the requirement for even more advanced techniques. As in the previous results simple nice loops with 3 or 4 strong links or bivalue cells show up high on the list. The numbers in parentheses are the number of times that a technique was the highest required for sucessfully completed puzzles out of 10000 randomly generated puzzles.

Code: Select all
` 1 (4472)  L_HIDDEN1 2 (1243)  L_LOCKED1    'include line/box and box/box eliminations 3 ( 630)  L_XWING      'includes basic, finned, big fin, and franken 4 ( 496)  L_XY         'XY-wing 5 ( 434)  L_NAKED2 6 ( 347)  L_NICE4      '4 strong links/bivalue cells 7 ( 239)  L_XYCHAIN6   '6-node XY-chain 8 ( 237)  L_NICE3      '3 strong links/bivalue cells 9 ( 203)  L_NAKED310 ( 192)  L_XYCHAIN5   '5-node XY-chain11 ( 176)  L_ALS1xz     'xz rule (set A is a bivalue cell)12 ( 157)  L_WXYZ       'generalized (allows 2-4 candidate pilots)13 ( 153)  L_NAKED114 ( 113)  L_XYCHAIN7   '7-node XY-chain15 ( 104)  L_NICE5      '5 strong links/bivalue cells16 (  72)  L_SWORDFISH  'includes basic, finned, big fin, and franken17 (  68)  L_XYZ        'generalized (allows 2-3 candidate pilots)18 (  60)  L_VWXYZ      'generalized (allows 2-5 candidate pilots)19 (  55)  L_XYCHAIN8   '8-node XY-chain20 (  52)  L_HIDDEN221 (  44)  L_UNIQUE1    'UR+1 (type 1)22 (  30)  L_UVWXYZ     'generalized (allows 2-6 candidate pilots)23 (  26)  L_BUG2       '2 rows or columns (all types including advanced)24 (  26)  L_BUG3       '3 rows or columns (all types including advanced)25 (  26)  L_NICE6      '6 strong links/bivalue cells26 (  26)  L_ALS2xz     'xz rule (A=2 cell ALS)27 (  21)  L_XYRING5    '5-node XY-ring28 (  21)  L_NICE3G     '3 grouped strong links/ALS29 (  19)  L_XYCHAIN9   '9-node XY-chain30 (  16)  L_NICE4G     '4 grouped strong links/ALS31 (  15)  L_XYRING6    '6-node XY-ring32 (  14)  L_ALS3xz     'xz rule (A=3 cell ALS)33 (  14)  L_ALS2xy     'xy rule (B=2 cell ALS)34 (  13)  L_UNIQUE7    'UR+3(X,C,N,U,E)/2SL35 (  13)  L_UNIQUE10   'UR+2K(X,D), UR+3K(X,D)36 (  13)  L_ALS1xy     'xy rule (B=1 cell ALS)37 (  12)  L_UNIQUE9    'UR+2k(x,d)38 (  11)  L_UNIQUE6    'UR+2r(x,d)39 (  11)  L_ALS3xy     'xy rule (B=3 cell ALS)40 (  10)  L_JELLYFISH  'includes basic, finned, big fin, and franken41 (  10)  L_XYRING4    '4-node XY-ring42 (  10)  L_UNIQUE3    'UR+2X (types 3/3B)43 (  10)  L_UNIQUE4    'UR+2(X,D,B)/1SL (types 4/4B,...)44 (  10)  L_BUG4       '4 rows or columns (all types including advanced)45 (  10)  L_ALS4xy     'xy rule (B=4 cell ALS)46 (   9)  L_XYRING7    '7-node XY-ring47 (   8)  L_UNIQUE2    'UR+2x (types 2/2B)48 (   7)  L_HIDDEN349 (   6)  L_TUVWXYZ    'generalized (allows 2-7 candidate pilots)50 (   6)  L_UNIQUE12   'UR+4(x,X)/2SL, UR+4(x,X)/1SL51 (   5)  L_XYRING8    '8-node XY-ring52 (   4)  L_STRONG3    'three strong links (basic and grouped)53 (   4)  L_ALS4xz     'xz rule (A=4 cell ALS)54 (   3)  L_UNIQUE8    'UR+4(X,C)/3SL55 (   3)  L_NICE5G     '5 grouped strong links/ALS56 (   2)  L_STRONG2    'two strong links (basic and grouped)57 (   2)  L_UNIQUE11   'UR+2D, UR+3(x,X)/1SL58 (   2)  L_NICE8      '8 strong links/bivalue cells59 (   2)  L_NICE6G     '6 grouped strong links/ALS60 (   1)  L_HIDDEN461 (   1)  L_SQUIRMBAG  'includes basic, finned, big fin, and franken62 (   1)  L_NICE7      '7 strong links/bivalue cells63 (   0)  L_NAKED464 (   0)  L_EMPTY      'empty rectangle65 (   0)  L_STRONG4    'four strong links (basic and grouped)66 (   0)  L_SUEDECOQ   'SueDeCoq67 (   0)  L_UNIQUE5    'UR+2d, UR+3x (types 5/5B,...)68 (   0)  L_BUG5       '5 rows or columns (all types including advanced)69 (   0)  L_NICE2      '2 strong links/bivalue cells70 (   0)  L_NICE9      '9 strong links/bivalue cells71 (   0)  L_ALS5xz     'xz rule (A=5 cell ALS)72 (   0)  L_ALS6xz     'xz rule (A=6 cell ALS)73 (   0)  L_ALS5xy     'xy rule (B=5 cell ALS)74 (   0)  L_ALS6xy     'xy rule (B=6 cell ALS)75 (   0)  L_NICE2G     '2 grouped strong links/ALS`
Mike Barker

Posts: 458
Joined: 22 January 2006

Mike,

If you get a spare moment, may I ask that you test your 10,000 puzzles using the following hierarchy and give me a count/ordering on frequency of use for all techniques. There are so many techniques and I'd like to implement new ones based on this information as a starting point. TIA!!!!!!!!!

Code: Select all
`L_NAKED1      Naked  SingleL_HIDDEN1     Hidden SingleL_NAKED2      Naked  PairL_HIDDEN2     Hidden PairL_NAKED3      Naked  TripleL_HIDDEN3     Hidden TripleL_NAKED4      Naked  QuadL_HIDDEN4     Hidden QuadL_LOCKED1    'include line/box and box/box eliminationsL_XY         'XY-wingL_SWORDFISH  'includes basic, finned, big fin, and frankenL_JELLYFISH  'includes basic, finned, big fin, and frankenL_SQUIRMBAG  'includes basic, finned, big fin, and franken???           XYZ-WingL_UNIQUE1    'UR+1 (type 1)???           Colors???           Multi-Colorsany order you'd prefer for the remaining techniques`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

I am thinking about an ordering of strategies, which does not depend on
taste or matching order.

This is not so trivial, as a strategy like "hidden quad" alone does not normally solve a puzzle on its own.

So we have to look at combinations. If there is a particular set of n
"helper strategies" {S_1, ... S_n}, you can compare two other strategies T and U "modulo" these strategies {S_1, ... S_n}:

If any puzzle which can be solved using {S1, ... S_n, T} can
also be solved by using {S1, ... S_n, U} we will say that
"U is greater than T (modulo {S_1, ... S_n})".

