【TECHNIQUE SHARE】ALS NET

Advanced methods and approaches for solving Sudoku puzzles

【TECHNIQUE SHARE】ALS NET

Postby borescoper » Tue Jun 14, 2016 6:01 am

it's a very rare structure, even less than double loop.
look at the example:
in row2,5,8, there are 3 sets of ALS. each one has a set of candidates({4,5,6}) which can't be eliminated together. and the three "4" in same column, same situation occurs on "5" and "6".
Code: Select all
          ↓4                ↓5                ↓6
*-----------------------------------------------------*
|    .    .      .|    .    .      .|    .    .      .|
|    .    489    .|    .    589    .|    .    689    .|←{4,5,6}+89
|    .    .      .|    .    .      .|    .    .      .|
|-----------------+-----------------+-----------------|
|    .    .      .|    .    .      .|    .    .      .|
|    .    347    .|    .    357    .|    .    367    .|←{4,5,6}+37
|    .    .      .|    .    .      .|    .    .      .|
|-----------------+-----------------+-----------------|
|    .    .      .|    .    .      .|    .    .      .|
|    .    124    .|    .    125    .|    .    126    .|←{4,5,6}+12
|    .    .      .|    .    .      .|    .    .      .|
*-----------------------------------------------------*


in this condition, great amout of candidates can be eliminated:
Code: Select all
*-----------------------------------------------------*
|    .    -4     .|    .    -5     .|    .    -6     .|
|  -89   #489  -89|  -89   #589  -89|  -89   #689  -89|
|    .    -4     .|    .    -5     .|    .    -6     .|
|-----------------+-----------------+-----------------|
|    .    -4     .|    .    -5     .|    .    -6     .|
|  -37   #347  -37|  -37   #357  -37|  -37   #367  -37|
|    .    -4     .|    .    -5     .|    .    -6     .|
|-----------------+-----------------+-----------------|
|    .    -4     .|    .    -5     .|    .    -6     .|
|  -12   #124  -12|  -12   #125  -12|  -12   #126  -12|
|    .    -4     .|    .    -5     .|    .    -6     .|
*-----------------------------------------------------*


proof procedure:
look at r2.r2c2(4),r2c5(5),r2c8(6) can't be eliminated together.so, at least one of them is true.
if r2c2(4) is true:
look at r5 and r8, r58c2<>4, there is a "Doubly Linked ALS-XZ"(a "nice continuous loop" with 2 sets of ALS), r5c5(5)==r5c8(6)--r8c8(6)==r8c8(5), so:
all of the "4" in c2 can be eliminated, of course;
all of the "37" in other grids in row 5 can be eliminated, because of in this row, one of r5c5(5)/r5c8(6) is true and the other is false.
all of the "12" in other grids in row 8 can be eliminated; because of in this row, one of r8c5(5)/r8c8(6) is true and the other is false.
all of "5" in c5 can be eliminated, because of the nice continuous loop.
all of "6" in c8 can be eliminated, because of the nice continuous loop.
in r2, a pair of 89 formed, all of the "89" in other grids in r2 can be eliminated.
if r2c5(5) is true or r2c8(6) is true, similar procedure as above, and same candidates eliminated.

2 real puzzle example:
1.standard "ALS NET":
the 9 "#" grids formed a "ALS NET", so, all of the candidates with the "-" in front can be eliminated, then, r8c3=1, r8c89={47}, all solved.
Code: Select all
*--------------------------------------------------------------------------------------------*
|       268      1468    1247-6|     12568      1567      1568|       247         3         9|
|      2689     14689    1247-6|     12689         3      1689|       247      1246         5|
|         5       169         3|      1269         4      1679|         8      1267       127|
|------------------------------+------------------------------+------------------------------|
|        23       345         8|        35         9       357|         1       247         6|
|       369         7      #456|     13568       156         2|      359-4    #489      #348|
|         1      3569      #256|         4       567      3568|     3579-2     #289      #238|
|------------------------------+------------------------------+------------------------------|
|         7       136         9|       136         8      1346|       234         5     124-3|
|        38         2       1-5|        39        15       349|         6      47-89    47-38|
|         4     3568-1     #156|         7         2    3569-1|        39      #189      #138|
*--------------------------------------------------------------------------------------------*


2.degraded ALS NET:
the 7 "#" grids formed a degraded ALS NET(similar to a degraded swordfish). so, all of the candidates with the "-" in front can be eliminated.
Code: Select all
*--------------------------------------------------------------------------------------------*
|         7         3       589|        89         4        59|         6         2         1|
|         2         4       189|         7         6       139|        38         5      89-3|
|         6      #189     15-89|      #289        13    1235-9|         7         4      #389|
|------------------------------+------------------------------+------------------------------|
|        18         6         2|         5       138         4|        13         9         7|
|       189         5         7|         6       138       139|         4        13         2|
|         4       #19         3|       #29         7      12-9|         5         8         6|
|------------------------------+------------------------------+------------------------------|
|         5       #18         6|         4         2         7|         9        13       #38|
|         3         7         4|         1         9         8|         2         6         5|
|        19         2       189|         3         5         6|        18         7         4|
*--------------------------------------------------------------------------------------------*


borescoper
Last edited by borescoper on Tue Jun 14, 2016 12:20 pm, edited 1 time in total.
borescoper
 
Posts: 15
Joined: 11 June 2016

Re: 【NEW TECH SHARE】ALS NET

Postby JC Van Hay » Tue Jun 14, 2016 7:46 am

ALS NET has already been described here.
They are not so rare and can easily been designed.
Here are 2 puzzles similar to yours that I designed some time ago :
..9.5.3...........6..9.1..7.6.........5.3.27.1....7..8..3.4.5...........7....8..1
..3..7..87....6...5..9..4....8..1..7.........6..4..9....7..8..2.........9..6..5..
JC Van Hay
 
Posts: 714
Joined: 22 May 2010

Re: 【NEW TECH SHARE】ALS NET

Postby Leren » Tue Jun 14, 2016 7:57 am

I'm not wanting to rain on your parade but I wanted to see if your methods offer anything substantially new (not covered by other well established moves).

The first puzzle I managed to solve in 3 moves (plus intervening basics) as follows. Actually it's only 2 moves following the Swordfish, which as far as I can see is your start position.

Code: Select all
*--------------------------------------------------------------------------------*
| 268     1468    12467    | 12568   1567    1568-7   | 247     3       9        |
| 2689    14689   12467    | 12689   3       1689-7   | 247     1246-7  5        |
| 5       169     3        | 1269    4      *1679     | 8      *1267   *127      |
|--------------------------+--------------------------+--------------------------|
| 23      345     8        | 35      9      *357      | 1      *247     6        |
| 369     7       456      | 13568   156     2        | 3459    489     348      |
| 1       3569    256      | 4       567     3568-7   | 23579   289-7   238-7    |
|--------------------------+--------------------------+--------------------------|
| 7       136     9        | 136     8       1346     | 234     5       1234     |
| 38      2       15       | 39      15      349      | 6      *4789   *3478     |
| 4       13568   156      | 7       2       13569    | 39      189     138      |
*--------------------------------------------------------------------------------*

Swordfish in 7's r348 c689 => - 7 r1c6, r2c68, r6c689

*---------------------------------------------------------------------------------*
| 268     1468    12467    |  12568   1567    1568     | 247     3       9        |
| 2689    14689   12467    |  12689   3       1689     | 247     1246    5        |
| 5       169     3        |  1269    4       169-7    | 8       1267    127      |
|--------------------------+---------------------------+--------------------------|
|a23     c345     8        | ca35      9    ca7-53     | 1       24-7    6        |
| 369     7      b456      |  13568   156     2        | 3459    489     348      |
| 1       3569   b256      |  4       56-7    3568     | 23579   289     238      |
|--------------------------+---------------------------+--------------------------|
| 7       136     9        |  136     8       1346     | 234     5       1234     |
| 38      2      b15       |  39      15      349      | 6       4789    3478     |
| 4       13568  b156      |  7       2       13569    | 39      189     138      |
*---------------------------------------------------------------------------------*

ALS XY Wing: (7=2) r4c146 - (2=4) r5689c3 - (4=7) r4c246 => r4c6 = 7 (- 53 r4c6, - 7 r3c6, r4c8, r6c5)

*--------------------------------------------------------------------------------*
| 26      1468    1246     | 568     7       1568     | 24      3       9        |
| 269     14689   7        | 689     3       1689     | 24      16      5        |
| 5       169     3        | 2       4       169      | 8       167     17       |
|--------------------------+--------------------------+--------------------------|
| 23      45      8        | 35      9       7        | 1       24      6        |
| 369     7       46       | 138     16      2        | 5       489     348      |
| 1       569     2        | 4       56      358      | 7       289     38       |
|--------------------------+--------------------------+--------------------------|
| 7       16      9-6      |b16      8       4        | 3       5       2        |
| 8       2      a15       |b39      15      39       | 6       47      47       |
| 4       3      a56       | 7       2       56       | 9       18      18       |
*--------------------------------------------------------------------------------*

XY Chain / ALS XZ Rule: X = 1, Z = 6: (6=1) r89c3 - (1=6) r68c5 => - 6 r7c3

The second puzzle was presumably an end-of-solution situation. An outline of my solution path was (again ignoring intervening basics) :

Skyscraper => - 1 r3c2, Skyscraper => - 1 r5c1, XWing => - 1 r4c5, Finned XWing/Grouped Skyscraper => - 9 r3c6, W Wing => - 1 r5c5, XY Wing with transport => - r1c3, XWing => - 9 r3c39, r6c6

Again, not anything new or particularly advanced there.

Leren
Leren
 
Posts: 2929
Joined: 03 June 2012

Re: 【NEW TECH SHARE】ALS NET

Postby borescoper » Tue Jun 14, 2016 12:19 pm

JC Van Hay wrote:ALS NET has already been described here.
They are not so rare and can easily been designed.
Here are 2 puzzles similar to yours that I designed some time ago :
..9.5.3...........6..9.1..7.6.........5.3.27.1....7..8..3.4.5...........7....8..1
..3..7..87....6...5..9..4....8..1..7.........6..4..9....7..8..2.........9..6..5..


thank you very much for remind me that! i found the technique, and my english is very terrible so i havn't read so many other topics.
i'll remove the "new" title immediately!
borescoper
 
Posts: 15
Joined: 11 June 2016

Re: 【NEW TECH SHARE】ALS NET

Postby borescoper » Tue Jun 14, 2016 1:15 pm

Leren wrote:I'm not wanting to rain on your parade but I wanted to see if your methods offer anything substantially new (not covered by other well established moves).

The first puzzle I managed to solve in 3 moves (plus intervening basics) as follows. Actually it's only 2 moves following the Swordfish, which as far as I can see is your start position.

Code: Select all
*--------------------------------------------------------------------------------*
| 268     1468    12467    | 12568   1567    1568-7   | 247     3       9        |
| 2689    14689   12467    | 12689   3       1689-7   | 247     1246-7  5        |
| 5       169     3        | 1269    4      *1679     | 8      *1267   *127      |
|--------------------------+--------------------------+--------------------------|
| 23      345     8        | 35      9      *357      | 1      *247     6        |
| 369     7       456      | 13568   156     2        | 3459    489     348      |
| 1       3569    256      | 4       567     3568-7   | 23579   289-7   238-7    |
|--------------------------+--------------------------+--------------------------|
| 7       136     9        | 136     8       1346     | 234     5       1234     |
| 38      2       15       | 39      15      349      | 6      *4789   *3478     |
| 4       13568   156      | 7       2       13569    | 39      189     138      |
*--------------------------------------------------------------------------------*

Swordfish in 7's r348 c689 => - 7 r1c6, r2c68, r6c689

*---------------------------------------------------------------------------------*
| 268     1468    12467    |  12568   1567    1568     | 247     3       9        |
| 2689    14689   12467    |  12689   3       1689     | 247     1246    5        |
| 5       169     3        |  1269    4       169-7    | 8       1267    127      |
|--------------------------+---------------------------+--------------------------|
|a23     c345     8        | ca35      9    ca7-53     | 1       24-7    6        |
| 369     7      b456      |  13568   156     2        | 3459    489     348      |
| 1       3569   b256      |  4       56-7    3568     | 23579   289     238      |
|--------------------------+---------------------------+--------------------------|
| 7       136     9        |  136     8       1346     | 234     5       1234     |
| 38      2      b15       |  39      15      349      | 6       4789    3478     |
| 4       13568  b156      |  7       2       13569    | 39      189     138      |
*---------------------------------------------------------------------------------*

ALS XY Wing: (7=2) r4c146 - (2=4) r5689c3 - (4=7) r4c246 => r4c6 = 7 (- 53 r4c6, - 7 r3c6, r4c8, r6c5)

*--------------------------------------------------------------------------------*
| 26      1468    1246     | 568     7       1568     | 24      3       9        |
| 269     14689   7        | 689     3       1689     | 24      16      5        |
| 5       169     3        | 2       4       169      | 8       167     17       |
|--------------------------+--------------------------+--------------------------|
| 23      45      8        | 35      9       7        | 1       24      6        |
| 369     7       46       | 138     16      2        | 5       489     348      |
| 1       569     2        | 4       56      358      | 7       289     38       |
|--------------------------+--------------------------+--------------------------|
| 7       16      9-6      |b16      8       4        | 3       5       2        |
| 8       2      a15       |b39      15      39       | 6       47      47       |
| 4       3      a56       | 7       2       56       | 9       18      18       |
*--------------------------------------------------------------------------------*

XY Chain / ALS XZ Rule: X = 1, Z = 6: (6=1) r89c3 - (1=6) r68c5 => - 6 r7c3

The second puzzle was presumably an end-of-solution situation. An outline of my solution path was (again ignoring intervening basics) :

Skyscraper => - 1 r3c2, Skyscraper => - 1 r5c1, XWing => - 1 r4c5, Finned XWing/Grouped Skyscraper => - 9 r3c6, W Wing => - 1 r5c5, XY Wing with transport => - r1c3, XWing => - 9 r3c39, r6c6

Again, not anything new or particularly advanced there.

Leren


thank u for your reply! JC Van Hay have told me that the technique is NOT a new one, it's my fault, because of my terrible English, i havn't read many other topics. i have removed the title "NEW" already.
in my opinion, sometimes, one technique maybe substituted by another, but sometimes maybe not.
as you mentioned, ALS XY-WING substitute the ALS NET in puzzle 1(in fact i found it before, and i call this "advanced sue de coq", unofficial name, LOL), we can use it to solve the puzzle from another "path", it's another angle of view, but in puzzle solving, i think, maybe one more technique mastering should help me to solve a puzzle more quickly.
i'm sorry for my terrible english, i don't know whether i have expressed my real opnion or not:)

borescoper
borescoper
 
Posts: 15
Joined: 11 June 2016

Re: 【TECHNIQUE SHARE】ALS NET

Postby eleven » Tue Jun 14, 2016 6:32 pm

borescoper,

not your fault. Only a few people knew this technique, and i see little chances for an outsider to find it on this forum.

Great, that you found it on your own too.
eleven
 
Posts: 1580
Joined: 10 February 2008

Re: 【TECHNIQUE SHARE】ALS NET

Postby borescoper » Tue Jun 14, 2016 9:32 pm

eleven wrote:borescoper,

not your fault. Only a few people knew this technique, and i see little chances for an outsider to find it on this forum.

Great, that you found it on your own too.


thank you! :)
borescoper
 
Posts: 15
Joined: 11 June 2016

Re: 【TECHNIQUE SHARE】ALS NET

Postby Leren » Tue Jun 14, 2016 10:36 pm

On further investigation it now seems that what you are describing is close to, or identical to, Multi-Sector Locked sets, or MSLS for short.

This is a relatively advanced technique, although your example puzzle was a relatively easy one to solve, and could be done by other more routine moves.

Here is my MSLS version of your first puzzle:

Code: Select all
*--------------------------------------------------------------------------------*
| 268     1468    247-16   | 12568   1567    1568     | 247     3       9        |
| 2689    14689   247-16   | 12689   3       1689     | 247     1246    5        |
| 5       169     3        | 1269    4       1679     | 8       1267    127      |
|--------------------------+--------------------------+--------------------------|
| 23      345     8        | 35      9       357      | 1       247     6        |
| 369     7      *456      | 13568   156     2        | 359-4  *489    *348      |
| 1       3569   *256      | 4       567     3568     | 3579-2 *289    *238      |
|--------------------------+--------------------------+--------------------------|
| 7       136     9        | 136     8       1346     | 234     5       24-13    |
| 38      2      *15       | 39      15      349      | 6       47-89   47-13    |
| 4       13568  *156      | 7       2       13569    | 39     *189    *138      |
*--------------------------------------------------------------------------------*

MSLS 1 : Base 24; r569 c389 + r8c3 : 10 Links; 4r5 2r6 ; 156c3 89c8 38c9 ; 1b9 ; => - 16 r12c3, - 4 r5c7, - 2 r6c7, -13 r7c9, - 89 r8c8, -38 r8c9

JC Van Hay's Puzzles were harder and don't appear to be solvable by more routine methods.

Here is a MSLS move for his second puzzle ;

Code: Select all
*--------------------------------------------------------------------------------*
|*124     469-12  3        |*125     45-12   7        |*126     569-12  8        |
| 7       124     1249     | 8       12345   6        | 123     1235    1359     |
| 5       8       126      | 9       123     23       | 4       7       136      |
|--------------------------+--------------------------+--------------------------|
|*234     459-23  8        |*235     569-23  1        |*236     456-23  7        |
| 123     12345   12459    | 7       2356    2359     | 8       123456  13456    |
| 6       7       125      | 4       8       235      | 9       1235    135      |
|--------------------------+--------------------------+--------------------------|
|*134     456-13  7        |*135     59-13   8        |*136     469-23  2        |
| 8       123456  12456    | 123-5   1235    23459    | 7       1346    13469    |
| 9       1234    124      | 6       7       234      | 5       8       134      |
*--------------------------------------------------------------------------------*

MSLS 1 : Base 123; r147 c147 : 9 Links; 12r1 23r4 13r7 ; 4c1 5c4 6c7 ; => - 12 r1c258, -23 r4c258, -13 r7c258, - 5 r8c4.