It is obvious that this would allow that:
"U greater than T" as well as "T greater than U", even modulo the same
helper strategies.
This is especially true if e.g. S_1 = "Full Backtracking", so S_1 alone
would solve any puzzle.
At least the ordering is transitive and reflexive.

But for limited helper strategies {S_1, ... S_n} perhaps some definite
results could be achieved.

I suspect that "simple coloring" is greater than "remote pairs" modulo
any set of helper strategies. Independency from the helper strategies
is not so easy to achieve, as some puzzles may need only one last step
to solve, so the "greater" strategie must be able to make the very same
eliminations, and the helper set might be empty!

Even if the dependency on "helper strategies" might seem ugly,
I think this reasoning shows the limits of hierarchies independant
from personal taste.

Would you consider this a legitimate approach?
Do you know more examples of strategies which could be ordered
this way, preferably independent from the helper strategies, or
with a "simple enough" helper set (singles only or such)?
Hat "helper set" would you find most appropriate to mimic human
perception of a good ordering?
algernon

Posts: 25
Joined: 26 June 2006

Algernon, I'm not sure it will be simple to do what you propose. Although there is some hierarchy (nice loops include advanced coloring(?) includes X-cycles includes X-wings) comparison of different types of techniques (X-wings vs XY-wings) may not be as easy. I will have to think about it more, but I wanted to get DAJ his results.

DAJ, here are the results. Since I don't have a multi-color algorithm, I modified my nice loop algorithm to implement a form of advanced colors - nice loops with only strong links. My coloring algorithm is a little dusty, but I believe is correct. One reason I don't use it is that coloring seems to be a subset of many other techniques (my solver only used grouped coloring Type 1 12 times given its location in the hierarchy).

The solving order (I almost feel bad for having one - the inputs on reducing dependence on hierarchy are valid):
L_NAKED1 'naked single
L_HIDDEN1 'hidden single
L_NAKED2 'naked pair
L_HIDDEN2 'hidden pair
L_NAKED3 'naked triple
L_HIDDEN3 'hidden triple
L_LOCKED1 'include line/box and box/box eliminations
L_XWING 'X-wing (basic, finned, big fin, and franken)
L_SWORDFISH 'swordfish (basic, finned, big fin, and franken)
L_JELLYFISH 'jellyfish (basic, finned, big fin, and franken)
L_SQUIRMBAG 'squirmbag (basic, finned, big fin, and franken)
L_XY 'XY-wing
L_XYZ 'generalized XYZ-wing (2-3 candidate pilots)
L_UNIQUE1 'UR+1 (type 1)
L_COLOR1 'coloring type 1 (basic and grouped)
L_COLOR2 'coloring type 2 (basic and grouped)
L_COLOR3 'coloring type 3 (basic and grouped)
L_EMPTY 'empty rectangle
L_BUG1 'basic BUG eliminations (+1, +nx, +nX)
L_UNIQUE2 'UR+2x (types 2/2B)
L_UNIQUE5 'UR+2d, UR+3x (types 5/5B,...)
L_UNIQUE3 'UR+2X (types 3/3B)
L_UNIQUE6 'UR+2r(x,d)
L_UNIQUE9 'UR+2k(x,d)
L_UNIQUE4 'UR+2(X,D,B)/1SL (types 4/4B,...)
L_TURBOT4 '4-node X-cycle (locked candidates)
L_STRONG2 'two strong links (basic and grouped)
L_XYRING4 '4-node XY-ring
L_WXYZ 'generalized WXYZ-wing (2-4 candidate pilots)
L_TURBOT5 'turbot fish (basic, grouped, and backwing)
L_XYCHAIN5 '5-node XY-chain
L_XYRING5 '5-node XY-ring
L_VWXYZ 'generalized VWXYZ-wing (2-5 candidate pilots)
L_TURBOT6 '6-node X-cycle (basic, finned, and grouped)
L_STRONG3 'three strong links (basic and grouped)
L_XYCHAIN6 '6-node XY-chain
L_XYRING6 '6-node XY-ring
L_UVWXYZ 'generalized UVWXYZ-wing (2-6 candidate pilots)
L_SUEDECOQ 'SueDeCoq
L_ALS1xz 'xz rule (set A is a bivalue cell)
L_TURBOT7 'turbot chain (basic, grouped, and backwing)
L_XYCHAIN7 '7-node XY-chain
L_XYRING7 '7-node XY-ring
L_TUVWXYZ 'generalized TUVWXYZ-wing (2-7 candidate pilots)
L_STRONG4 'four strong links (basic and grouped)
L_XYCHAIN8 '8-node XY-chain
L_XYRING8 '8-node XY-ring
L_XYCHAIN9 '9-node XY-chain
L_UNIQUE7 'UR+3(X,C,N,U,E)/2SL
L_UNIQUE8 'UR+4(X,C)/3SL
L_UNIQUE11 'UR+2D, UR+3(x,X)/1SL
L_UNIQUE10 'UR+2K(X,D), UR+3K(X,D)
L_UNIQUE12 'UR+4(x,X)/2SL, UR+4(x,X)/1SL
L_BUGLITE2 '2 line BUG-lite (all types including advanced)
L_BUGLITE3 '3 line BUG-lite (all types including advanced)
L_BUGLITE4 '4 line BUG-lite (all types including advanced)
L_BUGLITE5 '5 line BUG-lite (all types including advanced)
L_ALS2xz 'xz rule (A=2 cell ALS)
L_ALS3xz 'xz rule (A=3 cell ALS)
L_ALS4xz 'xz rule (A=4 cell ALS)
L_ALS5xz 'xz rule (A=5 cell ALS)
L_ALS6xz 'xz rule (A=6 cell ALS)
L_ALS1xy 'xy rule (B=1 cell ALS)
L_ALS2xy 'xy rule (B=2 cell ALS)
L_ALS3xy 'xy rule (B=3 cell ALS)
L_ALS4xy 'xy rule (B=4 cell ALS)
L_ALS5xy 'xy rule (B=5 cell ALS)
L_ALS6xy 'xy rule (B=6 cell ALS)

The results based on frequency of total occurances is:
1) Naked Single (432621)
2) Hidden Single (135222)
3) Naked Pair (9580)
4) Locked Line/Box (7488)
5) Finned X-wing (3615)
6) Hidden Pair (3493)
9) Locked Box/Box (2125)
10) XY-wing (1536)
11) Naked Triple (1126)
12) Nice Loops with 4 Strong Links/Bivalue Cells (640)
13) FrankenFish (581)
14) X-wing (571)
15) Generalized XYZ-wing (548)
16) Finned Swordfish (533)
17) ALS-xz rule with A=1 cell (396)
18) Nice Loops with 5 Strong Links/Bivalue Cells (366)
19) Nice Loops with 3 Strong Links/Bivalue Cells (310)
20) Grouped Advanced Colouring with 4 Links = Grouped Strong Nice Loops (305)
21) UR+1 (Type 1) (277)
22) Generalized WXYZ-wing (250)
23) UR+3(X,C,N,U,E)/2SL (228)
24) Hidden Triple (223)
25) UR+2(X,D,B)/1SL (Type 4,...) (221)
27) Grouped Advanced Colouring with 3 Links = Grouped Strong Nice Loops (199)
28) UR+2r(x,d) (178)
29) UR+2K(X,D),UR+3K(X,D) (174)
30) Generalized VWXYZ-wing (165)
31) 6-node XY-chain (165)
32) UR+4(x,X)/2SL, UR+4(x,X)/1SL (160)
33) UR+2k(x,d) (158)
34) Big Finned Fish (130)
35) 5-node XY-chain (120)
36) Swordfish (118)
37) 7-node XY-chain (77)
38) Nice Loops with 6 Strong Links/Bivalue Cells (74)
39) UR+4(X,C)/3SL (66)
40) ALS-xz rule with A=2 cells (64)
41) Grouped Nice Loops with 4 GSL/ALS (60)
42) Generalized UVWXYZ-wing (59)
43) Grouped Nice Loops with 3 GSL/ALS (59)
44) Three Grouped Strong Links (49)
45) ALS-xy rule with B=1 cell (48)
46) 8-node XY-chain (46)
47) SueDeCoq (46)
48) ALS-xz rule with A=3 cells (37)
49) ALS-xy rule with B=2 cells (36)
50) UR+2X (Type 3) (28)
51) ALS-xy rule with B=3 cells (28)
52) ALS-xy rule with B=4 cells (25)
54) 5-node XY-ring (23)
55) UR+2D,UR+3(x,X)/1SL (22)
56) 9-node XY-chain (21)
57) Nice Loops with 7 Strong Links/Bivalue Cells (20)
58) Finned Jellyfish (15)
59) BUG-Lite with 2 lines (15)
60) 7-node XY-ring (14)
61) 6-node XY-ring (13)
62) UR+2x (Type 2) (13)
63) Grouped Simple Colouring Type 1 (12)
64) 8-node XY-ring (10)
65) Grouped Nice Loops with 5 GSL/ALS (10)
66) BUG (basic) (8)
67) ALS-xz rule with A=4 cells (6)
68) ALS-xy rule with B=5 cells (6)
69) Jellyfish (5)
70) Nice Loops with 8 Strong Links/Bivalue Cells (5)
71) Nice Loops with 9 Strong Links/Bivalue Cells (5)
72) Two Grouped Strong Links (2)
73) Four Grouped Strong Links (2)
74) BUG-Lite with 3 lines (2)
77) 9-node XY-ring (1)
78) UR+2d,UR+3x (Type 5,...) (1)
79) ALS-xz rule with A=5 cells (1)
80) ALS-xy rule with B=6 cells (1)
81) Grouped Nice Loops with 6 GSL/ALS (1)
82) Squirmbag (0)
83) Finned Squirmbag (0)
84) Empty Rectangle (0)
85) Generalized TUVWXYZ-wing (0)
86) BUG-Lite with 4 lines (0)
87) BUG-Lite with 5 lines (0)
91) ALS-xz rule with A=6 cells (0)
92) Nice Loops with 2 Strong Links/Bivalue Cells (0)
93) Grouped Nice Loops with 2 GSL/ALS (0)
94) Grouped Nice Loops with 7 GSL/ALS (0)
95) Simple Colouring Type 1 (0)
96) Simple Colouring Type 2 (0)
97) Simple Colouring Type 3 (0)
98) Grouped Simple Colouring Type 2 (0)
99) Grouped Simple Colouring Type 3 (0)
100) Grouped Advanced Colouring with 2 Links = Grouped Strong Nice Loops (0)

Here's the ordering based on the highest order technique used to complete a puzzle:
Code: Select all
` 1 (4467)  L_HIDDEN1    'hidden single 2 ( 967)  L_NAKED2     'naked pair 3 ( 713)  L_ADVANCED4  'advanced coloring 4-links (basic) 4 ( 656)  L_XWING      'X-wing (basic, finned, big fin, and franken) 5 ( 487)  L_XY         'XY-wing 6 ( 426)  L_LOCKED1    'include line/box and box/box eliminations 7 ( 406)  L_ADVANCED3  'advanced coloring 3-links (basic) 8 ( 397)  L_HIDDEN2    'hidden pair 9 ( 168)  L_NAKED1     'naked single10 ( 167)  L_NICE4      '4 strong links/bivalue cells11 ( 105)  L_NAKED3     'naked triple12 (  94)  L_NICE5      '5 strong links/bivalue cells13 (  88)  L_ALS1xz     'xz rule (set A is a bivalue cell)14 (  87)  L_UNIQUE1    'UR+1 (type 1)15 (  65)  L_XYZ        'generalized XYZ-wing (2-3 candidate pilots)16 (  58)  L_SWORDFISH  'swordfish (basic, finned, big fin, and franken)17 (  54)  L_NICE3      '3 strong links/bivalue cells18 (  47)  L_XYCHAIN6   '6-node XY-chain19 (  46)  L_WXYZ       'generalized WXYZ-wing (2-4 candidate pilots)20 (  38)  L_ADVANCED4G 'advanced coloring 4-links (grouped)21 (  29)  L_XYCHAIN7   '7-node XY-chain22 (  29)  L_NICE4G     '4 grouped strong links/ALS23 (  27)  L_UNIQUE6    'UR+2r(x,d)24 (  26)  L_XYCHAIN5   '5-node XY-chain25 (  25)  L_VWXYZ      'generalized VWXYZ-wing (2-5 candidate pilots)26 (  25)  L_NICE6      '6 strong links/bivalue cells27 (  20)  L_ALS2xz     'xz rule (A=2 cell ALS)28 (  17)  L_ADVANCED3G 'advanced coloring 3-links (grouped)29 (  16)  L_ALS1xy     'xy rule (B=1 cell ALS)30 (  15)  L_HIDDEN3    'hidden triple31 (  15)  L_NICE3G     '3 grouped strong links/ALS32 (  13)  L_SUEDECOQ   'SueDeCoq33 (  13)  L_UNIQUE7    'UR+3(X,C,N,U,E)/2SL34 (  12)  L_UNIQUE3    'UR+2X (types 3/3B)35 (  12)  L_UNIQUE9    'UR+2k(x,d)36 (  12)  L_XYRING4    '4-node XY-ring37 (  12)  L_UVWXYZ     'generalized UVWXYZ-wing (2-6 candidate pilots)38 (  11)  L_BUGLITE2   '2 line BUG-lite (all types including advanced)39 (  10)  L_ALS2xy     'xy rule (B=2 cell ALS)40 (   9)  L_UNIQUE4    'UR+2(X,D,B)/1SL (types 4/4B,...)41 (   9)  L_BUGLITE3   '3 line BUG-lite (all types including advanced)42 (   9)  L_ALS3xy     'xy rule (B=3 cell ALS)43 (   8)  L_XYCHAIN8   '8-node XY-chain44 (   8)  L_UNIQUE10   'UR+2K(X,D), UR+3K(X,D)45 (   8)  L_ALS3xz     'xz rule (A=3 cell ALS)46 (   8)  L_ALS4xy     'xy rule (B=4 cell ALS)47 (   7)  L_UNIQUE2    'UR+2x (types 2/2B)48 (   6)  L_NICE5G     '5 grouped strong links/ALS49 (   5)  L_BUG1       'basic BUG eliminations (+1, +nx, +nX)50 (   5)  L_STRONG3    'three strong links (basic and grouped)51 (   5)  L_XYRING6    '6-node XY-ring52 (   5)  L_XYCHAIN9   '9-node XY-chain53 (   4)  L_JELLYFISH  'jellyfish (basic, finned, big fin, and franken)54 (   4)  L_XYRING5    '5-node XY-ring55 (   4)  L_XYRING7    '7-node XY-ring56 (   4)  L_UNIQUE12   'UR+4(x,X)/2SL, UR+4(x,X)/1SL57 (   4)  L_NICE7      '7 strong links/bivalue cells58 (   3)  L_UNIQUE11   'UR+2D, UR+3(x,X)/1SL59 (   2)  L_COLOR1     'coloring type 1 (basic and grouped)60 (   2)  L_NICE8      '8 strong links/bivalue cells61 (   1)  L_NAKED4     'naked quadruple62 (   1)  L_SQUIRMBAG  'squirmbag (basic, finned, big fin, and franken)63 (   1)  L_UNIQUE8    'UR+4(X,C)/3SL64 (   1)  L_ALS4xz     'xz rule (A=4 cell ALS)65 (   1)  L_ALS5xy     'xy rule (B=5 cell ALS)66 (   1)  L_NICE6G     '6 grouped strong links/ALS67 (   0)  L_HIDDEN4    'hidden quadruple68 (   0)  L_COLOR2     'coloring type 2 (basic and grouped)69 (   0)  L_COLOR3     'coloring type 3 (basic and grouped)70 (   0)  L_ADVANCED2  'advanced coloring 2-links (basic)71 (   0)  L_EMPTY      'empty rectangle72 (   0)  L_UNIQUE5    'UR+2d, UR+3x (types 5/5B,...)73 (   0)  L_BUG2       'strong link BUG eliminations74 (   0)  L_BUG3       'advanced BUG eliminations75 (   0)  L_TURBOT4    '4-node X-cycle (locked candidates)76 (   0)  L_STRONG2    'two strong links (basic and grouped)77 (   0)  L_ADVANCED2G 'advanced coloring 2-links (grouped)78 (   0)  L_TURBOT5    'turbot fish (basic, grouped, and backwing)79 (   0)  L_TURBOT6    '6-node X-cycle (basic, finned, and grouped)80 (   0)  L_TURBOT7    'turbot chain (basic, grouped, and backwing)81 (   0)  L_TUVWXYZ    'generalized TUVWXYZ-wing (2-7 candidate pilots)82 (   0)  L_STRONG4    'four strong links (basic and grouped)83 (   0)  L_XYRING8    '8-node XY-ring84 (   0)  L_BUGLITE4   '4 line BUG-lite (all types including advanced)85 (   0)  L_BUGLITE5   '5 line BUG-lite (all types including advanced)86 (   0)  L_NICE2      '2 strong links/bivalue cells87 (   0)  L_NICE9      '9 strong links/bivalue cells88 (   0)  L_ALS5xz     'xz rule (A=5 cell ALS)89 (   0)  L_ALS6xz     'xz rule (A=6 cell ALS)90 (   0)  L_ALS6xy     'xy rule (B=6 cell ALS)91 (   0)  L_NICE2G     '2 grouped strong links/ALS`
Mike Barker