This topic hasn't been active for about 3 years, which is why I overlooked it at first. Like most topics on this forum it's not well documented.

The best thing you can do is follow JC Van Hay's link, or put "Multi", "Sector" and "locked", or "MSLS" into the search box.

If you are interested, here is a list of puzzles which contain MSLS moves. The location of each move is listed with each puzzle. Click on the 'Show" link to display the list.

Hidden Text: Show
1 : 98.7..6..7..6..5......84...6..5..9...35.............2.5...7..69..79....1.....57.. ;4;3;10.9;1.2;1.2;fl; 679;tr; 7; MSLS 1 : Base 67; r2458 c268 + r7c2 r1c6 r7c6 r1c8 r9c8 : 15 Links; 7r4 7r5 6r8 ; 124c2 12389c6 1348c8 ;
2 : 98.7..6..7...5......6..9.746.....3...9...4.67..4...2..4....7.9..6..........1....3 ;;4;3;10.9;1.2;1.2;fl; 679;tr; 7; MSLS 3 : Base 79; r3458 c135 + r6c1 r9c1 r1c3 r2c3 r7c3 r7c5 : 16 Links; 7r4 9r8 ; 12358c1 12358c3 1238c5 ;
3 : 98.7..6..5..9..7......84...7...5.....69..75...3.6...7.6..5..9....2.............51 ;4;3;10.8;1.2;1.2;fl; 679;tr; 7; MSLS 1 : Base 79; r1679 c359 + r2c3 r4c3 r2c5 r5c5 r2c9 r5c9 : 16 Links; 9r6 7r7 7r9 ; 1348c3 12346c5 2348c9 ;
4 : 98.76.5..75...9.....6......4...3.....974..8....8..76...2.....1...9..87..........8 ;4;4;10.6;1.2;1.2;fl; 6789;tr; 8; 14 + 1
5 : 98.7..6..7..5..9.........4.6..9..7....3....6.....2..8.5...9.....6..571....16..... ;2;3;10.6;1.2;1.2;fl; 679;tr; 6; MSLS 4 : Base 679; c1279 r569 + r5c4 r5c6 r6c4 r9c5 r9c6 : 17 Links; 79c2 9c9 ; 12458r5 1345r6 23458r9 ;
6 : 98.7..6..7..5..4....3.8....6....7.9....9...46.....57..5..4..9...7...2...........1 ;4;3;10.6;1.2;1.2;fl; 579;tr; 9; MSLS 4 : Base 79; r2467 c459 + r3c4 r8c4 r9c4 r1c5 r5c5 r1c9 : 16 Links; 9r2 7r7 ; 12368c4 12346c5 2358c9 ;
7 : 98.7..6..7..5...8...4.....38..2...9..1...........6.5.85...2.9...7.9....5..8....2. ;4;5;10.6;1.2;1.2;fl; 12346;tr; 17; 75 + 0
8 : 98.7..6..5..9..4....3.8....7..6..5...9...2..........1.4....9..5...5...46.....79.. ;4;3;10.6;1.2;1.2;fl; 579;tr; 9; MSLS 1 : Base 59; r1479 c458 + r3c4 r5c4 r6c4 r2c5 r8c5 r2c8 : 16 Links; 5r1 9r4 ; 12348c4 12346c5 2378c8 ;
9 : 98.7..6..75.....9...6.....74...7......89...7......32...1..4.3....98...6.....2...1 ;4;3;10.5;1.5;1.5;fl; 379;tr; 7; #MSLS 3 : Base 79; r3489 c267 + r5c2 r1c6 r2c6 r5c6 r2c7 r5c7 : 18 Links; 9r4 7r8 79r9 ; 2346c2 124568c6 1458c7 ;
10 : 98.76....7..5..9....4..9...6...9.3...2.....4...8......3....65.....35..94....7...1 ;1;5;10.5;1.2;1.2;fl; 35679;tr; 14; MSLS 1 : Base 1248; r356 c1457 : 12 Links; 128r3 18r5 124r6 ; 5c1 6c4 3c5 7c7 ;
11 : 98.7..6..75..6..8...6......5..4......4...3..2..8.7.5..1..2...3...5.8.7.1.....1... ;2;3;10.5;1.2;1.2;fl; 568;tr; 11; MSLS 1 : Base 58; c357 r257 + r2c4 r2c6 r2c9 r5c8 : 12 Links; 5c5 8c7 ; 12349r2 179r5 49r7 ;
12 : 98.7..6..7..5...8...6.....48..3...7..7..2.....1.......5....9..7.38....9....8....5 ;4;4;10.5;1.2;1.2;fl; 5789;tr; 7; 30 + 3
13 : 98.7..6..7......8...6.5.....4......6..76...9.....3.2....95...6...89...7.....8...1 ;1;3;10.5;1.2;1.2;fl; 679;tr; 8; MSLS 4 : Base 679; r3578 c125 + r4c1 r9c1 r2c2 r1c5 : 15 Links; 7r7 6r8 ; 123458c1 1235c2 124c5 ;
14 : 98.7..6..5...9......7..4...3......7...84..5.......5..8.7...2.1...98..4....59..8.. ;4;3;10.5;1.2;1.2;fl; 789;tr; 6; MSLS 1 : Base 789; c3579 r347 + r3c1 r3c2 r3c4 r4c4 r7c4 : 16 Links; 8c5 9c7 9c9 ; 12356r3 1246r4 3456r7 ;
15 : 98.76....75..4.8....3..8....7.8..4....9.7..3........2..6...75.....65...2...4....1 ;1;4;10.4;10.4;2.6;fl; 1239;tr; 17; MSLS 1 : Base 4568; r1247 c3689 + r8c6 r9c6 : 17 Links; 45r1 6r2 56r4 48r7 ; 12c3 1239c6 19c8 39c9 ;
16 : 98.76....75..4.8....3..8....7.8..4....9.7..3........2..6...75.....65...1...4....2 ;1;4;10.4;10.4;2.6;fl; 1239;tr; 17; MSLS 1 : Base 4568; r1247 c3689 + r8c6 r9c6 : 17 Links; 45r1 6r2 56r4 48r7 ; 12c3 1239c6 19c8 39c9 ;
17 : 98.76....75..4.8....3..8....7.8..4....9.7..3........2..6...75.....6....2...45...1 ;1;4;10.4;10.4;2.6;fl; 1239;tr; 17; MSLS 1 : Base 4568; r1247 c3689 + r8c6 r9c6 : 17 Links; 45r1 6r2 56r4 48r7 ; 12c3 1239c6 19c8 39c9 ;
18 : 98.7..6..75..6..8...6......4..3...2...5.8.7.4.....4....1.........7.5.8.....1.2..3 ;2;4;10.4;10.4;2.6;fl; 5678;tr; 17; 14 + 0
19 : 98.76.5..75...9.....6......4...3.....974..8....8..76...2.....1...9..87..........6 ;4;4;10.4;1.2;1.2;fl; 6789;tr; 8; 15 + 1
20 : 98.76.5..7..5..9...4.......6....7.....3.567.....3...9.5..6..3....8.2..5.........1 ;4;3;10.4;1.2;1.2;fl; 567;tr; 6; MSLS 1 : Base 67; r24679 c2358 + r5c2 r1c3 r3c5 r1c8 r5c8 : 24 Links; 6r2 7r6 7r7 67r9 ; 12359c2 1249c3 13489c5 12348c8 ;
21 : 98.76.5..7..5..9.........4.6...7..9....9...3.....567..5..6..3...6......2..1.8...9 ;1;3;10.4;1.2;1.2;fl; 567;tr; 8; MSLS 1 : Base 567; c1257 r359 + r3c4 r3c6 r5c6 r9c4 : 15 Links; 57c2 6c7 ; 12389r3 1248r5 234r9 ;
22 : 98.76.5..7..5..4....3.2..6.6...45....976..............5..4..7.6.....1..4.......8. ;4;3;10.4;1.2;1.2;fl; 457;tr; 7; MSLS 1 : Base 457; r2678 c258 + r4c2 r5c5 r1c8 : 15 Links; 4r6 57r8 ; 1236c2 1389c5 1239c8 ;
23 : 98.76.5..7...5.8....4......8...7.9...3.2............1.5.......9.7..9..85...6..7.. ;2;4;10.4;1.2;1.2;fl; 5789;tr; 10; MSLS 1 : Base 589; r1247 c348 + r8c3 r8c4 r9c8 : 14 Links; 9r2 5r4 8r7 ; 1236c3 134c4 2346c8 ;
24 : 98.76.5..7...4.9...3...8...6......9..7..9..65..9..47..5...7.6.....2.............1 ;4;5;10.4;1.2;1.2;fl; 12348;tr; 24; 40 + 3
25 : 98.76.5..7...4.9...3...8...6......9..7..9...5..96.47..5...7.6.....2.............1 ;4;5;10.4;1.2;1.2;fl; 12348;tr; 24; 40 + 3
26 : 98.76.5..7....5.6..5.4..8..3.......2.4.8..1.......9....7...4.58...5...1.....7.4.. ;1;3;10.4;1.2;1.2;fl; 458;tr; 6; MSLS 7 : Base 58; c2369 r189 + r4c3 r1c8 r8c5 r8c7 r9c4 r9c8 : 17 Links; 58c3 8c6 ; 1234r1 23679r8 12369r9 ;
27 : 98.76.5..5..4..8....3....6.8..9..4...2..8............14...9..5..9.5....8....479.. ;4;4;10.4;1.2;1.2;fl; 4589;tr; 11; MSLS 1 : Base 4589; r12457 c3689 + r8c3 r8c6 r9c8 r9c9 : 23 Links; 4r1 9r2 5r4 459r5 8r7 ; 1267c3 1236c6 1237c8 2367c9 ;
28 : 98.76....7..5..9....4..9...6...9.3...2.....4...8......3....65.....37..91....5...4 ;1;5;10.4;1.2;1.2;fl; 35679;tr; 14; MSLS 1 : Base 1248; r356 c1457 : 12 Links; 128r3 18r5 124r6 ; 5c1 6c4 3c5 7c7 ;
29 : 98.76....7..5..9....4..9...6...9.3...2.....4...8......3....65.....35..91....7...4 ;1;5;10.4;1.2;1.2;fl; 35679;tr; 14; MSLS 1 : Base 1248; r356 c1457 : 12 Links; 128r3 18r5 124r6 ; 5c1 6c4 3c5 7c7 ;
30 : 98.76....5.7..48....3...4..7..25......8..73.........1...5.7...4...48.5.......5.3. ;4;3;10.4;1.2;1.2;fl; 458;tr; 6; MSLS 1 : Base 48; c2369 r489 + r4c7 r8c1 r8c8 r9c4 r9c5 r9c7 : 17 Links; 4c2 8c9 ; 1369r4 123679r8 12679r9 ;
31 : 98.7..6..76..9..5...5......4...7......69...7....6.34...2....3....78.2.9.....1...2 ;4;3;10.4;1.2;1.2;fl; 379;tr; 6; MSLS 1 : Base 679; r2459 c267 + r3c2 r8c2 r1c6 r8c7 : 15 Links; 9r4 79r9 ; 1345c2 1458c6 1258c7 ;
32 : 98.7..6..75.4.......3.8..7.8...7..3....29.1.......4...3..1....6.7..3..9.......2.. ;4;5;10.4;1.2;1.2;fl; 12456;tr; 20; #MSLS 5 : Base 89; r3468 c479 + r1c9 r5c9 : 13 Links; 9r3 8r6 8r8 ; 56c4 45c7 12457c9 ; 9b6 ;
33 : 98.7..6..75..6..9...6......8....4..3..5.7...9...5.8....2.....81..7.8.9......5.7.. ;2;3;10.4;1.2;1.2;fl; 567;tr; 12; MSLS 1 : Base 56; c347 r247 + r2c6 r2c9 r4c5 r7c5 : 13 Links; 6c4 5c7 ; 12348r2 129r4 349r7 ;
34 : 98.7..6..75..6..9...6......4..........8.9.7.....4.8..3.2.3.6.1...9.7.8.......1..2 ;2;3;10.4;1.2;1.2;fl; 789;tr; 8; MSLS 1 : Base 79; r34589 c289 + r1c8 r6c8 r1c9 r2c9 : 18 Links; 7r3 9r4 7r9 ; 1346c2 234568c8 14568c9 ;
35 : 98.7..6..75.....9...6.......4..5...3..58...6......7.....967..5...89...7......21.. ;2;3;10.4;1.2;1.2;fl; 679;tr; 9; *MSLS 177 : Base 679; r23567 c5679 + r5c2 r6c2 r1c5 r8c5 r9c5 r1c6 r8c6 r8c7 r1c9 : 27 Links; 6r2 79r3 79r5 69r6 ; 12348c5 13458c6 23458c7 12458c9 ;
36 : 98.7..6..75.....9...6.......4..3...9..98...6......2.....89.5.7...72...8.......1.2 ;4;5;10.4;1.2;1.2;fl; 12345;tr; 22; *MSLS 174 : Base 67; c1479 r469 + r4c3 r4c8 r6c3 r6c8 r9c3 r9c8 : 15 Links; 6c1 6c4 ; 1258r4 13458r6 345r9 ; 7b6 ;
37 : 98.7..6..75.....8...6......4.......3..89...5.....2......96.5.7...581..6.........1 ;4;5;10.4;1.2;1.2;fl; 12349;tr; 20; 31 + 2
38 : 98.7..6..7.6.5......4....8.4.3...7...7.2....9.......6.26.9...7......12........9.6 ;4;5;10.4;1.2;1.2;fl; 13458;tr; 24; 40 + 3
39 : 98.7..6..7.6....5.........886..9.7.....8.7........6..463...89....293...........1. ;4;3;10.4;1.2;1.2;fl; 679;tr; 7; MSLS 1 : Base 78; c127 r268 + r2c4 r2c6 r6c4 r6c5 r8c6 : 13 Links; 7c2 8c7 ; 1234r2 1235r6 145r8 ;
40 : 98.7..6..7.6.......54....7.8..6...5.....3.4.......2..1.6...1..3..89...6.....4.2.. ;4;4;10.4;1.2;1.2;fl; 1234;tr; 16; MSLS 1 : Base 579; r12348 c5679 : 18 Links; 5r1 59r2 9r3 79r4 57r8 ; 12c5 34c6 13c7 24c9 ; 8b2 8b3 ;
41 : 98.7..6..7.56..8...4.....5.6...9...8.5.8.........675..5..9..7...3......2.....1... ;2;4;10.4;1.2;1.2;fl; 6789;tr; 12; #MSLS 10 : Base 1234; r3589 c13457 + r5c6 : 19 Links; 123r3 1234r5 14r8 234r9 ; 79c3 78c5 9c7 ; 8b7 5b8 ;
42 : 98.7..6..7.56..4...3..5....6..2..9.......1.4........8.2....7..9..79....4....267.. ;1;3;10.4;1.2;1.2;fl; 679;tr; 9; MSLS 3 : Base 79; r2478 c578 + r1c5 r3c7 r5c7 r6c7 r1c8 r9c8 : 16 Links; 9r2 7r4 ; 1348c5 12358c7 12356c8 ;
43 : 98.7..6..7..9..85..46......3..8..9....8.2...1.......6..3..9.7.....3...8.....57... ;4;5;10.4;1.2;1.2;fl; 12456;tr; 22; *MSLS 161 : Base 37; c2367 r356 + r3c1 r3c4 r5c1 r5c4 r6c1 r6c4 : 15 Links; 3c6 3c7 ; 125r3 4569r5 12459r6 ; 7b4 ;
44 : 98.7..6..7..9..8....5.4....8..6..97..3............9..21...97.8....8...1.....6.7.. ;2;3;10.4;1.2;1.2;fl; 167;tr; 9; MSLS 1 : Base 16; r12478 c2359 + r9c2 r9c9 : 20 Links; 1r1 1r2 1r4 6r7 6r8 ; 2459c2 234c3 235c5 3459c9 ; 7b7 ;
45 : 98.7..6..7..9..8....5.4....8..6..79..3............7..21...79.8....8...1.....6.9.. ;2;3;10.4;1.2;1.2;fl; 169;tr; 9; MSLS 1 : Base 16; r12478 c2359 + r9c2 r9c9 : 20 Links; 1r1 1r2 1r4 6r7 6r8 ; 2457c2 234c3 235c5 3457c9 ; 9b7 ;
46 : 98.7..6..7..9..58.....8..4.6..5..9...3...........21.6.2...97....6.2.......7.5.2.. ;4;3;10.4;1.2;1.2;fl; 679;tr; 6; MSLS 1 : Base 79; c1359 r168 + r1c6 r1c8 r6c4 r6c7 r8c6 r8c7 : 16 Links; 9c3 7c9 ; 12345r1 3458r6 13458r8 ;
47 : 98.7..6..7..9..58.....8..4.6..5..7...3...........21.6.2...79....6.2.......9.5.2.. ;4;3;10.4;1.2;1.2;fl; 679;tr; 6; MSLS 1 : Base 79; c1359 r168 + r1c6 r1c8 r6c4 r6c7 r8c6 r8c7 : 16 Links; 7c3 9c9 ; 12345r1 3458r6 13458r8 ;
48 : 98.7..6..7..9..5....6.8....6....7.94.7.4...5.....6.7..4..6..9....3....2.....1.... ;4;3;10.4;1.2;1.2;fl; 479;tr; 8; MSLS 1 : Base 479; r1257 c358 + r4c3 r4c5 r6c8 : 14 Links; 4r1 4r2 9r5 7r7 ; 1258c3 235c5 138c8 ;
49 : 98.7..6..7..6..85...4.5....8..9..7.......3..2.......3.1...97....9...61....81..... ;2;4;10.4;1.2;1.2;fl; 2345;tr; 18; MSLS 1 : Base 2345; r3569 c1247 + r9c5 r9c6 : 17 Links; 23r3 45r5 245r6 2345r9 ; 6c1 167c2 8c4 9c7 ;
50 : 98.7..6..7..6..8......5....8..4..9....3....2......1..86...7...9.7.8...46..8...7.. ;4;5;10.4;1.2;1.2;fl; 12345;tr; 23; MSLS 1 : Base 79; c3479 r357 + r3c1 r3c2 r5c1 r7c2 r7c6 : 15 Links; 9c4 7c9 ; 12346r3 145r5 12345r7 ;
51 : 98.7..6..7..5..9....4....3.6...7..5..92...7.....2...6.2..9..5......5...1.....8... ;1;3;10.4;1.2;1.2;fl; 579;tr; 10; *MSLS 225 : Base 57; c1256 r3569 + r3c4 r3c7 r5c4 r5c8 r5c9 r6c7 r6c9 r9c4 r9c7 r9c9 : 24 Links; 5c1 57c2 5c6 ; 12689r3 13468r5 13489r6 12346r9 ;
52 : 98.7..6..7..5..9......4..8.5....7.6..93...7.....3...5.3..9..5...7...2.9.........1 ;4;3;10.4;1.2;1.2;fl; 357;tr; 7; MSLS 1 : Base 35; c1379 r348 + r3c4 r4c2 r4c4 r4c5 r8c4 : 15 Links; 5c3 3c7 3c9 ; 126r3 12489r4 1468r8 ;
53 : 98.7..6..7..5..9......4..8.5....7.6..93...7.....3...5.3..9..5...7...2.....9.....1 ;4;3;10.4;1.2;1.2;fl; 357;tr; 7; MSLS 1 : Base 35; c1379 r348 + r3c4 r4c2 r4c4 r4c5 r8c4 : 15 Links; 5c3 3c7 3c9 ; 126r3 12489r4 1468r8 ;
54 : 98.7..6..7..5..8....4....3.6...75..8..98.........6.7..2..6..5.......2..........21 ;4;5;10.4;1.2;1.2;fl; 12349;tr; 23; MSLS 1 : Base 678; r127 c368 + r4c3 r5c6 r6c6 r4c8 r6c8 : 14 Links; 6r2 78r7 ; 123c3 1349c6 1459c8 ;
55 : 98.7..6..7..5..8....4......8..6..7...3.....2.....1....6...57..8..98..........65.. ;2;5;10.4;1.2;1.2;fl; 12349;tr; 20; MSLS 1 : Base 57; c149 r358 + r3c6 r3c7 r5c7 r8c5 r8c6 r8c7 : 14 Links; 5c1 57c9 ; 1239r3 149r5 1234r8 ;
56 : 98.7..6..7..5..8....4......8...75.6...96.........8.5..6..8..7...3......2.....1... ;2;5;10.4;1.2;1.2;fl; 12349;tr; 20; MSLS 1 : Base 57; c148 r358 + r3c5 r3c7 r5c5 r5c6 r5c7 r8c7 : 14 Links; 5c1 57c8 ; 1239r3 1234r5 149r8 ;
57 : 98.7..6..7..5..49.........86..4..9....3..........2..1.4...57....6...47....96...4. ;2;4;10.4;1.2;1.2;fl; 4679;tr; 11; MSLS 5 : Base 4679; r1248 c359 + r7c3 r9c5 r9c9 : 15 Links; 4r1 6r2 7r4 9r8 ; 1258c3 138c5 1235c9 ;
58 : 98.7..6..7..5..4...3.....8.5...9...4...4....6....579..4..9..7....9.7...2.....1... ;1;4;10.4;1.2;1.2;fl; 4579;tr; 9; MSLS 1 : Base 457; c1357 r359 + r1c3 r3c4 r5c6 r9c4 : 16 Links; 457c3 4c5 5c7 ; 126r3 1238r5 2368r9 ;
59 : 98.7..6..7..5...8...6.....48..9...7..3..2..........5..5...9.1...7.1..8.5..8....9. ;4;3;10.4;1.2;1.2;fl; 579;tr; 7; MSLS 2 : Base 57; c12469 r579 + r5c7 r5c8 r7c3 r7c8 r9c7 : 18 Links; 57c6 7c9 ; 14689r5 23468r7 12346r9 ;
60 : 98.7..6..7..5.......4.8.9..8...7.34..4.........3..2....7..4.89....1....6........7 ;2;3;10.4;1.2;1.2;fl; 489;tr; 9; MSLS 4 : Base 89; c1258 r268 + r2c3 r2c7 r8c7 : 14 Links; 9c2 9c5 8c8 ; 1236r2 156r6 2345r8 ;
61 : 98.7..6..7...9..5......6...64..7.9....7..9.6.........349...78....284...........1. ;2;3;10.4;1.2;1.2;fl; 679;tr; 8; MSLS 2 : Base 79; c14578 r368 + r3c2 r3c3 r6c2 r6c6 r8c6 : 18 Links; 7c7 79c8 ; 123458r3 124568r6 135r8 ;
62 : 98.7..6..7...9......5..6...8....4.7..4......3..7.8.9..2....3..1..8.7.5.....1...2. ;1;3;10.4;1.2;1.2;fl; 789;tr; 12; MSLS 1 : Base 89; r268 c169 + r3c1 r5c1 r9c1 r1c6 r1c9 r4c9 : 14 Links; 8r2 9r8 ; 13456c1 125c6 2456c9 ;
63 : 98.7..6..7...6..9...6..5...4....3....9......4..84...7..2......1..95...6...76...8. ;4;3;10.4;1.2;1.2;fl; 789;tr; 10; MSLS 1 : Base 78; r268 c269 + r3c2 r9c2 r1c6 r9c6 r1c9 r9c9 : 14 Links; 8r2 7r8 ; 1345c2 1249c6 2359c9 ;
64 : 98.7..6..7...6..9...6..5....9......4..89...7...75...6..3.........96...8......21.. ;2;3;10.4;1.2;1.2;fl; 678;tr; 7; MSLS 1 : Base 67; r258 c269 + r3c2 r6c2 r1c6 r6c6 r1c9 r6c9 : 15 Links; 6r5 7r8 ; 1245c2 1348c6 12358c9 ;
65 : 98.7..6..7...6..9...6..5....4......3..79...5......2.....95...6...86...7......91.. ;4;3;10.4;1.2;1.2;fl; 567;tr; 8; MSLS 1 : Base 67; r257 c269 + r3c2 r8c2 r1c6 r8c6 r1c9 r9c9 : 15 Links; 6r5 7r7 ; 1235c2 1348c6 12458c9 ;
66 : 98.7..6..7...6......6..5....4....93...79....5.....2.....95....6..86....7.....91.. ;4;3;10.4;1.2;1.2;fl; 567;tr; 8; MSLS 1 : Base 67; r257 c268 + r3c2 r8c2 r1c6 r8c6 r1c8 r9c8 : 15 Links; 6r5 7r7 ; 1235c2 1348c6 12458c8 ;
67 : 98.7..6..7...5..9........7846.8....7....3.9............7.4...8...2..6.....1...4.6 ;2;5;10.4;1.2;1.2;fl; 12359;tr; 17; MSLS 1 : Base 46; c149 r258 + r2c2 r2c7 r5c2 r8c8 : 12 Links; 6c4 4c9 ; 123r2 125r5 1359r8 ;
68 : 98.7..6..7...5..8........7946.9....7....3.8............7.4...9...2..6.....1...4.6 ;2;5;10.4;1.2;1.2;fl; 12358;tr; 16; MSLS 1 : Base 46; c149 r258 + r2c2 r2c7 r5c2 r8c8 : 12 Links; 6c4 4c9 ; 123r2 125r5 1358r8 ;
69 : 98.7..6..7...5..4...3......5..4...2..3..92........51..4....7.5..5..4...1..6.....8 ;4;3;10.4;1.2;1.2;fl; 457;tr; 7; 66 + 1
70 : 98.7..6..7......9...6.5....4....3.....95..38...86...7..2.........79...6.......8.1 ;2;4;10.4;1.2;1.2;fl; 6789;tr; 15; #MSLS 22 : Base 789; c247 r345 + r7c7 r3c1 r3c8 r4c3 r4c8 : 12 Links; 7c2 8c4 79c7 ; 1234r3 125r4 ; 6b4 ;
71 : 98.7..6..7......8...6.5....46......3..95...6...8..4.7..2...5.....78...5.....6.1.. ;4;3;10.4;1.2;1.2;fl; 578;tr; 8; 51 + 2
72 : 98.7..6..7......8...6.5....46......3..9..4.7...85...6..2...5.....78...5.....6.1.. ;4;3;10.4;1.2;1.2;fl; 578;tr; 8; 50 + 2
73 : 98.7..6..7............8..9.67...58....4.........67...359..6.7....25........9...1. ;4;5;10.4;1.2;1.2;fl; 12345;tr; 23; 0 + 2
74 : 98.7..6..7............8..9.67...58....4.........67...359....7...6.9...2...15...6. ;4;5;10.4;1.2;1.2;fl; 12345;tr; 23; 0 = 1
75 : 98.7..6..5.4.8........3....76.8...9.......8.6........727.9....8..5...........192. ;4;3;10.4;1.2;1.2;fl; 689;tr; 7; MSLS 3 : Base 69; r1578 c358 + r4c3 r4c5 r2c8 r6c8 : 15 Links; 9r5 6r7 6r8 ; 123c3 1245c5 13457c8 ;
76 : 98.7..6..5.4..........3....76.8...9.......8.6........727.9....8..5..8........192. ;4;3;10.4;1.2;1.2;fl; 689;tr; 7; MSLS 3 : Base 69; r1578 c358 + r4c3 r4c5 r2c8 r6c8 : 15 Links; 9r5 6r7 6r8 ; 123c3 1245c5 13457c8 ;
77 : 98.7..6..5.4..........3....76.5...9...2.....5....8.7.661.9....7.....8.1.......9.. ;2;3;10.4;1.2;1.2;fl; 679;tr; 9; 25 + 1
78 : 98.7..6..5..9..78.....84...7..6..9....3....6......2.1.1...59....9..6.1....71..... ;1;3;10.4;1.2;1.2;fl; 169;tr; 6; MSLS 1 : Base 69; c1278 r369 + r3c4 r6c4 r6c9 r9c5 r9c6 : 15 Links; 6c1 6c2 9c8 ; 235r3 3458r6 23458r9 ;
79 : 98.7..6..5..9..7......8..5.7...6...5.495..........79..4..6..5....3.....6.....2.1. ;2;4;10.4;1.2;1.2;fl; 5679;tr; 15; 23 + 1
80 : 98.7..6..5..9..4....3.6....6....9.5....5...4.....769..4..6..5...2.....68....1.... ;4;3;10.4;1.2;1.2;fl; 569;tr; 8; MSLS 2 : Base 59; c1468 r389 + r3c2 r3c7 r8c7 r9c7 : 15 Links; 5c6 9c8 ; 12478r3 1347r8 2378r9 ;
81 : 98.7..6..5..9..4....3....2.6......47..94....6..5...9..4..6..7...9..1........8.... ;2;3;10.4;1.2;1.2;fl; 467;tr; 9; MSLS 26 : Base 67; c168 r136 + r1c5 r1c9 r3c4 r3c7 r6c4 r6c9 : 13 Links; 7c1 6c6 ; 1235r1 158r3 1238r6 ;
82 : 98.7..6..5..9..4......85...7..4..5....3.2...........1.4......65.9....7...7.5....4 ;1;3;10.4;1.2;1.2;fl; 479;tr; 9; MSLS 4 : Base 79; r1249 c358 + r7c3 r8c5 r8c8 : 14 Links; 7r2 9r4 9r9 ; 1268c3 1346c5 238c8 ;
83 : 98.7..6..5..9..4......85...7..4..5....3.2...........1.4......6..95...7...7.5....4 ;1;3;10.4;1.2;1.2;fl; 479;tr; 9; MSLS 4 : Base 79; r1249 c358 + r7c3 r8c5 r8c8 : 14 Links; 7r2 9r4 9r9 ; 1268c3 1346c5 238c8 ;
84 : 98.7..6..5..9..4......8..3.7...5......4.9.5.....4...764..5..7...2.........9..1... ;2;3;10.4;1.2;1.2;fl; 579;tr; 12; #MSLS 1 : Base 79; r12478 c289 + r5c2 r5c8 r9c8 r5c9 r9c9 : 18 Links; 7r2 9r4 ; 136c2 124568c8 123458c9 ; 9b9 ;
85 : 98.7..6..5..9..4......3..8.7...5.....4..9.5.....4...764..5..7...9...2.....1...... ;2;4;10.4;1.2;1.2;fl; 4579;tr; 17; 4 + 1
86 : 98.7..6..5..9..4......3..8.7...5.....4...95.....4...764..5..7...92...........1... ;2;4;10.4;1.2;1.2;fl; 4579;tr; 15; MSLS 22 : Base 579; c267 r136 + r9c2 r3c1 r3c4 r6c1 r6c5 : 12 Links; 57c2 5c6 9c7 ; 126r3 1238r6 ; 4b2 ;
87 : 98.7..6..5..9..4......3..8.7....9.6..45...9.....4...7.4..5..7...5......2..9..1... ;4;3;10.4;1.2;1.2;fl; 457;tr; 8; 50 + 2
88 : 98.7..6..5..8..7....6.4....7......8..5.9...67..9...5..6..5..8...3..8.........2..1 ;4;3;10.4;1.2;1.2;fl; 578;tr; 8; MSLS 2 : Base 578; r12578 c368 + r4c3 r4c6 r3c8 r6c8 : 18 Links; 8r5 7r7 57r8 ; 1234c3 13469c6 12349c8 ;
89 : 98.7..6..5..6..7......8..4.7..9..5...5...3.....9....2.1....9..6...1...5.....671.. ;2;3;10.4;1.2;1.2;fl; 679;tr; 7; 27 + 1
90 : 98.7..6..5..6..7......8..4.6..9..5...5...3.....9....2.1....9..7...1...5.....761.. ;2;3;10.4;1.2;1.2;fl; 679;tr; 7; 27 + 1
91 : 98.7..6..5..6..4......3..5.7..9..5...2.....8......1...6......45.9....7....75....6 ;4;3;10.4;1.2;1.2;fl; 567;tr; 8; MSLS 2 : Base 67; c1349 r356 + r3c6 r3c7 r5c7 r6c7 : 16 Links; 6c3 7c9 ; 12489r3 1349r5 23489r6 ;
92 : 98.7..6..5..4.......7.8..5.7....32...5..2..7...2..41..2...5..8......1..6......3.. ;2;3;10.4;1.2;1.2;fl; 278;tr; 7; MSLS 4 : Base 78; r357 c267 + r2c2 r4c2 r6c2 r9c2 r2c6 : 13 Links; 8r5 7r7 ; 123469c2 269c6 49c7 ;
93 : 98.7..6..5...9..7...7..6...4....3..2..6.7.5.......1.4..3.2...1...9.6.7........... ;1;4;10.4;1.2;1.2;fl; 5679;tr; 8; MSLS 15 : Base 59; c357 r467 + r6c1 : 10 Links; 5c3 5c5 9c7 ; 18r4 238r6 48r7 ;
94 : 98.7..6..5...8..7...7..4...3.........2..9.8....84...9..7...2..1..98...5.....1.3.. ;1;3;10.4;1.2;1.2;fl; 789;tr; 7; MSLS 1 : Base 89; c12478 r379 + r3c5 r7c3 r7c5 r9c3 : 17 Links; 8c1 9c4 9c7 8c8 ; 12356r3 3456r7 2456r9 ;
95 : 98.7..6..5...8......7..6...4......7...6.7.8.....3.4..2.1...7.3...9.6.7.....2...1. ;4;3;10.4;1.2;1.2;fl; 678;tr; 7; MSLS 4 : Base 68; r3578 c1489 + r2c4 r1c8 r2c8 r1c9 r4c9 : 20 Links; 8r3 68r7 8r8 ; 123c1 1459c4 2459c8 13459c9 ;
96 : 98.7..6....7.5..9...4......37.8....9..2...83......1...2...9...7.9.6...8......7..6 ;4;3;10.4;1.2;1.2;fl; 678;tr; 6; MSLS 1 : Base 68; r1469 c358 + r8c3 r8c5 r3c8 r7c8 : 15 Links; 6r4 6r6 8r9 ; 135c3 1234c5 12457c8 ;
97 : 98.7..6....7.5..9........7886.9....7..4.6.........3...72.6...8......12..........6 ;1;3;10.4;1.2;1.2;fl; 689;tr; 7; MSLS 1 : Base 68; r1349 c356 + r6c3 r7c3 r7c5 r7c6 : 16 Links; 6r3 8r9 ; 12359c3 12349c5 2459c6 ;
98 : 98.7..6....7.5..9........7886.9....7..4...8.......3...72.6...8......12..........6 ;4;3;10.4;1.2;1.2;fl; 689;tr; 8; MSLS 1 : Base 68; r1349 c356 + r6c3 r7c3 r7c5 r7c6 : 16 Links; 6r3 8r9 ; 12359c3 12349c5 2459c6 ;
99 : 98.7..6....7.5..9........7886.9....7..4..........83...72.6...8......12..........6 ;4;3;10.4;1.2;1.2;fl; 689;tr; 8; MSLS 1 : Base 68; r1349 c356 + r6c3 r7c3 r7c5 r7c6 : 16 Links; 6r3 8r9 ; 12359c3 12349c5 2459c6 ;
100 : 98.7..6....7.5..9.........886.9....7..4.6.........3...72.6...8......12........7.6 ;1;3;10.4;1.2;1.2;fl; 689;tr; 7; MSLS 1 : Base 68; r1349 c356 + r6c3 r7c3 r7c5 r7c6 : 16 Links; 6r3 8r9 ; 12359c3 12349c5 2459c6 ;
101 : 98.7..6....7.5..9.........886.9....7..4..........83...72.6...8......12........7.6 ;4;3;10.4;1.2;1.2;fl; 689;tr; 8; MSLS 1 : Base 68; r1349 c356 + r6c3 r7c3 r7c5 r7c6 : 16 Links; 6r3 8r9 ; 12359c3 12349c5 2459c6 ;
102 : 98.7..6....7.5..9.........886.9....7..4...........3.6.72.6...8......12........7.6 ;1;3;10.4;1.2;1.2;fl; 689;tr; 7; MSLS 1 : Base 68; r1349 c356 + r6c3 r7c3 r7c5 r7c6 : 16 Links; 6r3 8r9 ; 12359c3 12349c5 2459c6 ;
103 : 98.7..6....7.5..9.........886.9.......4.67........3...72.6...8......12........7.6 ;1;3;10.4;1.2;1.2;fl; 689;tr; 7; MSLS 1 : Base 68; r1349 c356 + r6c3 r7c3 r7c5 r7c6 : 16 Links; 6r3 8r9 ; 12359c3 12349c5 2459c6 ;
104 : 98.7..6....7.5..9.........886.9.......4..7.......83...72.6...8......12........7.6 ;4;3;10.4;1.2;1.2;fl; 689;tr; 8; MSLS 1 : Base 68; r1349 c356 + r6c3 r7c3 r7c5 r7c6 : 16 Links; 6r3 8r9 ; 12359c3 12349c5 2459c6 ;
105 : 98.7..6....7.5..9.........886.9.......4..7........3.6.72.6...8......12........7.6 ;1;3;10.4;1.2;1.2;fl; 689;tr; 7; MSLS 1 : Base 68; r1349 c356 + r6c3 r7c3 r7c5 r7c6 : 16 Links; 6r3 8r9 ; 12359c3 12349c5 2459c6 ;
106 : 98.7..6....7....5...4.96...76...83....2..........7...13...6.8...4.8...3....3....7 ;4;3;10.4;1.2;1.2;fl; 368;tr; 8; 51 + 2
107 : 98.7..6....7....5...4.96...67...83....2..........7...14..8...3..3..6.8.....3....7 ;4;3;10.4;1.2;1.2;fl; 368;tr; 8; 50 + 2
108 : 98.7.....6...5.8....5....7.4...3...2..85..6......84....1.........68..7.......2.31 ;2;3;10.4;1.2;1.2;fl; 567;tr; 11; 54 + 0
109 : 98.7.....6...5.8....5....7.4....3.....85..6.......7.32.1.........98..7......21..4 ;4;3;10.4;1.2;1.2;fl; 478;tr; 6; MSLS 1 : Base 78; r1257 c169 + r3c1 r6c1 r8c1 r8c6 r3c9 r8c9 : 16 Links; 7r5 8r7 ; 1235c1 24569c6 13569c9 ;
110 : 98.7.....6...5.8....5....7.4..........78..5......3..42.1...2.5...95..7.......1..3 ;4;3;10.4;1.2;1.2;fl; 578;tr; 7; MSLS 5 : Base 78; r3578 c1569 + r1c5 r4c5 r1c6 r2c6 r2c9 : 20 Links; 8r3 78r7 8r8 ; 123c1 12469c5 3469c6 1469c9 ;
111 : 98.7.......6.5.4.......6.3.8...2.....5...4..1..46..5..3...6..9...5..76.....5...1. ;4;3;10.4;1.2;1.2;fl; 467;tr; 9; MSLS 1 : Base 46; r258 c148 + r6c1 r3c4 r4c4 r6c8 : 13 Links; 6r5 4r8 ; 127c1 12389c4 278c8 ;
112 : 98.7..6..7...8..9..5.4..8..3.........6.3..7....7.2...1.3......6..56...8.....435.. ;4;3;10.3;10.3;7.1;fl; 368;tr; 7; MSLS 2 : Base 36; c1679 r268 + r2c2 r2c4 r6c2 r6c4 r8c2 r8c5 : 16 Links; 6c6 3c7 3c9 ; 1245r2 4589r6 12479r8 ;
113 : 98.7.....6...8.7....7..5...4....3.....89..6.........43.2......1..96..8......51.2. ;2;4;10.3;10.3;2.6;fl; 6789;tr; 12; MSLS 7 : Base 679; r1258 c689 : 12 Links; 6r1 9r2 7r5 7r8 ; 24c6 135c8 245c9 ;
114 : 98.7..6..75.....9...6......4...5...3..59...6......24...1..3.2.6..95...7......1... ;4;3;10.3;1.5;1.5;fl; 579;tr; 7; MSLS 3 : Base 79; r1458 c267 + r3c2 r9c2 r2c6 r3c6 r2c7 : 15 Links; 79r4 7r5 ; 2346c2 34568c6 138c7 ;
115 : 98.76.5..7..8..9....6......8..5..7....4.7.........3.2.1......59.5.9...87..8...1.. ;2;3;10.3;1.2;1.2;fl; 579;tr; 6; MSLS 1 : Base 59; r1245 c368 + r8c3 r7c6 r8c6 r9c8 : 15 Links; 5r2 9r4 9r5 ; 123c3 12468c6 1346c8 ;
116 : 98.76.5..7......6..4.5..7..8..9...57.7.....49......8..3...21....9.8..4.......9... ;1;3;10.3;1.2;1.2;fl; 789;tr; 8; 15 + 2
117 : 98.76.5..5..4..9....3....6.8......95..75...4.....8.7..7..8..4...5.........2.7...1 ;2;3;10.3;1.2;1.2;fl; 589;tr; 8; *MSLS 14 : Base 58; r25678 c568 + r4c5 r1c6 r1c8 : 15 Links; 8r2 5r7 ; 1234c5 12346c6 123c8 ; 9b5 ;
118 : 98.76.5..5..4..9....3....6.8......59..79...4.....8.7..7..8..4...9.........2.7...1 ;2;3;10.3;1.2;1.2;fl; 589;tr; 8; *MSLS 25 : Base 89; r25678 c568 + r4c5 r1c6 r1c8 : 15 Links; 8r2 9r7 ; 1234c5 12346c6 123c8 ; 5b5 ;
119 : 98.76.5..5..4..9.........867..9..4......3.........2.1.6......4..95...7...7.6....5 ;4;5;10.3;1.2;1.2;fl; 12348;tr; 20; MSLS 1 : Base 59; r489 c568 + r2c5 r1c6 r2c6 r1c8 : 11 Links; 5r4 9r9 ; 128c5 138c6 23c8 ; 4b8 ;