Posts: 458
Joined: 22 January 2006

Wow Mike !!!!!!!!!!

Your results are way more than I'd hoped to get!!!

Thank You Very Much!!!!!!!

daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

There have been several changes since the last time I updated my method hierarchy results. Mutant fish, endo fins, Obi-Wahn's improvement to broken wings, RW convinced me that uniqueness and BUG tests should be relatively early in the solving order, BUG eliminations, and overlapping ALS and nice loops. I've added Kraken techniques which occur last in my solver. Note that with these added my solver solves approximately 9998 out of 10000 randomly generated puzzles (prior it was closer to 9940-9960). Of course there are other ways to achieve this result including using larger ALS and "nice networks", but this is the one I chose (of course I'm biased). Although 99.98% seems like a pretty big number, there are still .133*10^19 puzzles that my solver can't solve which means there is still lots of room for improvement!

Here is the order of solving techniques I used. The biggest difference (besides addition of new techniques) was moving shorter nice loops and advanced coloring earlier. This made sense because of their effectiveness. Similarly locked candidates were also moved up. This reflects the way I solve puzzles in which locked candidates are often easy to identify without knowing pencil marks. ALS have been moved later given the concensus that finding ALS is tough. As before techniques are broken down by the size of the chains and/or the size of the ALS involved with the idea that shorter or smaller is better.
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` 0    L_NAKED1     'naked single 1    L_HIDDEN1    'hidden single 2    L_LOCKED1    'include line/box and box/box eliminations 3    L_NAKED2     'naked pair 4    L_NAKED3     'naked triple 5    L_HIDDEN2    'hidden pair 6    L_HIDDEN3    'hidden triple 7    L_NAKED4     'naked quadruple 8    L_HIDDEN4    'hidden quadruple 9    L_XWING      'X-wing (basic and finned)10    L_FRANK2     'Franken X-wing11    L_XY         'XY-wing12    L_XYZ        'generalized XYZ-wing (2-3 candidate pilots)13    L_EMPTY      'empty rectangle14    L_BUG1       'BUG+1 eliminations15    L_UNIQUE1    'UR+1 (type 1)16    L_UNIQUE2    'UR+2x (types 2/2B)17    L_UNIQUE5    'UR+2d, UR+3x (types 5/5B,...)18    L_UNIQUE3    'UR+2X (types 3/3B)19    L_UNIQUE4    'UR+2(X,D,B)/1SL (types 4/4B,...)20    L_UNIQUE6    'UR+2r(x,d)21    L_UNIQUE9    'UR+2k(x,d)22    L_BUG2       'BUG+n(x,X) eliminations23    L_BUG3       'strong link BUG eliminations24    L_BUGLITE2   'basic 2-line BUG-lite25    L_BUGLITE3   'basic 3-line BUG-lite26    L_STRONG2    'two strong links (basic and grouped)27    L_MUTANT2    'finless & finned mutant x-wing28    L_SWORDFISH  'swordfish (basic and finned)29    L_FRANK3     'Franken Swordfish30    L_XYRING4    '4-node XY-ring31    L_WXYZ       'generalized WXYZ-wing (2-4 candidate pilots)32    L_ADVANCED2  '2-link advanced coloring33    L_NICE2      '2-element nice loop (strong links/bivalue cells)34    L_XYCHAIN5   '5-node XY-chain35    L_XYRING5    '5-node XY-ring36    L_VWXYZ      'generalized VWXYZ-wing (2-5 candidate pilots)37    L_STRONG3    'three strong links (basic and grouped)38    L_MUTANT3    'finless & finned mutant swordfish39    L_JELLYFISH  'jellyfish (basic and finned)40    L_FRANK4     'Franken Jellyfish41    L_XYCHAIN6   '6-node XY-chain42    L_XYRING6    '6-node XY-ring43    L_UVWXYZ     'generalized UVWXYZ-wing (2-6 candidate pilots)44    L_ADVANCED3  '3-link advanced coloring45    L_NICE3      '3-element nice loop (strong links/bivalue cells)47    L_ALS1xz     'A=1 cell ALS xz-rule46    L_SUEDECOQ   'SueDeCoq48    L_UNIQUE7    'UR+3(X,C,N,U,E)/2SL49    L_XYCHAIN7   '7-node XY-chain50    L_XYRING7    '7-node XY-ring51    L_TUVWXYZ    'generalized TUVWXYZ-wing (2-7 candidate pilots)52    L_STRONG4    'four strong links (basic and grouped)53    L_MUTANT4    'finless & finned mutant jellyfish54    L_SQUIRMBAG  'squirmbag (basic and finned)55    L_FRANK5     'Franken Squirmbag56    L_XYCHAIN8   '8-node XY-chain57    L_XYRING8    '8-node XY-ring58    L_ADVANCED4  '4-link advanced coloring59    L_NICE4      '4-element nice loop (strong links/bivalue cells)60    L_TURBOT4    '4-node X-cycle (locked candidates)61    L_XYCHAIN9   '9-node XY-chain62    L_XYRING9    '9-node XY-ring63    L_MUTANT5    'finless & finned mutant squirmbag64    L_XYCHAIN10  '10-node XY-chain65    L_XYRING10   '10-node XY-ring66    L_ADVANCED5  '5-link advanced coloring67    L_NICE5      '5-element nice loop (strong links/bivalue cells)68    L_TURBOT5    'turbot fish (basic, grouped, and backwing)69    L_XYCHAIN11  '11-node XY-chain70    L_COLOR1     'coloring type 1 (basic and grouped)71    L_COLOR2     'coloring type 2 (basic and grouped)72    L_COLOR3     'coloring type 3 (basic and grouped)73    L_MUTANT6    'finless & finned mutant whale74    L_ADVANCED6  '6-link advanced coloring75    L_NICE6      '6-element nice loop (strong links/bivalue cells)76    L_TURBOT6    '6-node X-cycle (basic, finned, and grouped)77    L_ADVANCED7  '7-link advanced coloring78    L_TURBOT7    'turbot chain (basic, grouped, and backwing)79    L_NICE7      '7-element nice loop (strong links/bivalue cells)80    L_NICE8      '8-element nice loop (strong links/bivalue cells)81    L_NICE9      '9-element nice loop (strong links/bivalue cells)82    L_UNIQUE8    'UR+4(X,C)/3SL83    L_UNIQUE11   'UR+2D, UR+3(x,X)/1SL84    L_UNIQUE10   'UR+2K(X,D), UR+3K(X,D)85    L_UNIQUE12   'UR+4(x,X)/2SL, UR+4(x,X)/1SL86    L_BUGLITE4   'basic 4-line BUG-lite87    L_BUGLITE2A  'advanced 2-line BUG-lite88    L_BUGLITE3A  'advanced 3-line BUG-lite89    L_BUGLITE4A  'advanced 4-line BUG-lite90    L_BUG4       'advanced BUG eliminations91    L_BUGLITE5   'basic 5-line BUG-lite92    L_BUGLITE5A  'advanced 5-line BUG-lite93    L_ALS1xy     'B=1 cell ALS xy-rule94    L_ALS2xz     'A=2 cell ALS xz-rule95    L_ALS2xy     'B=2 cell ALS xy-rule96    L_ALS3xz     'A=3 cell ALS xz-rule97    L_ALS3xy     'B=3 cell ALS xy-rule98    L_ALS4xz     'A=4 cell ALS xz-rule99    L_ALS4xy     'B=4 cell ALS xy-rule100    L_ALS5xz     'A=5 cell ALS xz-rule101    L_ALS5xy     'B=5 cell ALS xy-rule102    L_ALS6xz     'A=6 cell ALS xz-rule103    L_ALS6xy     'B=6 cell ALS xy-rule104    L_ADVANCED2G '2-link grouped advanced coloring105    L_NICE2G     '2-element grouped nice loop (GSL/ALS)106    L_ADVANCED3G '3-link grouped advanced coloring107    L_NICE3G     '3-element grouped nice loop (GSL/ALS)108    L_ADVANCED4G '4-link grouped advanced coloring109    L_NICE4G     '4-element grouped nice loop (GSL/ALS)110    L_ADVANCED5G '5-link grouped advanced coloring111    L_NICE5G     '5-element grouped nice loop (GSL/ALS)112    L_ADVANCED6G '6-link grouped advanced coloring113    L_NICE6G     '6-element grouped nice loop (GSL/ALS)114    L_ADVANCED7G '7-link grouped advanced coloring115    L_NICE7G     '7-element grouped nice loop (GSL/ALS)116    L_SUMCELL2   'bivalued/1-link kraken blossom117    L_SUMUNIT2   'bivalued/1-link kraken unit118    L_SUMCELL3   '3-valued/1-link kraken blossom119    L_SUMUNIT3   '3-valued/1-link kraken unit120    L_SUMCELL4   '4-valued/1-link kraken blossom121    L_SUMUNIT4   '4-valued/1-link kraken unit122    L_SUMCELL5   '5-valued/1-link kraken blossom123    L_SUMUNIT5   '5-valued/1-link kraken unit124    L_SUM2CELL2  'bivalued/2-link kraken blossom125    L_SUM2UNIT2  'bivalued/2-link kraken unit126    L_SUM2CELL3  '3-valued/2-link kraken blossom127    L_SUM2UNIT3  '3-valued/2-link kraken unit128    L_SUM2CELL4  '4-valued/2-link kraken blossom129    L_SUM2UNIT4  '4-valued/2-link kraken unit130    L_SUM2CELL5  '5-valued/2-link kraken blossom131    L_SUM2UNIT5  '5-valued/2-link kraken unit132    L_SUMALS     '1-link kraken ALS133    L_SUM2ALS    '2-link kraken ALS134    L_SUMXWING   '1-link kraken X-wing135    L_SUMSWORD   '1-link kraken swordfish136    L_SUMJELLY   '1-link kraken jellyfish137    L_SUMSQUIRM  '1-link kraken squirmbag138    L_SUM2XWING  '2-link kraken x-wing139    L_SUM2SWORD  '2-link kraken swordfish140    L_SUM2JELLY  '2-link kraken jellyfish141    L_SUM2SQUIRM '2-link kraken squirmbag142    L_SUMURB     'bivalued/1-link kraken UR143    L_SUMUR      '1-link kraken UR144    L_SUM2UR     '2-link kraken UR145    L_SUMBUG2    '2-line/1-link kraken BUG-lite146    L_SUMBUG3    '3-line/1-link kraken BUG-lite147    L_SUM2BUG2   '2-line/2-link kraken BUG-lite148    L_SUM2BUG3   '3-line/2-link kraken BUG-lite149    L_SUMAALS2   '2-cell/1-link kraken Almost ALS150    L_SUMAALS3   '3-cell/1-link kraken Almost ALS151    L_SUM2AALS2  '2-cell/2-link kraken Almost ALS152    L_SUM2AALS3  '3-cell/2-link kraken Almost ALS153    L_MUTANT21   '1-link kraken mutant x-wing154    L_MUTANT31   '1-link kraken mutant swordfish155    L_MUTANT41   '1-link kraken mutant jellyfish156    L_MUTANT51   '1-link kraken mutant squirmbag157    L_MUTANT22   '2-link kraken mutant x-wing158    L_MUTANT32   '2-link kraken mutant swordfish159    L_MUTANT42   '2-link kraken mutant jellyfish160    L_MUTANT52   '2-link kraken mutant squirmbag`