120 : 98.76.5..5..4..9.........867..5..4......3.........2.1.6......4..7.6....9.59...7.. ;4;5;10.3;1.2;1.2;fl; 12348;tr; 20; MSLS 1 : Base 59; r489 c568 + r2c5 r1c6 r2c6 r1c8 : 11 Links; 9r4 5r8 ; 128c5 138c6 23c8 ; 4b8 ;
121 : 98.76.5..5..4..7....3....864..5..9...7......5.....2...1...5..4....1....9....741.. ;1;3;10.3;1.2;1.2;fl; 457;tr; 8; MSLS 1 : Base 47; r1279 c369 + r4c3 r5c3 r6c3 r5c6 r8c6 r4c9 : 17 Links; 4r1 7r7 ; 125689c3 13689c6 1238c9 ;
122 : 98.76....5.7..48....3...4..3..25......8..73.........1...5.7...4...48.5.......5.3. ;4;3;10.3;1.2;1.2;fl; 348;tr; 6; MSLS 3 : Base 48; r3567 c158 + r8c1 r2c5 r9c5 r1c8 r2c8 r8c8 : 16 Links; 4r5 4r6 8r7 ; 1267c1 1239c5 25679c8 ;
123 : 98.7..6..75.4.......3.9..7.5...3..9..3...9..6...2..1..3.......1.9..8..5......42.. ;4;3;10.3;1.2;1.2;fl; 239;tr; 6; MSLS 1 : Base 39; r3578 c147 + r6c1 r9c1 r4c4 r4c7 : 15 Links; 9r7 3r8 ; 12468c1 1568c4 4578c7 ;
124 : 98.7..6..75..6..9...6......4.........6.4.3..2..8.7.9...1.2...3...7.9.8..........1 ;2;3;10.3;1.2;1.2;fl; 678;tr; 12; MSLS 16 : Base 78; c357 r157 + r1c6 r1c8 r1c9 r5c1 : 11 Links; 8c5 7c7 ; 12345r1 15r5 45r7 ;
125 : 98.7..6..75..6..8...6......4....3..2..8.7.5.........3..1.........7.5.8.....2.1.4. ;2;4;10.3;1.2;1.2;fl; 5678;tr; 14; 25 + 0
126 : 98.7..6..75..6..8..........64...3.....8.7.9....7.8.5.6.6.....9...9.5.8.......2..1 ;2;4;10.3;1.2;1.2;fl; 5689;tr; 14; 17 + 4
127 : 98.7..6..75.....9...6......4...6...3..59...6......2..4.1...9.....96...7.....132.. ;4;3;10.3;1.2;1.2;fl; 679;tr; 7; MSLS 5 : Base 79; r3458 c2679 + r1c6 r2c7 r7c7 r1c9 r2c9 : 20 Links; 7r3 79r4 7r5 ; 234c2 1458c6 13458c7 1258c9 ;
128 : 98.7..6..75.....9...6......4...3...6..86...7.....4.2...1..6.7....79...6......23.1 ;4;3;10.3;1.2;1.2;fl; 679;tr; 7; MSLS 5 : Base 79; r3458 c2567 + r1c5 r2c5 r1c6 r7c6 r2c7 : 20 Links; 9r3 79r4 9r5 ; 234c2 1258c5 13458c6 1458c7 ;
129 : 98.7..6..75.....8...6.....74...3.2....85...9.........4.1..92..3..98...5.....1.... ;4;3;10.3;1.2;1.2;fl; 358;tr; 7; 53 + 0
130 : 98.7..6..75.....8...6......8.54...7..4......3..782..6...86...5.....1.2.......4..6 ;2;3;10.3;1.2;1.2;fl; 567;tr; 12; MSLS 6 : Base 56; c1347 r589 + r5c8 r8c8 r9c2 r9c8 : 14 Links; 56c1 5c4 ; 129r5 349r8 12379r9 ;
131 : 98.7..6..75.....8...6......4...7.5.3..75...6.....24....6....8....98...5......32.1 ;2;3;10.3;1.2;1.2;fl; 568;tr; 9; MSLS 1 : Base 58; r12357 c1569 + r8c1 r8c5 r8c6 : 21 Links; 5r1 58r3 8r5 5r7 ; 123c1 1349c5 1279c6 2479c9 ; 6b2 ;
132 : 98.7..6..75.....8...6......4.......3..943..5...56..87...79...6.....2...1.....4... ;1;4;10.3;1.2;1.2;fl; 1234;tr; 18; MSLS 5 : Base 1234; r3489 c23478 + r3c1 : 19 Links; 1234r3 12r4 34r8 123r9 ; 9c2 8c3 58c4 579c7 9c8 ;
133 : 98.7..6..7.6.5..9..........5.4.7...9.3.9..57....2..4..4.5.6.9.......1.4.........6 ;4;3;10.3;1.2;1.2;fl; 459;tr; 6; MSLS 2 : Base 45; r2358 c149 + r6c1 r9c1 r4c4 r7c4 r6c9 r7c9 : 16 Links; 4r3 5r8 ; 12368c1 1368c4 12378c9 ;
134 : 98.7..6..7.6.5..4..3.8......7.6..8....9....2......1.7....9...87....6.9.......8..3 ;4;3;10.3;1.2;1.2;fl; 789;tr; 7; MSLS 1 : Base 78; r1369 c358 + r4c3 r7c3 r4c5 r7c5 r4c8 r8c8 : 16 Links; 8r6 7r9 ; 12345c3 12349c5 1359c8 ;
135 : 98.7..6..7.56..8...6..5....6..9..7...4.....3...9..2...1...9...8...1...7.....869.. ;4;5;10.3;1.2;1.2;fl; 12345;tr; 23; MSLS 1 : Base 68; r1247 c238 + r6c2 r3c3 r9c3 r3c8 r9c8 : 15 Links; 8r4 6r7 ; 1235c2 1234c3 12459c8 ;
136 : 98.7..6..7.54..9...3..8....5..9..7.......6.2.........14...9.....5.6.......6.475.. ;4;4;10.3;1.2;1.2;fl; 1238;tr; 20; MSLS 2 : Base 1238; r568 c3457 + r5c1 r6c1 r8c1 r8c6 : 15 Links; 138r5 238r6 1238r8 ; 79c3 7c5 4c7 ; 5b5 ;
137 : 98.7..6..7.5.8..4...3.4....5.....7.2..8.3..5....1.......7..45.....3...7.....7.8.4 ;4;3;10.3;1.2;1.2;fl; 478;tr; 6; MSLS 1 : Base 48; r3567 c147 + r9c1 r2c4 r9c4 r2c7 r8c7 : 15 Links; 4r5 4r6 8r7 ; 1236c1 2569c4 1239c7 ;
138 : 98.7..6..7.5.8..4...3.4....3.....7.2..8.3..5....1.......7..45.....3...7.....7.8.4 ;4;3;10.3;1.2;1.2;fl; 348;tr; 6; MSLS 1 : Base 48; r3567 c147 + r9c1 r2c4 r9c4 r2c7 r8c7 : 15 Links; 4r5 4r6 8r7 ; 1256c1 2569c4 1239c7 ;
139 : 98.7..6..7.5.6..4...3..9...89..7.3...4.9.3......8....263...78.........3.........1 ;1;3;10.3;1.2;1.2;fl; 389;tr; 7; MSLS 38 : Base 389; c4678 r269 + r2c2 r6c2 r6c3 r6c5 r9c1 r9c2 : 16 Links; 3c4 8c6 9c7 9c8 ; 12r2 14567r6 24567r9 ;
140 : 98.7..6..7.5.6..4...3..8...89..7.3...4.8.3......9....263...79.........3.........1 ;1;3;10.3;1.2;1.2;fl; 389;tr; 7; MSLS 38 : Base 389; c4678 r269 + r2c2 r6c2 r6c3 r6c5 r9c1 r9c2 : 16 Links; 3c4 9c6 8c7 8c8 ; 12r2 14567r6 24567r9 ;
141 : 98.7..6..7.5.6......4......89...67.....8........39..2.47..8.9...3...7..4.......1. ;4;5;10.3;1.2;1.2;fl; 12345;tr; 22; *MSLS 20 : Base 68; r2357 c389 + r1c3 r4c3 r1c8 r4c8 r1c9 r4c9 : 15 Links; 6r5 6r7 ; 123c3 3459c8 12359c9 ; 8b3 ;
142 : 98.7..6..7.5....9..4.......63..7.9....49.6.7......3.2.36...78.....3....1....8.... ;4;3;10.3;1.2;1.2;fl; 367;tr; 6; MSLS 3 : Base 36; r1358 c158 + r6c1 r9c1 r6c5 r7c5 r4c8 r7c8 : 16 Links; 3r3 6r8 ; 12458c1 12459c5 1458c8 ;
143 : 98.7..6..7.5....8..6.......6...4...3.9.5...6......21....96...7.....3...4.....12.. ;4;4;10.3;1.2;1.2;fl; 1234;tr; 16; MSLS 1 : Base 578; r12357 c5679 : 18 Links; 5r1 578r3 78r5 58r7 ; 12c5 34c6 34c7 12c9 ; 9b2 9b3 ;
144 : 98.7..6..7.5....8..........64..7.8....7..8..3...4.....46....9....296..7.....4..1. ;4;3;10.3;1.2;1.2;fl; 467;tr; 6; MSLS 1 : Base 46; r346 c368 + r7c3 r1c6 r8c6 r9c6 r1c8 r7c8 : 14 Links; 4r3 6r6 ; 138c3 12359c6 2359c8 ;
145 : 98.7..6..7.5....8..........64....9....396..7.....4..2.46..7.8....7..8..1...4..... ;4;3;10.3;1.2;1.2;fl; 467;tr; 6; MSLS 1 : Base 46; r379 c368 + r4c3 r1c6 r5c6 r6c6 r1c8 r4c8 : 14 Links; 4r3 6r9 ; 128c3 12359c6 1359c8 ;
146 : 98.7..6..7.5....4...4.8....84...73.....89...2....3....63..7.9....9....1......6... ;2;3;10.3;1.2;1.2;fl; 389;tr; 12; 34 + 0
147 : 98.7..6..7.5....4..........86..4.7....38..........7.2.64...89.....96..1....4..... ;1;3;10.3;1.2;1.2;fl; 478;tr; 10; MSLS 6 : Base 78; c25679 r2368 + r2c4 r3c1 r3c4 r6c1 r6c3 r6c4 r8c1 : 25 Links; 8c5 8c7 78c9 ; 12369r2 123459r3 134569r6 2345r8 ;
148 : 98.7..6..7..9..5...4..83...5..6..9...2.....4...4.1..5..5.4.......7..64......97... ;4;3;10.3;1.2;1.2;fl; 679;tr; 10; MSLS 12 : Base 679; r489 c248 + r2c2 r3c4 r5c4 r6c4 r1c8 r2c8 : 14 Links; 7r4 9r8 6r9 ; 13c2 12358c4 1238c8 ;
149 : 98.7..6..7..9..5...4..83...5..6..7...2.....4...4.1..5..5.4.......9..64......79... ;4;3;10.3;1.2;1.2;fl; 679;tr; 10; MSLS 12 : Base 679; r489 c248 + r2c2 r3c4 r5c4 r6c4 r1c8 r2c8 : 14 Links; 9r4 7r8 6r9 ; 13c2 12358c4 1238c8 ;
150 : 98.7..6..7..9..5...4..8....6..3..79.....2...........1.5....9..7.6....9....96...35 ;4;3;10.3;1.2;1.2;fl; 567;tr; 6; MSLS 1 : Base 57; c13469 r3568 + r3c7 r5c7 r6c7 r8c8 : 22 Links; 7c3 5c4 57c6 ; 123r3 13468r5 23468r6 12348r8 ;
151 : 98.7..6..7..9..5......8....5......6..94.5.7...7.4....54..5..9...3..9.........2.1. ;4;3;10.3;1.2;1.2;fl; 579;tr; 8; MSLS 8 : Base 79; r12678 c368 + r3c3 r4c3 r3c6 r5c6 r5c8 : 19 Links; 9r6 7r7 7r8 ; 123568c3 134568c6 2348c8 ;
152 : 98.7..6..7..65.9....4......6..5..3....8.2..9........1.5....7..9...9....3....657.. ;2;3;10.3;1.2;1.2;fl; 567;tr; 6; MSLS 2 : Base 67; r1467 c358 + r2c3 r9c3 r3c5 r8c5 r2c8 r9c8 : 16 Links; 7r4 7r6 6r7 ; 1239c3 13489c5 2348c8 ;
153 : 98.7..6..7..65.8....5.8..4.8..3..9...2............8..16...37..8..9.....6......7.. ;4;3;10.3;1.2;1.2;fl; 679;tr; 7; MSLS 1 : Base 67; r1246 c358 + r7c3 r8c5 r7c8 r8c8 r9c8 : 16 Links; 67r4 67r6 ; 1234c3 124c5 12359c8 ;
154 : 98.7..6..7..65.8....5....4.8..3..9...2............8..16...37..8..98....6......7.. ;4;3;10.3;1.2;1.2;fl; 679;tr; 7; MSLS 1 : Base 67; r1246 c358 + r7c3 r8c5 r7c8 r8c8 r9c8 : 16 Links; 67r4 67r6 ; 1234c3 124c5 12359c8 ;
155 : 98.7..6..7..65.8....5....4.6...37.....98....6..8...7...2.....8....3..9.......8..1 ;4;3;10.3;1.2;1.2;fl; 679;tr; 7; MSLS 1 : Base 67; r1289 c358 + r4c3 r5c5 r4c8 r5c8 r6c8 : 16 Links; 67r8 67r9 ; 1234c3 124c5 12359c8 ;
156 : 98.7..6..7..65......5.8..4.8..3..9...2.....8......8..16...37..8..9.....6......7.. ;4;3;10.3;1.2;1.2;fl; 679;tr; 7; MSLS 1 : Base 67; r1246 c358 + r7c3 r8c5 r7c8 r8c8 r9c8 : 16 Links; 67r4 67r6 ; 1234c3 124c5 12359c8 ;
157 : 98.7..6..7..65......5.8..4.8..3..9...2.....8.........16...37..8..98....6......7.. ;4;3;10.3;1.2;1.2;fl; 679;tr; 7; MSLS 1 : Base 67; r1246 c358 + r7c3 r8c5 r7c8 r8c8 r9c8 : 16 Links; 67r4 67r6 ; 1234c3 124c5 12359c8 ;
158 : 98.7..6..7..65......5....4.8..3..9...2.....8......8..16...37..8..98....6......7.. ;4;3;10.3;1.2;1.2;fl; 679;tr; 7; MSLS 1 : Base 67; r1246 c358 + r7c3 r8c5 r7c8 r8c8 r9c8 : 16 Links; 67r4 67r6 ; 1234c3 124c5 12359c8 ;
159 : 98.7..6..7..65......5....4.6...37..8..98....6..8...7...2.....8....3..9.......8..1 ;4;3;10.3;1.2;1.2;fl; 679;tr; 7; MSLS 1 : Base 67; r1289 c358 + r4c3 r5c5 r4c8 r5c8 r6c8 : 16 Links; 67r8 67r9 ; 1234c3 124c5 12359c8 ;
160 : 98.7..6..7..6..9....6.5....8...7..9....8....4....968..4..9..7....3.2.........7..1 ;4;3;10.3;1.2;1.2;fl; 789;tr; 7; MSLS 6 : Base 78; r1467 c349 + r2c3 r3c4 r8c4 r9c4 r2c9 : 15 Links; 7r6 8r7 ; 1245c3 12345c4 2356c9 ;
161 : 98.7..6..7..6..5...4..8....5....7.93..79...6.....5.7..3..5..9....9.....2....1.... ;2;3;10.3;1.2;1.2;fl; 567;tr; 7; MSLS 3 : Base 67; r457 c259 + r2c2 r1c5 : 9 Links; 6r4 67r7 ; 123c2 234c5 ;
162 : 98.7..6..7..6..5....4.8..7.6......5..39...7....73....63..5..2....2...........2.1. ;4;3;10.3;1.2;1.2;fl; 356;tr; 8; 8 + 1
163 : 98.7..6..7..6..5......94.8.6....7.93...3...5.....6.7..3..5..9...2......5..9.1.... ;2;4;10.3;1.2;1.2;fl; 1248;tr; 14; 29 + 1
164 : 98.7..6..7..5..98.....8...45....7.6...3...7.....3...593..9..5...2..1......9...... ;2;3;10.3;1.2;1.2;fl; 359;tr; 9; MSLS 1 : Base 35; r12579 c2568 + r4c2 r6c2 r4c5 r6c5 r6c6 : 23 Links; 3r1 3r2 5r5 35r9 ; 14679c2 24679c5 12468c6 124c8 ;
165 : 98.7..6..7..5..9...6..8..4.3..6..5....6.....2.....1....379....6....6.7......5...9 ;4;3;10.3;1.2;1.2;fl; 579;tr; 7; MSLS 1 : Base 79; r1245 c258 + r9c2 r7c5 r7c8 r8c8 r9c8 : 16 Links; 79r4 79r5 ; 124c2 1234c5 12358c8 ;
166 : 98.7..6..7..5..9...6..8..4.3.....5....6.....2.....1.6..379.........6.7......5...9 ;4;3;10.3;1.2;1.2;fl; 579;tr; 7; MSLS 1 : Base 79; r1245 c258 + r9c2 r7c5 r7c8 r8c8 r9c8 : 16 Links; 79r4 79r5 ; 124c2 1234c5 12358c8 ;
167 : 98.7..6..7..5..9...5..8..4.5....7.69.3....7.....9...5.3..6..5......5...2.....1... ;4;3;10.3;1.2;1.2;fl; 679;tr; 7; MSLS 1 : Base 79; r1279 c258 + r4c2 r4c5 r5c5 r6c5 r5c8 : 16 Links; 79r7 79r9 ; 124c2 12346c5 1238c8 ;
168 : 98.7..6..7..5..9...5..8..4.5....7.6..39...7.....9...5.3..6..5......5...2.....1... ;4;3;10.3;1.2;1.2;fl; 679;tr; 7; MSLS 1 : Base 79; r1279 c258 + r4c2 r4c5 r5c5 r6c5 r5c8 : 16 Links; 79r7 79r9 ; 124c2 12346c5 1238c8 ;
169 : 98.7..6..7..5..9....4.3....8...76....6...58....98.....5..9..7....2....1.........6 ;2;4;10.3;1.2;1.2;fl; 5789;tr; 11; MSLS 3 : Base 578; r1457 c389 + r2c3 r2c8 r2c9 : 15 Links; 5r1 5r4 7r5 8r7 ; 136c3 234c8 1234c9 ; 9b6 ;
170 : 98.7..6..7..5..9....4.3....5....7.6..92...7.....9....52..69.5.......8..........1. ;4;5;10.3;1.2;1.2;fl; 12348;tr; 22; 14 + 1
171 : 98.7..6..7..5..9......8..4.6...5...9.379....6....6.7..3..6..5....6.....2.....1... ;4;3;10.3;1.2;1.2;fl; 579;tr; 7; MSLS 1 : Base 79; r1278 c258 + r4c2 r5c5 r4c8 r5c8 r6c8 : 16 Links; 79r7 79r8 ; 124c2 1234c5 12358c8 ;
172 : 98.7..6..7..5..9......8..4.6...5...9.379.........6.7..3..6..5....6.....2.....1.6. ;4;3;10.3;1.2;1.2;fl; 579;tr; 7; MSLS 1 : Base 79; r1278 c258 + r4c2 r5c5 r4c8 r5c8 r6c8 : 16 Links; 79r7 79r8 ; 124c2 1234c5 12358c8 ;
173 : 98.7..6..7..5..9......43...8...6.....978...6..5...98..5..6..7....2..........5...1 ;4;3;10.3;1.2;1.2;fl; 789;tr; 8; MSLS 5 : Base 789; r167 c359 + r2c3 r3c3 r4c3 r5c5 r2c9 r5c9 : 15 Links; 7r6 89r7 ; 13456c3 123c5 2345c9 ;
174 : 98.7..6..7..5..9......43...8...6.....978......5...98..5..6..7....2....6.....5..1. ;4;3;10.3;1.2;1.2;fl; 789;tr; 8; MSLS 5 : Base 789; r167 c358 + r2c3 r3c3 r4c3 r5c5 r2c8 r5c8 : 15 Links; 7r6 89r7 ; 13456c3 123c5 2345c8 ;
175 : 98.7..6..7..5..9.........8.6...5.....9...64...479.....4..6..7....3....2.....1..6. ;4;4;10.3;1.2;1.2;fl; 4679;tr; 11; MSLS 1 : Base 4679; r1257 c358 + r4c3 r6c5 r6c8 : 15 Links; 4r1 46r2 7r5 9r7 ; 1258c3 238c5 135c8 ;
176 : 98.7..6..7..5..9.........4.6...7..9...9.365....59.....5..6..7...2...........1...8 ;4;3;10.3;1.2;1.2;fl; 679;tr; 9; MSLS 1 : Base 69; r257 c259 + r4c2 r6c2 r1c5 r6c5 r4c9 : 13 Links; 6r2 9r7 ; 1347c2 248c5 1234c9 ;
177 : 98.7..6..7..5..9.........4.6...7......9.365....59.....5..6..7...2......9....1...8 ;4;3;10.3;1.2;1.2;fl; 679;tr; 9; MSLS 1 : Base 69; r257 c258 + r4c2 r6c2 r1c5 r6c5 r1c8 r6c8 : 14 Links; 6r2 9r7 ; 1347c2 248c5 12378c8 ;
178 : 98.7..6..7..5..8....4.3....8......6..7.6...98.....57..6..2..9...2.....1...9.....2 ;4;5;10.3;1.2;1.2;fl; 12345;tr; 19; MSLS 1 : Base 78; r1237 c389 + r4c3 r5c3 r6c3 r6c8 r4c9 r6c9 : 17 Links; 7r3 78r7 ; 12356c3 2345c8 13459c9 ;
179 : 98.7..6..7..5..8......4..3.8...57..6..96....8......5..6..8..9....7..2...........1 ;4;5;10.3;1.2;1.2;fl; 12345;tr; 23; 0 + 1
180 : 98.7..6..7..5..4....3.2....6...57.4..9.4.........6.5..4..6..7.......8..........51 ;2;4;10.3;1.2;1.2;fl; 4567;tr; 13; *MSLS 248 : Base 57; c128 r357 + r3c4 r3c6 r3c7 r5c5 r5c6 r5c7 r7c3 r7c5 r7c9 : 16 Links; 5c1 7c8 ; 14689r3 1238r5 12389r7 ;
181 : 98.7..6..7..5..4....3.2....6...5..4..794.........6.9..4..6..7.9.....4.1........8. 2;3;10.3;1.2;1.2;fl; 679;tr; 10; MSLS 38 : Base 79; c349 r134 + r1c6 r1c8 r3c1 r3c7 r4c2 r4c7 : 13 Links; 9c4 7c9 ; 1235r1 158r3 1238r4 ;
182 : 98.7..6..7..5..4......8..3.6..9..5...2.........7..1...5...9......6.7.9.....6...54 ;1;4;10.3;1.2;1.2;fl; 5679;tr; 8; 3 + 1
183 : 98.7..6..7..5..4.........8.6...5.....794...6..4...69..4..6..7....3..........2...1 ;4;3;10.3;1.2;1.2;fl; 469;tr; 8; MSLS 5 : Base 49; c467 r349 + r3c1 r3c2 r4c2 r4c3 r4c8 r9c1 : 15 Links; 9c4 49c6 ; 1235r3 12378r4 358r9 ;
184 : 98.7..6..7..5..4.........8.6...5.....794......4...69..4..6..7....3.....6....2...1 ;4;3;10.3;1.2;1.2;fl; 469;tr; 8; MSLS 5 : Base 49; c467 r349 + r3c1 r3c2 r4c2 r4c3 r4c8 r9c1 : 15 Links; 9c4 49c6 ; 1235r3 12378r4 358r9 ;
185 : 98.7..6..7..5...8...6.....48..3...7..9..2.....1.......5....9..7.38....9....8....5 ;4;4;10.3;1.2;1.2;fl; 5789;tr; 7; 28 + 3
186 : 98.7..6..7..5...8...6.....48..3...7..2....9......1....5....9..7.38....9....8....5 ;1;4;10.3;1.2;1.2;fl; 5789;tr; 16; 28 + 5
187 : 98.7..6..7..5...8...6.....48..3...7..2...........1.5..5....9..7.38....9....8....5 ;4;4;10.3;1.2;1.2;fl; 5789;tr; 7; 360 + 3
188 : 98.7..6..7...6..9...6..57...4....3....96...5......2.....85...7...79...6.........1 ;2;3;10.3;1.2;1.2;fl; 679;tr; 8; MSLS 1 : Base 679; r1257 c269 + r3c2 r8c2 r8c6 r3c9 r8c9 : 16 Links; 7r5 69r7 ; 1235c2 1348c6 23458c9 ;
189 : 98.7..6..7...6..8...6..57...6......4..95...6...86...7..3....2....78...5......1... ;4;3;10.3;1.2;1.2;fl; 678;tr; 8; MSLS 1 : Base 68; r1568 c169 + r3c1 r4c1 r2c6 r2c9 r3c9 : 16 Links; 8r5 6r8 ; 12345c1 2349c6 12359c9 ;
190 : 98.7..6..7...5..8...5...9..43....2....98...7...7.3....1....4.....85...9.........1 ;1;4;10.3;1.2;1.2;fl; 5789;tr; 8; MSLS 5 : Base 5789; r35689 c12567 + r2c2 r1c5 r1c6 r2c7 : 26 Links; 8r3 5r5 5r6 7r8 5789r9 ; 236c1 1246c2 1246c5 1236c6 134c7 ;
191 : 98.7..6..7...5..4...6..8..98....7.63..3.4.7...........6..2......7...3.96......1.. ;4;3;10.3;1.2;1.2;fl; 679;tr; 8; 11 + 1
192 : 98.7..6..7...5......4..9.3.4.......2.9...348...3.....63....794..4......7....1.... ;4;3;10.3;1.2;1.2;fl; 479;tr; 7; MSLS 1 : Base 79; r1458 c358 + r2c3 r7c3 r3c5 r7c5 r2c8 r9c8 : 16 Links; 79r4 7r5 9r8 ; 12568c3 268c5 1256c8 ;
193 : 98.7..6..7.....8....5.4....6....3....9..673.....9...2.3..8..9....8..6.1.....3.... ;2;5;10.3;1.2;1.2;fl; 12458;tr; 18; MSLS 6 : Base 367; r12457 c389 + r2c4 : 16 Links; 3r1 36r2 7r4 6r7 ; 124c3 45c8 1245c9 ; 8b6 9b6 ;
194 : 98.7..6..7......98..5.....43...2.....7.9...6......1....9.8....6..1.3.7.......5.4. ;2;4;10.3;1.2;1.2;fl; 6789;tr; 12; MSLS 1 : Base 678; r257 c356 + r1c3 r1c5 r1c6 : 12 Links; 6r2 8r5 7r7 ; 234c3 145c5 234c6 ;
195 : 98.7..6..7......9...6.5....4....3.....96..38...85...7..2.........79...6.......8.1 ;2;4;10.3;1.2;1.2;fl; 6789;tr; 16; 25 + 1
196 : 98.7..6..7......9.........765.9...7...46.........3...656.8....9..2..18.......6.5. ;4;5;10.3;1.2;1.2;fl; 12348;tr; 17; 0 + 6
197 : 98.7..6..7......9.........765.9...7...46.........3....56.8....9..2..186......6.5. ;4;5;10.3;1.2;1.2;fl; 12348;tr; 17; 0 + 8
198 : 98.7..6..7......9.........765.8....9..4.3.86.....6..5.56.9...7...26..........1... ;4;5;10.3;1.2;1.2;fl; 12348;tr; 17; 0 + 8
199 : 98.7..6..7......9.........765.8....9..4.3.8......6..5.56.9...7...26..........1..6 ;4;5;10.3;1.2;1.2;fl; 12348;tr; 17; 0 + 8
200 : 98.7..6..7......5.........464..7.9....96.......3..9.2.46...78.....84........6...1 ;4;5;10.3;1.2;1.2;fl; 12359;tr; 20; 23 + 6
201 : 98.7..6..7......5.........464..7.8.....8.4........6..346...79....96.......2.9..1. ;4;5;10.3;1.2;1.2;fl; 12359;tr; 20; 23 + 6
202 : 98.7..6..7..........5....9.64..7.8.....4..........8..346....9....7.4..2...196..7. ;4;3;10.3;1.2;1.2;fl; 467;tr; 7; MSLS 4 : Base 46; r1245 c268 + r3c2 r6c2 r9c2 r8c6 r9c6 r7c8 : 16 Links; 4r2 6r5 ; 12357c2 12359c6 1358c8 ;
203 : 98.7..6..7..........5....9.64....9....7.4..3...296..7.46..7.8.....4..........8..1 ;4;3;10.3;1.2;1.2;fl; 467;tr; 7; MSLS 4 : Base 46; r1268 c268 + r3c2 r9c2 r5c6 r7c6 r4c8 r7c8 : 16 Links; 4r2 6r8 ; 12357c2 12359c6 1258c8 ;
204 : 98.7..6..5.7.6........8....84..9.7....54.7..........3..9...84....2....7....97...1 ;4;3;10.3;1.2;1.2;fl; 489;tr; 7; MSLS 1 : Base 89; c1279 r258 + r2c4 r5c5 r8c4 r8c5 r8c6 : 16 Links; 89c7 89c9 ; 123r2 1236r5 13456r8 ;
205 : 98.7..6..5..9..7....4.8....6....9.3..5....9.....5...762..6..5...9...7..2....12... ;4;3;10.3;1.2;1.2;fl; 569;tr; 7; MSLS 12 : Base 69; c1249 r349 + r3c7 r4c3 r4c5 r4c7 r9c7 : 15 Links; 6c2 9c9 ; 1237r3 12478r4 3478r9 ;
206 : 98.7..6..5..9..7....4.3....6..5..4...2.....1......8...4....9..6...6...74.....59.. ;4;3;10.3;1.2;1.2;fl; 459;tr; 7; MSLS 3 : Base 59; r1247 c268 + r3c2 r9c2 r3c6 r5c6 r8c6 r9c8 : 16 Links; 9r4 5r7 ; 1367c2 123467c6 2348c8 ;
207 : 98.7..6..5..9..7....4....3.7..2..5...1.....7.........82...9..5..9.5...6.....279.. ;4;3;10.3;1.2;1.2;fl; 259;tr; 8; MSLS 2 : Base 25; c1579 r358 + r3c4 r5c4 r8c3 r8c6 : 15 Links; 5c5 2c7 2c9 ; 168r3 3468r5 13478r8 ;
208 : 98.7..6..5..9..7....4....3.7..2..5...1...........7...82...9..5..9.5...6.....279.. ;4;3;10.3;1.2;1.2;fl; 259;tr; 8; MSLS 2 : Base 25; c1579 r358 + r3c4 r5c4 r8c3 r8c6 : 15 Links; 5c5 2c7 2c9 ; 168r3 3468r5 13478r8 ;
209 : 98.7..6..5..9..7......8....7....9.....6.5.9.....6...746..5..4...3..2...........1. ;1;4;10.3;1.2;1.2;fl; 5679;tr; 9; MSLS 2 : Base 1238; r689 c13467 + r6c5 : 15 Links; 1238r6 18r8 238r9 ; 59c3 6c6 5c7 ; 4b7 4b8 ;
210 : 98.7..6..5..9..7......8....7....9.....6.5.9.....6...746..5..4...3..2............1 ;1;4;10.3;1.2;1.2;fl; 5679;tr; 9; MSLS 12 : Base 1238; r689 c13467 + r6c5 : 15 Links; 1238r6 18r8 238r9 ; 59c3 6c6 5c7 ; 4b7 4b8 ;
211 : 98.7..6..5..9..7......6..8.7...9.....6..5.9.....6...476..5..4...5......3..2..1... ;1;3;10.3;1.2;1.2;fl; 569;tr; 6; MSLS 2 : Base 59; r12458 c389 + r3c3 r7c3 r7c8 r7c9 : 17 Links; 5r1 5r4 9r8 ; 13478c3 1237c8 1248c9 ; 6b6 ;
212 : 98.7..6..5..9..4....3....8.7..2..5...2...........1..626....9....5..7.9.....5...46 ;2;3;10.3;1.2;1.2;fl; 579;tr; 12; MSLS 1 : Base 79; c1257 r369 + r3c4 r3c6 r6c4 r9c6 : 15 Links; 79c2 7c7 ; 12456r3 348r6 1238r9 ;
213 : 98.7..6..5..9..4......3..8.7...5.....6...95.....6...746..5..7...92...........1... ;2;4;10.3;1.2;1.2;fl; 5679;tr; 16; 25 + 1
214 : 98.7..6..5..9............437...5.....2..9.5.....2...762..5..7....8.....5.....1... ;4;4;10.3;1.2;1.2;fl; 2579;tr; 8; 1 + 2
215 : 98.7..6..5..8...4...3.6...86....7.2..3..8...9.....1...3...9...6.5.....1...6..24.. ;1;4;10.3;1.2;1.2;fl; 3689;tr; 16; 60 + 2 : 19 Truths = { 1245R1 12457R3 12457R5 12457R7 } 19 Links = { 45c6 57c8 1n359 3n1247 5n1347 7n2347 }
216 : 98.7..6..5..6..7......9..847..5..9...5...3....2......12...5..7....2....9....672.. :1;3;10.3;1.2;1.2;fl; 257;tr; 6; 0 + 0
217 : 98.7..6..5..6..7......9..847..5..9...5......3.2...1...2...5..7....2....9....672.. :1;3;10.3;1.2;1.2;fl; 257;tr; 6; 0 + 0
218 : 98.7..6..5..6..7......9..846..5..9...5...3....2......12...5..6....2....9....762.. :1;3;10.3;1.2;1.2;fl; 256;tr; 6; 0 + 0
219 : 98.7..6..5..6..7......9..846..5..9...5......3.2...1...2...5..6....2....9....762.. ;1;3;10.3;1.2;1.2;fl; 256;tr; 6; 0 + 0
220 : 98.7..6..5..6..7......8..4.7..5..9...5.....3...9..2...1....5..6...1...9.....671.. ;2;3;10.3;1.2;1.2;fl; 567;tr; 7; 27 + 1
221 : 98.7..6..5..6..7......8..4.6..5..9...5.....3...9..2...1....5..7...1...9.....761.. ;2;3;10.3;1.2;1.2;fl; 567;tr; 7; 27 + 1
222 : 98.7..6..5..6..4....3....8.7...5...9.5.9....4....765..6..5..9.......2...........1 ;4;3;10.3;1.2;1.2;fl; 579;tr; 7; MSLS 6 : Base 57; r1278 c569 + r3c5 r5c5 r4c6 r5c6 r6c9 : 15 Links; 5r1 7r7 ; 123489c5 1348c6 238c9 ;
223 : 98.7..6..5...9..7...7..6...4..........6.7.5.....3.4.2..1.2....3..5.6.7.........51 ;2;3;10.3;1.2;1.2;fl; 579;tr; 9; MSLS 3 : Base 57; r1459 c268 + r3c2 r8c2 r2c6 r8c6 r3c8 r8c8 : 16 Links; 5r4 7r9 ; 2349c2 12389c6 13489c8 ;
224 : 98.7..6..5...9..4......8.3.4.........7..6.9....2..7.5.2...1.....6...98.....6....3 ;1;4;10.3;1.2;1.2;fl; 6789;tr; 11; MSLS 7 : Base 679; c2459 r467 + r4c6 r4c7 r6c7 r7c6 r7c7 : 16 Links; 9c2 9c4 67c9 ; 1235r4 134r6 3458r7 ; 8b5 ;
225 : 98.7..6..5...8..7...7..6...4.......3..8.6.7.......2.4..1.........9.7.8.....3.1.2. ;1;3;10.3;1.2;1.2;fl; 678;tr; 8; MSLS 1 : Base 67; c2347 r2469 + r2c6 r2c9 r4c5 r6c5 r9c5 : 20 Links; 67c2 6c3 ; 12349r2 1259r4 1359r6 459r9 ; 8b5 ;
226 : 98.7..6..5...8......76.....4..3...2...8.647..........4.1.8....3..9.7.8.......2.1. ;4;3;10.3;1.2;1.2;fl; 678;tr; 9; MSLS 1 : Base 678; r2378 c1689 + r5c1 r1c6 r1c8 r5c8 r1c9 r5c9 : 20 Links; 7r2 8r3 67r7 6r8 ; 123c1 1359c6 3459c8 1259c9 ;
227 : 98.7..6..5............9....8....4.3..6.2..1...2.1..8...1...7..6...6...8.....217.. ;4;3;10.3;1.2;1.2;fl; 267;tr; 6; 37 + 0
228 : 98.7..6....76...5.....9....4...6.5...3.2.4.....9.7.8....6.5.7.....9.6..........1. ;4;3;10.3;1.2;1.2;fl; 569;tr; 8; MSLS 3 : Base 69; r1467 c248 + r2c2 r8c2 r3c4 r9c4 r3c8 r8c8 : 16 Links; 6r6 9r7 ; 1247c2 13458c4 23478c8 ;
229 : 98.7..6....76...5.....9....4...6.5...3.2.4.....9.7.8....6.5.7.....9..........7.1. ;4;3;10.3;1.2;1.2;fl; 569;tr; 8; MSLS 3 : Base 69; r1467 c248 + r2c2 r8c2 r3c4 r9c4 r3c8 r8c8 : 16 Links; 6r6 9r7 ; 1247c2 13458c4 23478c8 ;
230 : 98.7..6....76...5.....9....4...6.5...3.2.4.....9.7.8....6.5.7.....9............16 ;4;3;10.3;1.2;1.2;fl; 569;tr; 8; MSLS 3 : Base 69; r1467 c248 + r2c2 r8c2 r3c4 r9c4 r3c8 r8c8 : 16 Links; 6r6 9r7 ; 1247c2 13458c4 23478c8 ;
231 : 98.7..6....7.9..5...4.....867...98....386............24.8..1....9..8.1.......7... ;4;3;10.3;1.2;1.2;fl; 679;tr; 7; MSLS 1 : Base 79; c1278 r257 + r3c7 r3c8 r2c4 r2c9 r5c6 r7c5 : 16 Links; 79c7 79c8 ; 12346r2 1245r5 235r7 ;
232 : 98.7..6....7.6.........5.4.76..8.9....39..........7...65...97....98....2.......1. ;4;3;10.3;1.2;1.2;fl; 568;tr; 7; MSLS 1 : Base 56; c23567 r589 + r8c1 r9c1 : 15 Links; 5c5 6c6 5c7 ; 124r5 1347r8 23478r9 ;
233 : 98.7..6....7....5.....4....8.........6...3.2...16..7..6..9..1...1...4..5....2...3 ;2;4;10.3;1.2;1.2;fl; 2345;tr; 18; MSLS 1 : Base 1789; r1467 c25689 + r2c2 r3c2 : 20 Links; 1r1 179r4 89r6 78r7 ; 2345c2 35c5 25c6 34c8 24c9 ;
234 : 98.7..6.....6...5.....9..7.7..4.......8.5.........7..3.7...2.1..16...9....9.6.5.. ;4;3;10.3;1.2;1.2;fl; 569;tr; 7; MSLS 1 : Base 69; r1245 c268 + r9c2 r3c6 r8c6 r9c6 r8c8 r9c8 : 16 Links; 69r4 69r5 ; 234c2 13458c6 2348c8 ;
235 : 98.7.....7...6......5..97..5....49...9.3...7...4.8..2..5...74.....6...1.....3...2 ;4;3;10.3;1.2;1.2;fl; 459;tr; 6; 9 + 2
236 : 98.7.....6...5.9....5....7.4...3...2..75..8.......4.5..1..2......98..5.........31 ;1;3;10.3;1.2;1.2;fl; 578;tr; 11; MSLS 39 : Base 78; c34567 r479 + r6c5 r4c8 r9c2 : 16 Links; 8c3 7c5 7c6 7c7 ; 169r4 346r7 2469r9 ; 5b8 8b5 ;
237 : 98.7.....6.....98...5.....7.4..3..6..3...2..1..96.......85..7......1...3.....4.2. ;1;4;10.3;1.2;1.2;fl; 1234;tr; 18; MSLS 2 : Base 1234; r34589 c1347 + r3c2 r3c8 : 20 Links; 1234r3 12r4 4r5 24r8 13r9 ; 578c1 7c3 89c4 568c7 ;
238 : 98.7.....6.....7....7.65...4...8......86..9.......3.42.1...6.3...98..6......2...1 ;1;3;10.3;1.2;1.2;fl; 679;tr; 10; MSLS 8 : Base 79; r23458 c2689 + r1c6 r1c8 r1c9 : 21 Links; 79r4 7r5 7r8 ; 2345c2 124c6 1256c8 3456c9 ; 9b3 8b3 ;
239 : 98.7.......7.65.........7..74..8......96..8.........433....2.1...89..6..........2 ;1;3;10.3;1.2;1.2;fl; 789;tr; 8; MSLS 5 : Base 79; r1458 c689 + r3c8 r3c9 : 14 Links; 9r4 7r5 7r8 ; 134c6 2356c8 1456c9 ;
240 : 98.7.......6.5.9.........4.6..3....2.5..1.6....1.....41...6.5...6......3..52.7... ;4;3;10.3;1.2;1.2;fl; 156;tr; 7; MSLS 1 : Base 16; r237 c249 + r4c2 r6c2 r9c2 r5c4 r5c9 : 14 Links; 1r2 16r3 ; 23479c2 489c4 789c9 ;
241 : 9..8..7...8..9..6...5..4..98..3..6...3..2..9...4..5...2..1...3..1..3.8.......2..6 ;4;3;10.3;1.2;1.2;fl; 348;tr; 7; MSLS 1 : Base 38; r1257 c369 + r4c3 r8c3 r4c6 r8c6 r4c9 r8c9 : 18 Links; 3r1 3r2 8r5 8r7 ; 12679c3 1679c6 12457c9 ;