The following summarizes the total number of times a technique is used for all successfully solved puzzles. A notable difference from previous results is the higher frequency of occurence of UR+2/1SL techniques which resulted from moving them before UR+2k and UR+2r eliminations which makes sense from a complexity viewpoint. Note that, just as before, even though there are many occurences of URs they "crack" a dispropotionately small number of puzzles (except for UR+1). Most Kraken techniques are not even used which is not surprising since they are a method of last resort in my solver. Kraken Blossom and Kraken Unit are actually quite common.
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`1) Naked Single (436922)2) Hidden Single (134411)3) Locked Line/Box (17810)4) Locked Box/Box (4370)5) Finned X-wing (3682)6) Naked Pair (3488)7) Naked Triple (1986)8) UR+2(X,D,B)/1SL (Type 4,...) (1692)9) XY-wing (1676)10) Nice Loops with 3 Strong Links/Bivalue Cells (1481)11) Advanced Colouring with 3 Links (992)12) 5-node XY-chain (985)13) Generalized WXYZ-wing (904)14) Nice Loops with 4 Strong Links/Bivalue Cells (862)15) Hidden Pair (796)16) Advanced Colouring with 4 Links (789)17) 6-node XY-chain (786)18) Generalized XYZ-wing (670)19) X-wing (602)20) Empty Rectangle (594)21) Generalized VWXYZ-wing (412)22) UR+3(X,C,N,U,E)/2SL (382)23) A=1 cell ALS-xz rule (352)24) Nice Loops with 5 Strong Links/Bivalue Cells (347)25) UR+1 (Type 1) (303)26) Finned Swordfish (282)27) B=1 cell ALS-xy rule (235)28) Advanced Colouring with 5 Links (199)29) 7-node XY-chain (181)30) Hidden Triple (175)31) BUG+1 (169)32) Grouped Nice Loops with 3 GSL/ALS (141)33) Generalized UVWXYZ-wing (136)34) 5-node XY-ring (107)35) X-cycle with 3 Grouped Strong Links (106)36) UR+2X (Type 3) (102)37) 4-node XY-ring (100)38) Grouped Nice Loops with 4 GSL/ALS (99)39) 8-node XY-chain (93)40) Swordfish (91)41) X-cycle with 2 Grouped Strong Links (91)42) Nice Loops with 6 Strong Links/Bivalue Cells (91)43) B=2 cell ALS-xy rule (78)44) UR+2k(x,d) (74)45) UR+4(x,X)/2SL, UR+4(x,X)/1SL (73)46) X-cycle with 3 Strong Links (71)47) UR+2K(X,D),UR+3K(X,D) (69)48) 6-node XY-ring (62)49) Basic BUG-Lite with 2 lines (62)50) UR+2x (Type 2) (58)51) Mutant Swordfish (56)52) SueDeCoq (51)53) B=3 cell ALS-xy rule (50)54) A=2 cell ALS-xz rule (42)55) Mutant Jellyfish (41)56) Basic BUG-Lite with 3 lines (41)57) X-cycle with 2 Strong Links (40)58) Advanced BUG-Lite with 2 lines (39)59) Franken JellyFish (36)60) A=3 cell ALS-xz rule (36)61) B=4 cell ALS-xy rule (36)62) UR+4(X,C)/3SL (33)63) Advanced Colouring with 6 Links (33)64) Franken SwordFish (29)65) BUG+n(x,X) (26)66) Nice Loops with 7 Strong Links/Bivalue Cells (26)67) UR+2r(x,d) (24)68) Grouped Nice Loops with 5 GSL/ALS (21)69) B=5 cell ALS-xy rule (19)70) Naked Quadruple (17)71) Advanced BUG-Lite with 3 lines (17)72) 3-valued/2-link Kraken Blossom (17)73) 7-node XY-ring (16)74) Strong Link BUG Eliminations (16)75) 4-valued/2-link Kraken Blossom (14)76) Bivalued/2-link Kraken Unit (14)77) 5-valued/2-link Kraken Blossom (11)78) 3-valued/2-link Kraken Unit (11)79) Bivalued/2-link Kraken Blossom (10)80) A=4 cell ALS-xz rule (9)81) B=6 cell ALS-xy rule (8)82) X-cycle with 4 Grouped Strong Links (7)83) 9-node XY-chain (7)84) UR+2D,UR+3(x,X)/1SL (7)85) 5-valued/1-link Kraken Blossom (7)86) 4-valued/2-link Kraken Unit (7)87) Mutant Squirmbag (5)88) 4-valued/1-link Kraken Blossom (5)89) Finned Jellyfish (3)90) Franken Squirmbag (3)91) 8-node XY-ring (3)92) Grouped Advanced Colouring with 4 Links (3)93) Nice Loops with 8 Strong Links/Bivalue Cells (3)94) Nice Loops with 9 Strong Links/Bivalue Cells (3)95) 3-valued/1-link Kraken Blossom (3)96) 5-valued/2-link Kraken Unit (3)97) 2-link Kraken ALS (3)98) 10-node XY-chain (2)99) Advanced BUG-Lite with 4 lines (2)100) Advanced Colouring with 7 Links (2)101) Grouped Nice Loops with 2 GSL/ALS (2)102) Grouped Nice Loops with 6 GSL/ALS (2)103) Jellyfish (1)104) Broken Wing (1)105) 11-node XY-chain (1)106) UR+2d,UR+3x (Type 5,...) (1)107) Grouped Advanced Colouring with 3 Links (1)108) A=5 cell ALS-xz rule (1)109) 3-valued/1-link Kraken Unit (1)110) 4-valued/1-link Kraken Unit (1)111) 5-valued/1-link Kraken Unit (1)112) 2-link Kraken X-wing (1)113) Hidden Quadruple (0)114) Squirmbag (0)115) Finned Squirmbag (0)116) Franken X-wing (0)117) Mutant X-wing (0)118) Mutant Whale (0)119) 4-node X-cycle = X-wing (0)120) Turbot Fish (0)121) 6-node X-cycle (0)122) 7-node Turbot Chain (0)123) Grouped 4-node X-cycle = Locked box/box (0)124) Grouped Turbot Fish (0)125) Grouped 6-node X-cycle (0)126) Grouped 7-node Turbot Chain (0)127) 7-node Broken Wing (0)128) Grouped Broken Wing (0)129) Grouped 7-node Broken Wing (0)130) X-cycle with 4 Strong Links (0)131) Grouped Empty Rectangle (0)132) Generalized TUVWXYZ-wing (0)133) 9-node XY-ring (0)134) 10-node XY-ring (0)135) Basic BUG-Lite with 4 lines (0)136) Basic BUG-Lite with 5 lines (0)137) Advanced BUG-Lite with 5 lines (0)138) Advanced BUG Eliminations (0)139) Simple Colouring Type 1 (0)140) Simple Colouring Type 2 (0)141) Simple Colouring Type 3 (0)142) Grouped Simple Colouring Type 1 (0)143) Grouped Simple Colouring Type 2 (0)144) Grouped Simple Colouring Type 3 (0)145) Advanced Colouring with 2 Links (0)146) Grouped Advanced Colouring with 2 Links (0)147) Grouped Advanced Colouring with 5 Links (0)148) Grouped Advanced Colouring with 6 Links (0)149) Grouped Advanced Colouring with 7 Links (0)150) Nice Loops with 2 Strong Links/Bivalue Cells (0)151) Grouped Nice Loops with 7 GSL/ALS (0)152) A=6 cell ALS-xz rule (0)153) Bivalued/1-link Kraken Blossom (0)154) Bivalued/1-link Kraken Unit (0)155) 1-link Kraken ALS (0)156) 2-cell/1-link Kraken Almost ALS (0)157) 3-cell/1-link Kraken Almost ALS (0)158) 2-cell/2-link Kraken Almost ALS (0)159) 3-cell/2-link Kraken Almost ALS (0)160) Bivalued/1-link Kraken UR (0)161) 1-link Kraken UR (0)162) 2-link Kraken UR (0)163) 2-line/1-link Kraken BUG-Lite (0)164) 3-line/1-link Kraken BUG-Lite (0)165) 2-line/2-link Kraken BUG-Lite (0)166) 3-line/2-link Kraken BUG-Lite (0)167) 1-link Kraken X-wing (0)168) 1-link Kraken Swordfish (0)169) 1-link Kraken Jellyfish (0)170) 1-link Kraken Squirmbag (0)171) 2-link Kraken Swordfish (0)172) 2-link Kraken Jellyfish (0)173) 2-link Kraken Squirmbag (0)174) 1-link Mutant X-wing (0)175) 1-link Mutant Swordfish (0)176) 1-link Mutant Jellyfish (0)177) 1-link Mutant Squirmbag (0)178) 2-link Mutant X-wing (0)179) 2-link Mutant Swordfish (0)180) 2-link Mutant Jellyfish (0)181) 2-link Mutant Squirmbag (0)`