Leren
Leren
 
Posts: 2929
Joined: 03 June 2012

Re: 【TECHNIQUE SHARE】ALS NET

Postby borescoper » Wed Jun 15, 2016 5:07 am

Leren wrote:On further investigation it now seems that what you are describing is close to, or identical to, Multi-Sector Locked sets, or MSLS for short.

This is a relatively advanced technique, although your example puzzle was a relatively easy one to solve, and could be done by other more routine moves.

Here is my MSLS version of your first puzzle:

Code: Select all
*--------------------------------------------------------------------------------*
| 268     1468    247-16   | 12568   1567    1568     | 247     3       9        |
| 2689    14689   247-16   | 12689   3       1689     | 247     1246    5        |
| 5       169     3        | 1269    4       1679     | 8       1267    127      |
|--------------------------+--------------------------+--------------------------|
| 23      345     8        | 35      9       357      | 1       247     6        |
| 369     7      *456      | 13568   156     2        | 359-4  *489    *348      |
| 1       3569   *256      | 4       567     3568     | 3579-2 *289    *238      |
|--------------------------+--------------------------+--------------------------|
| 7       136     9        | 136     8       1346     | 234     5       24-13    |
| 38      2      *15       | 39      15      349      | 6       47-89   47-13    |
| 4       13568  *156      | 7       2       13569    | 39     *189    *138      |
*--------------------------------------------------------------------------------*

MSLS 1 : Base 24; r569 c389 + r8c3 : 10 Links; 4r5 2r6 ; 156c3 89c8 38c9 ; 1b9 ; => - 16 r12c3, - 4 r5c7, - 2 r6c7, -13 r7c9, - 89 r8c8, -38 r8c9

JC Van Hay's Puzzles were harder and don't appear to be solvable by more routine methods.

Here is a MSLS move for his second puzzle ;

Code: Select all
*--------------------------------------------------------------------------------*
|*124     469-12  3        |*125     45-12   7        |*126     569-12  8        |
| 7       124     1249     | 8       12345   6        | 123     1235    1359     |
| 5       8       126      | 9       123     23       | 4       7       136      |
|--------------------------+--------------------------+--------------------------|
|*234     459-23  8        |*235     569-23  1        |*236     456-23  7        |
| 123     12345   12459    | 7       2356    2359     | 8       123456  13456    |
| 6       7       125      | 4       8       235      | 9       1235    135      |
|--------------------------+--------------------------+--------------------------|
|*134     456-13  7        |*135     59-13   8        |*136     469-23  2        |
| 8       123456  12456    | 123-5   1235    23459    | 7       1346    13469    |
| 9       1234    124      | 6       7       234      | 5       8       134      |
*--------------------------------------------------------------------------------*

MSLS 1 : Base 123; r147 c147 : 9 Links; 12r1 23r4 13r7 ; 4c1 5c4 6c7 ; => - 12 r1c258, -23 r4c258, -13 r7c258, - 5 r8c4.

This topic hasn't been active for about 3 years, which is why I overlooked it at first. Like most topics on this forum it's not well documented.

The best thing you can do is follow JC Van Hay's link, or put "Multi", "Sector" and "locked", or "MSLS" into the search box.

If you are interested, here is a list of puzzles which contain MSLS moves. The location of each move is listed with each puzzle. Click on the 'Show" link to display the list.

Leren


first of all I really appreciate you for helping me. from your reply i know that:
1.the official name of this technique is Multi-Sector Locked Sets(MSLS).
2.this technique is NOT so rare as i thought before.
3.there are lots of examples good than mine.
a few days ago, my friend introduced this forum to me, he said there are great amount of good techniques here. I read the top topic, the collection of solving techniques, learn a lot, but most detail content can't be understand(because of language barrier). so i think maybe i can post a topic, sharing my technique, maybe can help someone who don't know it; or some kind people will point out the inadequacies. so i write this 2 topics(maybe 2 more,LOL), consulting a dictionary while writing. and as i expected, you and Eleven and JC come here teaching me a lot of things:)

about this technique and the two puzzles i posted:
i found this technique in July 28, 2014(now i know it's not a new technique), and post a topic on a forum in my country. at first, no examples found. I deliberately seek it while solving puzzles but nothing gained. so i considered it's "very rare" apearence, and designed two puzzles (puzzle 1 is based on another puzzle, some givens modified).i'm not good at designing, so only 2 puzzles i found(now i know there are so many).

at last:
puzzle 1(by solving with MSLS), i have some different opinion in column 3, i think we can consider it as"r569 c389", 9 Links; 4r5 2r6 1r9; 56c3 89c8 38c9 ; then r8c3(5) eliminated and r8c3=1. :)

thank you again!

borescoper
borescoper
 
Posts: 15
Joined: 11 June 2016

Re: 【TECHNIQUE SHARE】ALS NET

Postby Leren » Wed Jun 15, 2016 7:48 am

borescoper wrote : puzzle 1(by solving with MSLS), i have some different opinion in column 3, i think we can consider it as"r569 c389", 9 Links; 4r5 2r6 1r9; 56c3 89c8 38c9 ; then r8c3(5) eliminated and r8c3=1.

Basically both MSLS are "correct", or I should say, "equivalent".

Just to prove the point I put my solver in MSLS survey mode. When it does this it records details of an MSLS pattern it finds, but ignores the eliminations and keeps looking for more. By varying some parameters I really put the solver through it's paces and found, would you believe, 203 MSLS patterns in your puzzle, which I've included here. I'm sure I could find more if I varied some parameters more widely, but my solver really slows down when I do this. You'll find that your pattern is number 33 in this list.

Hidden Text: Show
MSLS 1 : Base 24; r569 c389 + r8c3 : 10 Links; 4r5 2r6 ; 156c3 89c8 38c9 ; 1b9 ;
MSLS 2 : Base 24; r578 c389 + r9c3 r9c8 r9c9 & r6c389 : 13 Links; 4r5 2r7 & 2r6 ; 156c3 89c8 38c9 ; 471b9 ;
MSLS 3 : Base 24; r678 c389 + r9c3 r9c8 r9c9 & r5c389 : 13 Links; 2r6 2r7 & 4r5 ; 156c3 89c8 38c9 ; 471b9 ;
MSLS 4 : Base 24; r689 c389 & r5c389 : 12 Links; 2r6 4r8 & 4r5 ; 156c3 89c8 38c9 ; 17b9 ;
MSLS 5 : Base 24; r789 c789 : 7 Links; 2r7 ; ; 413789b9 ;
MSLS 6 : Base 24; r569 c3589 + r8c3 r1c5 r8c5 : 14 Links; 4r5 2r6 ; 156c3 1567c5 89c8 38c9 ; 1b9 ;
MSLS 7 : Base 24; r689 c3589 + r1c5 r5c5 & r5c389 : 16 Links; 2r6 4r8 & 4r5 ; 156c3 1567c5 89c8 38c9 ; 17b9 ;
MSLS 8 : Base 24; r5678 c389 + r9c3 r9c8 r9c9 : 13 Links; 4r5 2r6 2r7 ; 156c3 89c8 38c9 ; 471b9 ;
MSLS 9 : Base 24; r5689 c389 : 12 Links; 4r5 2r6 4r8 ; 156c3 89c8 38c9 ; 17b9 ;
MSLS 10 : Base 24; r5789 c389 & r6c389 : 13 Links; 4r5 2r7 & 2r6 ; 156c3 89c8 38c9 ; 417b9 ;
MSLS 11 : Base 24; r6789 c389 & r5c389 : 13 Links; 2r6 2r7 & 4r5 ; 156c3 89c8 38c9 ; 417b9 ;
MSLS 12 : Base 24; r5689 c3589 + r1c5 : 16 Links; 4r5 2r6 4r8 ; 156c3 1567c5 89c8 38c9 ; 17b9 ;
MSLS 13 : Base 24; r5689 c3789 & r7c79 : 17 Links; 4r5 2r6 & 2r7 ; 156c3 359c7 89c8 38c9 ; 7b6 174b9 ;
MSLS 14 : Base 24; r5689 c35789 + r1c5 & r7c79 : 21 Links; 4r5 2r6 & 2r7 ; 156c3 1567c5 359c7 89c8 38c9 ; 7b6 174b9 ;
MSLS 15 : Base 24; r56789 c389 : 13 Links; 4r5 2r6 2r7 ; 156c3 89c8 38c9 ; 417b9 ;
MSLS 16 : Base 35; r124 c246 + r3c2 r3c4 r3c6 & r124c1 : 15 Links; 5r1 35r4 & 2c1 ; 14c2 2c4 7c6 ; 689b1 1689b2 ;
MSLS 17 : Base 35; r124 c1246 + r3c2 r3c4 r3c6 : 15 Links; 5r1 35r4 ; 2c1 14c2 2c4 7c6 ; 689b1 1689b2 ;
MSLS 18 : Base 35; r134 c1246 + r2c1 r2c2 r2c4 r2c6 : 15 Links; 5r1 35r4 ; 2c1 14c2 2c4 7c6 ; 689b1 1689b2 ;
MSLS 19 : Base 35; r234 c1246 + r1c1 r1c2 & r1c46 : 15 Links; 35r4 & 5r1 ; 2c1 14c2 2c4 7c6 ; 689b1 1689b2 ;
MSLS 20 : Base 35; r1234 c126 + r4c4 & r123c4 : 15 Links; 5r1 35r4 & 2c4 ; 2c1 4c2 7c6 ; 6891b1 1689b2 ;
MSLS 21 : Base 35; r1234 c246 & r124c1 : 15 Links; 5r1 35r4 & 2c1 ; 14c2 2c4 7c6 ; 689b1 1689b2 ;
MSLS 22 : Base 35; r1234 c1246 : 15 Links; 5r1 35r4 ; 2c1 14c2 2c4 7c6 ; 689b1 1689b2 ;
MSLS 23 : Base 38; r2356 c789 + r1c7 r4c8 : 12 Links; ; 5c7 6c8 ; 1247b3 389247b6 ;
MSLS 24 : Base 39; r2356 c789 + r1c7 r4c8 : 12 Links; ; 5c7 6c8 ; 1247b3 398247b6 ;
MSLS 25 : Base 56; r23569 c789 + r1c7 r7c7 r4c8 r8c8 r7c9 r8c9 : 19 Links; ; 23479c7 124789c8 123478c9 ; 6b3 5b6 ;
MSLS 26 : Base 58; r25689 c789 + r1c7 r7c7 r3c8 r4c8 r3c9 r7c9 : 19 Links; ; 23479c7 124679c8 12347c9 ; 58b6 8b9 ;
MSLS 27 : Base 58; r35689 c789 + r1c7 r2c7 r7c7 r2c8 r4c8 r7c9 : 19 Links; ; 23479c7 124679c8 12347c9 ; 58b6 8b9 ;
MSLS 28 : Base 59; r25689 c789 + r1c7 r7c7 r3c8 r4c8 r3c9 r7c9 : 19 Links; ; 2347c7 124678c8 123478c9 ; 59b6 9b9 ;
MSLS 29 : Base 59; r35689 c789 + r1c7 r2c7 r7c7 r2c8 r4c8 r7c9 : 19 Links; ; 2347c7 124678c8 123478c9 ; 59b6 9b9 ;
MSLS 30 : Base 89; r25689 c789 + r1c7 r7c7 r3c8 r4c8 r3c9 r7c9 : 19 Links; ; 23457c7 12467c8 12347c9 ; 89b6 89b9 ;
MSLS 31 : Base 89; r35689 c789 + r1c7 r2c7 r7c7 r2c8 r4c8 r7c9 : 19 Links; ; 23457c7 12467c8 12347c9 ; 89b6 89b9 ;
MSLS 32 : Base 124; r568 c389 & r9c389 : 12 Links; 4r5 2r6 14r8 & 1r9 ; 56c3 89c8 38c9 ; 7b9 ;
MSLS 33 : Base 124; r569 c389 : 9 Links; 4r5 2r6 1r9 ; 56c3 89c8 38c9 ;
MSLS 34 : Base 124; r689 c389 & r5c389 : 12 Links; 2r6 14r8 1r9 & 4r5 ; 56c3 89c8 38c9 ; 7b9 ;
MSLS 35 : Base 124; r789 c789 : 7 Links; 2r7 ; ; 143789b9 ;
MSLS 36 : Base 124; r5689 c389 : 12 Links; 4r5 2r6 14r8 1r9 ; 56c3 89c8 38c9 ; 7b9 ;
MSLS 37 : Base 124; r5789 c389 & r6c389 : 13 Links; 4r5 2r7 & 2r6 ; 56c3 89c8 38c9 ; 1b7 417b9 ;
MSLS 38 : Base 124; r6789 c389 & r5c389 : 13 Links; 2r6 2r7 & 4r5 ; 56c3 89c8 38c9 ; 1b7 417b9 ;
MSLS 39 : Base 124; r56789 c389 : 13 Links; 4r5 2r6 2r7 ; 56c3 89c8 38c9 ; 1b7 417b9 ;
MSLS 40 : Base 135; r1234 c126 + r4c4 & r123c4 : 15 Links; 5r1 35r4 & 2c4 ; 2c1 4c2 7c6 ; 1689b1 1689b2 ;
MSLS 41 : Base 135; r1234 c246 & r124c1 : 15 Links; 5r1 35r4 & 2c1 ; 4c2 2c4 7c6 ; 1689b1 1689b2 ;
MSLS 42 : Base 135; r1234 c1246 : 15 Links; 5r1 35r4 ; 2c1 4c2 2c4 7c6 ; 1689b1 1689b2 ;
MSLS 43 : Base 138; r2356 c789 + r1c7 r4c8 : 12 Links; ; 5c7 6c8 ; 1247b3 389247b6 ;
MSLS 44 : Base 139; r2356 c789 + r1c7 r4c8 : 12 Links; ; 5c7 6c8 ; 1247b3 398247b6 ;
MSLS 45 : Base 159; r123 c456 : 7 Links; 5r1 ; 2c4 ; 16978b2 ;
MSLS 46 : Base 234; r789 c789 : 7 Links; 2r7 ; ; 341789b9 ;
MSLS 47 : Base 234; r5789 c389 + r7c7 & r6c389 : 14 Links; 4r5 2r7 & 2r6 ; 156c3 89c8 8c9 ; 3b6 3417b9 ;
MSLS 48 : Base 234; r6789 c389 + r7c7 & r5c389 : 14 Links; 2r6 2r7 & 4r5 ; 156c3 89c8 8c9 ; 3b6 3417b9 ;
MSLS 49 : Base 247; r578 c389 + r9c3 r9c8 r9c9 & r6c389 : 13 Links; 4r5 2r7 7r8 & 2r6 ; 156c3 89c8 38c9 ; 41b9 ;
MSLS 50 : Base 247; r678 c389 + r9c3 r9c8 r9c9 & r5c389 : 13 Links; 2r6 2r7 7r8 & 4r5 ; 156c3 89c8 38c9 ; 41b9 ;
MSLS 51 : Base 247; r689 c389 & r5c389 : 12 Links; 2r6 47r8 & 4r5 ; 156c3 89c8 38c9 ; 1b9 ;
MSLS 52 : Base 247; r789 c789 : 7 Links; 2r7 7r8 ; ; 41389b9 ;
MSLS 53 : Base 247; r5678 c389 + r9c3 r9c8 r9c9 : 13 Links; 4r5 2r6 2r7 7r8 ; 156c3 89c8 38c9 ; 41b9 ;
MSLS 54 : Base 247; r5689 c389 : 12 Links; 4r5 2r6 47r8 ; 156c3 89c8 38c9 ; 1b9 ;
MSLS 55 : Base 247; r5789 c389 & r6c389 : 13 Links; 4r5 2r7 7r8 & 2r6 ; 156c3 89c8 38c9 ; 41b9 ;
MSLS 56 : Base 247; r6789 c389 & r5c389 : 13 Links; 2r6 2r7 7r8 & 4r5 ; 156c3 89c8 38c9 ; 41b9 ;
MSLS 57 : Base 247; r5679 c3789 + r8c3 & r8c89 : 17 Links; 4r5 27r6 2r7 & 7r8 ; 156c3 359c7 89c8 38c9 ; 14b9 ;
MSLS 58 : Base 247; r5689 c3789 & r7c79 : 17 Links; 4r5 27r6 7r8 & 2r7 ; 156c3 359c7 89c8 38c9 ; 14b9 ;
MSLS 59 : Base 247; r5689 c35789 & r7c79 : 20 Links; 4r5 27r6 7r8 & 2r7 ; 156c3 156c5 359c7 89c8 38c9 ; 14b9 ;
MSLS 60 : Base 247; r56789 c389 : 13 Links; 4r5 2r6 2r7 7r8 ; 156c3 89c8 38c9 ; 41b9 ;
MSLS 61 : Base 248; r569 c389 + r8c3 : 10 Links; 4r5 2r6 8r9 ; 156c3 9c8 3c9 ; 8b6 1b9 ;
MSLS 62 : Base 248; r689 c389 & r5c389 : 12 Links; 2r6 4r8 & 4r5 ; 156c3 9c8 3c9 ; 8b6 817b9 ;
MSLS 63 : Base 248; r789 c789 : 7 Links; 2r7 ; ; 481379b9 ;
MSLS 64 : Base 248; r569 c3589 + r8c3 r1c5 r8c5 : 14 Links; 4r5 2r6 8r9 ; 156c3 1567c5 9c8 3c9 ; 8b6 1b9 ;
MSLS 65 : Base 248; r689 c3589 + r1c5 r5c5 & r5c389 : 16 Links; 2r6 4r8 & 4r5 ; 156c3 1567c5 9c8 3c9 ; 8b6 817b9 ;
MSLS 66 : Base 248; r5689 c358 + r1c5 & r5689c9 : 16 Links; 4r5 2r6 4r8 & 3c9 ; 56c3 1567c5 9c8 ; 8b6 1b7 871b9 ;
MSLS 67 : Base 248; r5689 c359 + r1c5 & r5689c8 : 16 Links; 4r5 2r6 4r8 & 9c8 ; 56c3 1567c5 3c9 ; 8b6 1b7 871b9 ;
MSLS 68 : Base 248; r5689 c389 : 12 Links; 4r5 2r6 4r8 ; 156c3 9c8 3c9 ; 8b6 817b9 ;
MSLS 69 : Base 248; r5789 c389 & r6c389 : 13 Links; 4r5 2r7 & 2r6 ; 156c3 9c8 3c9 ; 8b6 4817b9 ;
MSLS 70 : Base 248; r6789 c389 & r5c389 : 13 Links; 2r6 2r7 & 4r5 ; 156c3 9c8 3c9 ; 8b6 4817b9 ;
MSLS 71 : Base 248; r5689 c3589 + r1c5 : 16 Links; 4r5 2r6 4r8 ; 156c3 1567c5 9c8 3c9 ; 8b6 817b9 ;
MSLS 72 : Base 248; r5689 c3789 & r7c79 : 17 Links; 4r5 2r6 & 2r7 ; 156c3 359c7 9c8 3c9 ; 87b6 8174b9 ;
MSLS 73 : Base 248; r5689 c35789 + r1c5 & r7c79 : 21 Links; 4r5 2r6 & 2r7 ; 156c3 1567c5 359c7 9c8 3c9 ; 87b6 8174b9 ;
MSLS 74 : Base 248; r56789 c379 & r5689c8 : 17 Links; 4r5 2r6 2r7 & 9c8 ; 56c3 3579c7 3c9 ; 8b6 1b7 4871b9 ;
MSLS 75 : Base 248; r56789 c389 : 13 Links; 4r5 2r6 2r7 ; 156c3 9c8 3c9 ; 8b6 4817b9 ;
MSLS 76 : Base 249; r789 c789 : 7 Links; 2r7 ; ; 491378b9 ;
MSLS 77 : Base 249; r5689 c3789 & r7c79 : 17 Links; 4r5 2r6 & 2r7 ; 156c3 35c7 8c8 38c9 ; 97b6 9174b9 ;
MSLS 78 : Base 249; r5689 c35789 + r1c5 & r7c79 : 21 Links; 4r5 2r6 & 2r7 ; 156c3 1567c5 35c7 8c8 38c9 ; 97b6 9174b9 ;
MSLS 79 : Base 249; r56789 c379 & r5689c8 : 17 Links; 4r5 2r6 2r7 & 8c8 ; 56c3 357c7 38c9 ; 9b6 1b7 4791b9 ;
MSLS 80 : Base 249; r56789 c389 & r79c7 : 15 Links; 4r5 2r6 2r7 & 3c7 ; 56c3 8c8 38c9 ; 9b6 1b7 4917b9 ;
MSLS 81 : Base 289; r456 c789 : 7 Links; ; 5c7 ; 428937b6 ;
MSLS 82 : Base 289; r789 c789 : 7 Links; 2r7 ; ; 489137b9 ;
MSLS 83 : Base 356; r1234 c126 + r4c4 & r123c4 : 15 Links; 5r1 35r4 & 2c4 ; 2c1 4c2 7c6 ; 6891b1 6189b2 ;
MSLS 84 : Base 356; r1234 c246 & r124c1 : 15 Links; 5r1 35r4 & 2c1 ; 14c2 2c4 7c6 ; 689b1 6189b2 ;
MSLS 85 : Base 356; r1234 c1246 : 15 Links; 5r1 35r4 ; 2c1 14c2 2c4 7c6 ; 689b1 6189b2 ;
MSLS 86 : Base 358; r124 c246 + r3c2 r3c4 r3c6 & r124c1 : 15 Links; 58r1 8r2 35r4 & 2c1 ; 14c2 2c4 7c6 ; 69b1 169b2 ;
MSLS 87 : Base 358; r124 c1246 + r3c2 r3c4 r3c6 : 15 Links; 58r1 8r2 35r4 ; 2c1 14c2 2c4 7c6 ; 69b1 169b2 ;
MSLS 88 : Base 358; r134 c1246 & r2c1246 : 15 Links; 58r1 35r4 & 8r2 ; 2c1 14c2 2c4 7c6 ; 69b1 169b2 ;
MSLS 89 : Base 358; r124 c2456 + r3c2 r3c4 r3c6 & r124c1 : 16 Links; 58r1 8r2 35r4 & 2c1 ; 14c2 2c4 7c6 ; 69b1 1697b2 ;
MSLS 90 : Base 358; r124 c12456 + r3c2 r3c4 r3c6 : 16 Links; 58r1 8r2 35r4 ; 2c1 14c2 2c4 7c6 ; 69b1 1697b2 ;
MSLS 91 : Base 358; r1234 c126 + r4c4 & r123c4 : 15 Links; 58r1 8r2 35r4 & 2c4 ; 2c1 4c2 7c6 ; 691b1 169b2 ;
MSLS 92 : Base 358; r1234 c246 & r124c1 : 15 Links; 58r1 8r2 35r4 & 2c1 ; 14c2 2c4 7c6 ; 69b1 169b2 ;
MSLS 93 : Base 358; r1234 c1246 : 15 Links; 58r1 8r2 35r4 ; 2c1 14c2 2c4 7c6 ; 69b1 169b2 ;
MSLS 94 : Base 359; r124 c1246 & r3c246 : 15 Links; 5r1 9r2 35r4 & 9r3 ; 2c1 14c2 2c4 7c6 ; 68b1 168b2 ;
MSLS 95 : Base 359; r134 c1246 & r2c1246 : 15 Links; 5r1 9r3 35r4 & 9r2 ; 2c1 14c2 2c4 7c6 ; 68b1 168b2 ;
MSLS 96 : Base 359; r234 c1246 + r1c1 r1c2 & r1c46 : 15 Links; 9r2 9r3 35r4 & 5r1 ; 2c1 14c2 2c4 7c6 ; 68b1 168b2 ;
MSLS 97 : Base 359; r124 c12456 & r3c246 : 16 Links; 5r1 9r2 35r4 & 9r3 ; 2c1 14c2 2c4 7c5 7c6 ; 68b1 168b2 ;
MSLS 98 : Base 359; r1234 c126 + r4c4 & r123c4 : 15 Links; 5r1 9r2 9r3 35r4 & 2c4 ; 2c1 4c2 7c6 ; 681b1 168b2 ;
MSLS 99 : Base 359; r1234 c246 & r124c1 : 15 Links; 5r1 9r2 9r3 35r4 & 2c1 ; 14c2 2c4 7c6 ; 68b1 168b2 ;
MSLS 100 : Base 359; r1234 c1246 : 15 Links; 5r1 9r2 9r3 35r4 ; 2c1 14c2 2c4 7c6 ; 68b1 168b2 ;
MSLS 101 : Base 368; r2356 c789 + r1c7 r4c8 : 12 Links; ; 5c7 ; 61247b3 389247b6 ;
MSLS 102 : Base 389; r2356 c789 + r1c7 r4c8 : 12 Links; ; 5c7 6c8 ; 1247b3 389247b6 ;
MSLS 103 : Base 478; r789 c789 : 7 Links; 7r8 ; ; 481239b9 ;
MSLS 104 : Base 569; r123 c456 : 7 Links; 5r1 ; 2c4 ; 61978b2 ;
MSLS 105 : Base 12; c123 r123 : 7 Links; ; ; 6124789b1 ;
MSLS 106 : Base 12; c456 r123 : 7 Links; 2c4 ; 5r1 ; 16789b2 ;
MSLS 107 : Base 13; c789 r789 : 7 Links; ; 2r7 7r8 ; 13489b9 ;
MSLS 108 : Base 14; c123 r123 : 7 Links; ; ; 6142789b1 ;
MSLS 109 : Base 17; c123 r123 : 7 Links; 7c3 ; ; 612489b1 ;
MSLS 110 : Base 17; c2456 r123 + r1c1 r2c1 & r12c3 : 14 Links; & 7c3 ; 58r1 89r2 9r3 ; 4261b1 1726b2 ;
MSLS 111 : Base 24; c126 r1234 + r1c5 r4c4 & r123c4 : 16 Links; 2c1 4c2 & 2c4 ; 58r1 89r2 9r3 357r4 ; 16b1 167b2 ;
MSLS 112 : Base 24; c246 r1234 + r1c5 & r124c1 : 16 Links; 4c2 2c4 & 2c1 ; 58r1 89r2 9r3 357r4 ; 16b1 167b2 ;
MSLS 113 : Base 24; c126 r12349 + r1c5 r4c4 r9c3 r9c7 r9c8 r9c9 & r123c4 : 22 Links; 2c1 4c2 & 2c4 ; 58r1 89r2 9r3 357r4 135689r9 ; 16b1 167b2 ;
MSLS 114 : Base 24; c246 r12349 + r1c5 r9c3 r9c7 r9c8 r9c9 & r124c1 : 22 Links; 4c2 2c4 & 2c1 ; 58r1 89r2 9r3 357r4 135689r9 ; 16b1 167b2 ;
MSLS 115 : Base 24; c1236 r123 + r1c5 & r123c4 : 14 Links; & 2c4 ; 58r1 89r2 9r3 ; 24167b1 167b2 ;
MSLS 116 : Base 24; c6789 r789 + r7c2 r7c4 r8c1 r8c4 r9c2 r9c3 : 16 Links; 4c6 ; 136r7 3789r8 135689r9 ; 42b9 ;
MSLS 117 : Base 24; c1246 r1234 + r1c5 : 16 Links; 2c1 4c2 2c4 ; 58r1 89r2 9r3 357r4 ; 16b1 167b2 ;
MSLS 118 : Base 24; c12346 r123 + r1c5 : 14 Links; 2c4 ; 58r1 89r2 9r3 ; 24167b1 167b2 ;
MSLS 119 : Base 26; c123 r123 : 7 Links; ; ; 6124789b1 ;
MSLS 120 : Base 26; c456 r123 : 7 Links; 2c4 ; 5r1 ; 61789b2 ;
MSLS 121 : Base 27; c4789 r578 + r5c1 r5c3 r5c5 r7c2 r7c6 r8c1 r8c6 : 17 Links; ; 1345689r5 1346r7 3489r8 ; 27b9 ;
MSLS 122 : Base 27; c6789 r789 + r7c2 r7c4 r8c1 r8c4 r9c2 r9c3 : 16 Links; ; 1346r7 3489r8 135689r9 ; 27b9 ;
MSLS 123 : Base 28; c1236 r123 + r1c5 & r123c4 : 14 Links; & 2c4 ; 5r1 9r2 9r3 ; 284167b1 1678b2 ;
MSLS 124 : Base 28; c12346 r123 + r1c5 : 14 Links; 2c4 ; 5r1 9r2 9r3 ; 284167b1 8167b2 ;
MSLS 125 : Base 29; c1236 r123 + r1c5 & r123c4 : 14 Links; & 2c4 ; 58r1 8r2 ; 294167b1 1679b2 ;
MSLS 126 : Base 29; c12346 r123 + r1c5 : 14 Links; 2c4 ; 58r1 8r2 ; 294167b1 9167b2 ;
MSLS 127 : Base 35; c789 r456 : 7 Links; 5c7 ; ; 324789b6 ;
MSLS 128 : Base 47; c2456 r123 + r1c1 r2c1 & r12c3 : 14 Links; & 7c3 ; 58r1 89r2 9r3 ; 1264b1 7126b2 ;
MSLS 129 : Base 47; c6789 r789 + r7c2 r7c4 r8c1 r8c4 r9c2 r9c3 : 16 Links; 4c6 ; 1236r7 389r8 135689r9 ; 47b9 ;
MSLS 130 : Base 47; c23478 r126 + r1c1 r1c6 r2c1 r2c6 r6c6 r6c9 & r16c5 : 21 Links; 7c3 7c7 & 7c5 ; 12568r1 12689r2 235689r6 ; 4b1 4b3 ;
MSLS 131 : Base 47; c23568 r126 + r1c1 r1c4 r2c1 r2c4 r6c9 & r126c7 : 21 Links; 7c3 7c5 & 7c7 ; 12568r1 12689r2 235689r6 ; 4b1 4b3 ;
MSLS 132 : Base 47; c23578 r126 + r1c1 r1c4 r1c6 r2c1 r2c4 r2c6 r6c6 r6c9 : 21 Links; 7c3 7c5 7c7 ; 12568r1 12689r2 235689r6 ; 4b1 4b3 ;
MSLS 133 : Base 47; c23678 r126 + r1c1 r1c4 r2c1 r2c4 r6c9 & r16c5 : 21 Links; 7c3 7c7 & 7c5 ; 12568r1 12689r2 235689r6 ; 4b1 4b3 ;
MSLS 134 : Base 47; c25678 r126 + r1c1 r1c4 r2c1 r2c4 r6c3 r6c9 & r12c3 : 21 Links; 7c5 7c7 & 7c3 ; 12568r1 12689r2 235689r6 ; 4b1 4b3 ;
MSLS 135 : Base 47; c23678 r1269 + r1c1 r1c4 r2c1 r2c4 r6c9 r9c9 & r16c5 : 27 Links; 7c3 7c7 & 7c5 ; 12568r1 12689r2 235689r6 135689r9 ; 4b1 4b3 ;
MSLS 136 : Base 67; c123 r123 : 7 Links; 7c3 ; ; 612489b1 ;
MSLS 137 : Base 67; c456 r123 : 7 Links; ; 5r1 ; 612789b2 ;
MSLS 138 : Base 89; c12346 r123 + r1c5 r1c7 r2c7 r2c8 r3c8 r3c9 : 19 Links; ; 124567r1 12467r2 1267r3 ; 89b1 89b2 ;
MSLS 139 : Base 89; c12467 r123 + r1c3 r1c5 r2c3 r2c8 r3c8 r3c9 : 19 Links; ; 124567r1 12467r2 1267r3 ; 89b1 89b2 ;
MSLS 140 : Base 123; c789 r789 : 7 Links; ; 7r8 ; 123489b9 ;
MSLS 141 : Base 124; c123 r123 : 7 Links; ; ; 6124789b1 ;
MSLS 142 : Base 126; c123 r123 : 7 Links; ; ; 6124789b1 ;
MSLS 143 : Base 126; c456 r123 : 7 Links; 2c4 ; 5r1 ; 16789b2 ;
MSLS 144 : Base 127; c123 r123 : 7 Links; 7c3 ; ; 612489b1 ;
MSLS 145 : Base 127; c456 r123 : 7 Links; 2c4 ; 5r1 ; 16789b2 ;
MSLS 146 : Base 128; c123 r123 : 7 Links; ; ; 6128479b1 ;
MSLS 147 : Base 128; c456 r123 : 7 Links; 2c4 ; 5r1 ; 16879b2 ;
MSLS 148 : Base 129; c123 r123 : 7 Links; ; ; 6129478b1 ;
MSLS 149 : Base 129; c456 r123 : 7 Links; 2c4 ; 5r1 ; 16978b2 ;
MSLS 150 : Base 134; c789 r789 : 7 Links; ; 2r7 7r8 ; 41389b9 ;
MSLS 151 : Base 137; c789 r789 : 7 Links; ; 2r7 ; 137489b9 ;
MSLS 152 : Base 138; c789 r789 : 7 Links; ; 2r7 7r8 ; 13849b9 ;
MSLS 153 : Base 139; c789 r789 : 7 Links; ; 2r7 7r8 ; 13948b9 ;
MSLS 154 : Base 146; c123 r123 : 7 Links; ; ; 6142789b1 ;
MSLS 155 : Base 147; c123 r123 : 7 Links; 7c3 ; ; 614289b1 ;
MSLS 156 : Base 147; c2456 r123 + r1c1 r2c1 & r12c3 : 14 Links; & 7c3 ; 58r1 89r2 9r3 ; 2641b1 1726b2 ;
MSLS 157 : Base 148; c123 r123 : 7 Links; ; ; 6148279b1 ;
MSLS 158 : Base 149; c123 r123 : 7 Links; ; ; 6149278b1 ;
MSLS 159 : Base 167; c123 r123 : 7 Links; 7c3 ; ; 612489b1 ;
MSLS 160 : Base 167; c456 r123 : 7 Links; ; 5r1 ; 162789b2 ;
MSLS 161 : Base 178; c123 r123 : 7 Links; 7c3 ; ; 618249b1 ;
MSLS 162 : Base 178; c456 r123 : 7 Links; ; 5r1 ; 126789b2 ;
MSLS 163 : Base 179; c123 r123 : 7 Links; 7c3 ; ; 619248b1 ;
MSLS 164 : Base 189; c789 r789 : 7 Links; ; 2r7 7r8 ; 31894b9 ;
MSLS 165 : Base 235; c789 r456 : 7 Links; 5c7 ; ; 234789b6 ;
MSLS 166 : Base 246; c123 r123 : 7 Links; ; ; 6124789b1 ;
MSLS 167 : Base 247; c126 r1234 + r4c4 & r123c4 : 15 Links; 2c1 4c2 7c6 & 2c4 ; 58r1 89r2 9r3 35r4 ; 16b1 16b2 ;
MSLS 168 : Base 247; c246 r1234 & r124c1 : 15 Links; 4c2 2c4 7c6 & 2c1 ; 58r1 89r2 9r3 35r4 ; 16b1 16b2 ;
MSLS 169 : Base 247; c126 r12349 + r4c4 r9c3 r9c7 r9c8 r9c9 & r123c4 : 21 Links; 2c1 4c2 7c6 & 2c4 ; 58r1 89r2 9r3 35r4 135689r9 ; 16b1 16b2 ;
MSLS 170 : Base 247; c246 r12349 + r9c3 r9c7 r9c8 r9c9 & r124c1 : 21 Links; 4c2 2c4 7c6 & 2c1 ; 58r1 89r2 9r3 35r4 135689r9 ; 16b1 16b2 ;
MSLS 171 : Base 247; c1246 r1234 : 15 Links; 2c1 4c2 2c4 7c6 ; 58r1 89r2 9r3 35r4 ; 16b1 16b2 ;
MSLS 172 : Base 248; c126 r1234 + r1c5 r4c4 & r123c4 : 16 Links; 2c1 4c2 & 2c4 ; 5r1 9r2 9r3 357r4 ; 816b1 1678b2 ;
MSLS 173 : Base 248; c246 r1234 + r1c5 & r124c1 : 16 Links; 4c2 2c4 & 2c1 ; 5r1 9r2 9r3 357r4 ; 168b1 8167b2 ;
MSLS 174 : Base 248; c1236 r123 + r1c5 & r123c4 : 14 Links; & 2c4 ; 5r1 9r2 9r3 ; 248167b1 1678b2 ;
MSLS 175 : Base 248; c1246 r1234 + r1c5 : 16 Links; 2c1 4c2 2c4 ; 5r1 9r2 9r3 357r4 ; 816b1 8167b2 ;
MSLS 176 : Base 248; c12346 r123 + r1c5 : 14 Links; 2c4 ; 5r1 9r2 9r3 ; 248167b1 8167b2 ;
MSLS 177 : Base 249; c126 r1234 + r1c5 r4c4 & r123c4 : 16 Links; 2c1 4c2 & 2c4 ; 58r1 8r2 357r4 ; 916b1 1679b2 ;
MSLS 178 : Base 249; c246 r1234 + r1c5 & r124c1 : 16 Links; 4c2 2c4 & 2c1 ; 58r1 8r2 357r4 ; 169b1 9167b2 ;
MSLS 179 : Base 249; c1236 r123 + r1c5 & r123c4 : 14 Links; & 2c4 ; 58r1 8r2 ; 249167b1 1679b2 ;
MSLS 180 : Base 249; c1246 r1234 + r1c5 : 16 Links; 2c1 4c2 2c4 ; 58r1 8r2 357r4 ; 916b1 9167b2 ;
MSLS 181 : Base 249; c12346 r123 + r1c5 : 14 Links; 2c4 ; 58r1 8r2 ; 249167b1 9167b2 ;
MSLS 182 : Base 256; c456 r123 : 7 Links; 2c4 ; ; 561789b2 ;
MSLS 183 : Base 259; c789 r456 : 7 Links; 5c7 ; ; 293478b6 ;
MSLS 184 : Base 267; c123 r123 : 7 Links; 7c3 ; ; 612489b1 ;
MSLS 185 : Base 267; c456 r123 : 7 Links; 2c4 ; 5r1 ; 61789b2 ;
MSLS 186 : Base 268; c123 r123 : 7 Links; ; ; 6128479b1 ;
MSLS 187 : Base 268; c456 r123 : 7 Links; 2c4 ; 5r1 ; 61879b2 ;
MSLS 188 : Base 269; c123 r123 : 7 Links; ; ; 6129478b1 ;
MSLS 189 : Base 269; c456 r123 : 7 Links; 2c4 ; 5r1 ; 61978b2 ;
MSLS 190 : Base 278; c123 r123 : 7 Links; 7c3 ; ; 162849b1 ;
MSLS 191 : Base 289; c456 r123 : 7 Links; 2c4 ; 5r1 ; 16897b2 ;
MSLS 192 : Base 289; c1236 r123 + r1c5 & r123c4 : 14 Links; & 2c4 ; 5r1 ; 2894167b1 16789b2 ;
MSLS 193 : Base 289; c12346 r123 + r1c5 : 14 Links; 2c4 ; 5r1 ; 2894167b1 89167b2 ;
MSLS 194 : Base 345; c789 r456 : 7 Links; 5c7 ; ; 432789b6 ;
MSLS 195 : Base 356; c389 r56789 & r79c7 : 15 Links; 56c3 3c9 & 3c7 ; 4r5 2r6 2r7 7r8 ; 1b7 89b6 4891b9 ;
MSLS 196 : Base 357; c789 r456 : 7 Links; 5c7 ; ; 372489b6 ;
MSLS 197 : Base 358; c789 r456 : 7 Links; 5c7 ; ; 382479b6 ;
MSLS 198 : Base 457; c2456 r123 + r1c1 r2c1 & r12c3 : 14 Links; & 7c3 ; 8r1 89r2 9r3 ; 1264b1 57126b2 ;
MSLS 199 : Base 467; c123 r123 : 7 Links; 7c3 ; ; 614289b1 ;
MSLS 200 : Base 678; c123 r123 : 7 Links; 7c3 ; ; 618249b1 ;
MSLS 201 : Base 678; c456 r123 : 7 Links; ; 5r1 ; 612789b2 ;
MSLS 202 : Base 679; c123 r123 : 7 Links; 7c3 ; ; 619248b1 ;
MSLS 203 : Base 679; c456 r123 : 7 Links; ; 5r1 ; 612798b2 ;