This is probably the more interesting result which shows how many times out of 10000 runs a specific technique was the highest order techniques used to solve a puzzle. Based on previous results these results are not too surprising with basic/intermediate techniques followed by short XY chains, advanced coloring and nice loops. Again UR+1 (Type 1) and BUG+1 are the most useful forms of these techniques. mYZ-wings, for example WXYZ wings, (which in my solver are limited to a bivalue cell and an ALS limited to a box) are also fairly high up. As before, moving nice loops higher in the solving order would eliminate occurences of many of the techniques in this list, but I think I'd prefer looking for an X-wing before a nice loop.
Code: Select all
` 1 (4471)  L_HIDDEN1    'hidden single 2 (1257)  L_LOCKED1    'includes line/box and box/box eliminations 3 ( 663)  L_XWING      'X-wing (basic and finned) 4 ( 431)  L_XY         'XY-wing 5 ( 366)  L_NAKED2     'naked pair 6 ( 255)  L_XYCHAIN5   '5-node XY-chain 7 ( 208)  L_XYCHAIN6   '6-node XY-chain 8 ( 202)  L_NICE3      '3-element nice loop (strong links/bivalue cells) 9 ( 184)  L_NAKED3     'naked triple10 ( 174)  L_ADVANCED4  '4-link advanced coloring11 ( 163)  L_NICE4      '4-element nice loop (strong links/bivalue cells)12 ( 159)  L_WXYZ       'generalized WXYZ-wing (2-4 candidate pilots)13 ( 150)  L_ADVANCED3  '3-link advanced coloring14 ( 110)  L_NAKED1     'naked single15 ( 105)  L_UNIQUE1    'UR+1 (type 1)16 (  74)  L_XYZ        'generalized XYZ-wing (2-3 candidate pilots)17 (  69)  L_NICE5      '5-element nice loop (strong links/bivalue cells)18 (  61)  L_VWXYZ      'generalized VWXYZ-wing (2-5 candidate pilots)19 (  61)  L_XYCHAIN7   '7-node XY-chain20 (  57)  L_BUG1       'BUG+1 eliminations21 (  57)  L_UNIQUE4    'UR+2(X,D,B)/1SL (types 4/4B,...)22 (  50)  L_HIDDEN2    'hidden pair23 (  49)  L_ADVANCED5  '5-link advanced coloring24 (  48)  L_ALS1xz     'A=1 cell ALS xz-rule25 (  43)  L_ALS1xy     'B=1 cell ALS xy-rule26 (  36)  L_SWORDFISH  'swordfish (basic and finned)27 (  33)  L_EMPTY      'empty rectangle28 (  31)  L_XYCHAIN8   '8-node XY-chain29 (  29)  L_NICE3G     '3-element grouped nice loop (GSL/ALS)30 (  21)  L_NICE6      '6-element nice loop (strong links/bivalue cells)31 (  20)  L_STRONG2    'two strong links (basic and grouped)32 (  19)  L_UNIQUE3    'UR+2X (types 3/3B)33 (  19)  L_UVWXYZ     'generalized UVWXYZ-wing (2-6 candidate pilots)34 (  18)  L_XYRING5    '5-node XY-ring35 (  17)  L_ALS2xy     'B=2 cell ALS xy-rule36 (  17)  L_NICE4G     '4-element grouped nice loop (GSL/ALS)37 (  16)  L_UNIQUE2    'UR+2x (types 2/2B)38 (  16)  L_BUGLITE3   'basic 3-line BUG-lite39 (  16)  L_XYRING6    '6-node XY-ring40 (  15)  L_STRONG3    'three strong links (basic and grouped)41 (  14)  L_ALS3xy     'B=3 cell ALS xy-rule42 (  12)  L_BUGLITE2   'basic 2-line BUG-lite43 (  12)  L_ALS2xz     'A=2 cell ALS xz-rule44 (  12)  L_ALS3xz     'A=3 cell ALS xz-rule45 (  11)  L_ALS4xy     'B=4 cell ALS xy-rule46 (  10)  L_SUM2UNIT2  'bivalued/2-link kraken unit47 (   9)  L_BUG2       'BUG+n(x,X) eliminations48 (   9)  L_XYRING4    '4-node XY-ring49 (   9)  L_UNIQUE7    'UR+3(X,C,N,U,E)/2SL50 (   9)  L_ADVANCED6  '6-link advanced coloring51 (   8)  L_SUEDECOQ   'SueDeCoq52 (   7)  L_HIDDEN3    'hidden triple53 (   6)  L_NICE5G     '5-element grouped nice loop (GSL/ALS)54 (   6)  L_SUM2CELL4  '4-valued/2-link kraken blossom55 (   5)  L_BUG3       'strong link BUG eliminations56 (   5)  L_FRANK3     'Franken Swordfish57 (   5)  L_XYRING7    '7-node XY-ring58 (   5)  L_SUM2CELL5  '5-valued/2-link kraken blossom59 (   4)  L_XYCHAIN9   '9-node XY-chain60 (   4)  L_BUGLITE3A  'advanced 3-line BUG-lite61 (   4)  L_SUM2UNIT3  '3-valued/2-link kraken unit62 (   3)  L_UNIQUE9    'UR+2k(x,d)63 (   3)  L_SUMCELL5   '5-valued/1-link kraken blossom64 (   2)  L_NAKED4     'naked quadruple65 (   2)  L_MUTANT3    'finless & finned mutant swordfish66 (   2)  L_MUTANT4    'finless & finned mutant jellyfish67 (   2)  L_UNIQUE10   'UR+2K(X,D), UR+3K(X,D)68 (   2)  L_BUGLITE2A  'advanced 2-line BUG-lite69 (   2)  L_ALS4xz     'A=4 cell ALS xz-rule70 (   2)  L_SUMCELL3   '3-valued/1-link kraken blossom71 (   2)  L_SUMCELL4   '4-valued/1-link kraken blossom72 (   2)  L_SUM2CELL2  'bivalued/2-link kraken blossom73 (   2)  L_SUM2UNIT4  '4-valued/2-link kraken unit74 (   2)  L_SUM2UNIT5  '5-valued/2-link kraken unit75 (   2)  L_SUM2ALS    '2-link kraken ALS76 (   1)  L_FRANK4     'Franken Jellyfish77 (   1)  L_STRONG4    'four strong links (basic and grouped)78 (   1)  L_XYRING8    '8-node XY-ring79 (   1)  L_ADVANCED7  '7-link advanced coloring80 (   1)  L_NICE7      '7-element nice loop (strong links/bivalue cells)81 (   1)  L_UNIQUE11   'UR+2D, UR+3(x,X)/1SL82 (   1)  L_NICE2G     '2-element grouped nice loop (GSL/ALS)83 (   1)  L_NICE6G     '6-element grouped nice loop (GSL/ALS)84 (   1)  L_SUMUNIT3   '3-valued/1-link kraken unit85 (   1)  L_SUMUNIT4   '4-valued/1-link kraken unit86 (   1)  L_SUM2CELL3  '3-valued/2-link kraken blossom87 (   1)  L_SUM2XWING  '2-link kraken x-wing88 (   0)  L_HIDDEN4    'hidden quadruple89 (   0)  L_FRANK2     'Franken X-wing90 (   0)  L_UNIQUE5    'UR+2d, UR+3x (types 5/5B,...)91 (   0)  L_UNIQUE6    'UR+2r(x,d)92 (   0)  L_MUTANT2    'finless & finned mutant x-wing93 (   0)  L_ADVANCED2  '2-link advanced coloring94 (   0)  L_NICE2      '2-element nice loop (strong links/bivalue cells)95 (   0)  L_JELLYFISH  'jellyfish (basic and finned)96 (   0)  L_TUVWXYZ    'generalized TUVWXYZ-wing (2-7 candidate pilots)97 (   0)  L_SQUIRMBAG  'squirmbag (basic and finned)98 (   0)  L_FRANK5     'Franken Squirmbag99 (   0)  L_TURBOT4    '4-node X-cycle (locked candidates)100 (   0)  L_XYRING9    '9-node XY-ring101 (   0)  L_MUTANT5    'finless & finned mutant squirmbag102 (   0)  L_XYCHAIN10  '10-node XY-chain103 (   0)  L_XYRING10   '10-node XY-ring104 (   0)  L_TURBOT5    'turbot fish (basic, grouped, and backwing)105 (   0)  L_XYCHAIN11  '11-node XY-chain106 (   0)  L_COLOR1     'coloring type 1 (basic and grouped)107 (   0)  L_COLOR2     'coloring type 2 (basic and grouped)108 (   0)  L_COLOR3     'coloring type 3 (basic and grouped)109 (   0)  L_MUTANT6    'finless & finned mutant whale110 (   0)  L_TURBOT6    '6-node X-cycle (basic, finned, and grouped)111 (   0)  L_TURBOT7    'turbot chain (basic, grouped, and backwing)112 (   0)  L_NICE8      '8-element nice loop (strong links/bivalue cells)113 (   0)  L_NICE9      '9-element nice loop (strong links/bivalue cells)114 (   0)  L_UNIQUE8    'UR+4(X,C)/3SL115 (   0)  L_UNIQUE12   'UR+4(x,X)/2SL, UR+4(x,X)/1SL116 (   0)  L_BUGLITE4   'basic 4-line BUG-lite117 (   0)  L_BUGLITE4A  'advanced 4-line BUG-lite118 (   0)  L_BUG4       'advanced BUG eliminations119 (   0)  L_BUGLITE5   'basic 5-line BUG-lite120 (   0)  L_BUGLITE5A  'advanced 5-line BUG-lite121 (   0)  L_ALS5xz     'A=5 cell ALS xz-rule122 (   0)  L_ALS5xy     'B=5 cell ALS xy-rule123 (   0)  L_ALS6xz     'A=6 cell ALS xz-rule124 (   0)  L_ALS6xy     'B=6 cell ALS xy-rule125 (   0)  L_ADVANCED2G '2-link grouped advanced coloring126 (   0)  L_ADVANCED3G '3-link grouped advanced coloring127 (   0)  L_ADVANCED4G '4-link grouped advanced coloring128 (   0)  L_ADVANCED5G '5-link grouped advanced coloring129 (   0)  L_ADVANCED6G '6-link grouped advanced coloring130 (   0)  L_ADVANCED7G '7-link grouped advanced coloring131 (   0)  L_NICE7G     '7-element grouped nice loop (GSL/ALS)132 (   0)  L_SUMCELL2   'bivalued/1-link kraken blossom133 (   0)  L_SUMUNIT2   'bivalued/1-link kraken unit134 (   0)  L_SUMUNIT5   '5-valued/1-link kraken unit135 (   0)  L_SUMALS     '1-link kraken ALS136 (   0)  L_SUMXWING   '1-link kraken X-wing137 (   0)  L_SUMSWORD   '1-link kraken swordfish138 (   0)  L_SUMJELLY   '1-link kraken jellyfish139 (   0)  L_SUMSQUIRM  '1-link kraken squirmbag140 (   0)  L_SUM2SWORD  '2-link kraken swordfish141 (   0)  L_SUM2JELLY  '2-link kraken jellyfish142 (   0)  L_SUM2SQUIRM '2-link kraken squirmbag143 (   0)  L_SUMURB     'bivalued/1-link kraken UR144 (   0)  L_SUMUR      '1-link kraken UR145 (   0)  L_SUM2UR     '2-link kraken UR146 (   0)  L_SUMBUG2    '2-line/1-link kraken BUG-lite147 (   0)  L_SUMBUG3    '3-line/1-link kraken BUG-lite148 (   0)  L_SUM2BUG2   '2-line/2-link kraken BUG-lite149 (   0)  L_SUM2BUG3   '3-line/2-link kraken BUG-lite150 (   0)  L_SUMAALS2   '2-cell/1-link kraken Almost ALS151 (   0)  L_SUMAALS3   '3-cell/1-link kraken Almost ALS152 (   0)  L_SUM2AALS2  '2-cell/2-link kraken Almost ALS153 (   0)  L_SUM2AALS3  '3-cell/2-link kraken Almost ALS154 (   0)  L_MUTANT21   '1-link kraken mutant x-wing155 (   0)  L_MUTANT31   '1-link kraken mutant swordfish156 (   0)  L_MUTANT41   '1-link kraken mutant jellyfish157 (   0)  L_MUTANT51   '1-link kraken mutant squirmbag158 (   0)  L_MUTANT22   '2-link kraken mutant x-wing159 (   0)  L_MUTANT32   '2-link kraken mutant swordfish160 (   0)  L_MUTANT42   '2-link kraken mutant jellyfish161 (   0)  L_MUTANT52   '2-link kraken mutant squirmbag`
Last edited by Mike Barker on Wed May 09, 2007 11:17 pm, edited 2 times in total.
Mike Barker

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