Generally speaking, when one MSLS pattern exists, there exist more than one, which are more or less equivalent. Sometimes, with different patterns, the direct eliminations are slightly different, but usually come to the same result when follow-on basic eliminations are taken into account.

Perhaps, more importantly, the MSLS technique is just one of a more broadly defined solving technique called Multi-fish, or Rank 0 Logic Structures. With MSLS the Truth sets are limited to cells. In the more general Multi-fish case the Truth sets can include digits in rows, columns and boxes. You can find out more about Multi-fish in the Exotic Patterns a Resume thread here. Be prepared for a long ride, Multi-fish is a BIG topic.

Leren
Leren
 
Posts: 2929
Joined: 03 June 2012

Re: 【TECHNIQUE SHARE】ALS NET

Postby Leren » Wed Jun 15, 2016 10:12 am

To indicate the essential equivalence of different MSLS patterns in the same puzzle I decided to avoid using the preliminary Swordfish.

The reason being that this is a simple form of Rank 0 pattern albeit of a different shape to the MSLS. This is what came up:

Code: Select all
*--------------------------------------------------------------------------------*
| 268     1468    247-16   | 12568   1567    15678    | 247     3       9        |
| 2689    14689   247-16   | 12689   3       16789    | 247     12467   5        |
| 5       169     3        | 1269    4       1679     | 8       1267    127      |
|--------------------------+--------------------------+--------------------------|
| 23      345     8        | 35      9       357      | 1       24-7    6        |
| 369     7      *456      | 13568   156     2        |*3459   *489    *348      |
| 1       3569   *256      | 4       567     35678    |*23579  *2789   *2378     |
|--------------------------+--------------------------+--------------------------|
| 7       136     9        | 136     8       1346     |*234     5      *1234     |
| 38      2      *15       | 39      15      349      | 6      *4789   *3478     |
| 4       13568  *156      | 7       2       13569    |*39     *189    *138      |
*--------------------------------------------------------------------------------*

MSLS 1 : Base 24; r5689 c3789 & r7c79 : 17 Links; 4r5 2r6 & 2r7 ; 156c3 359c7 89c8 38c9 ; 7b6 174b9 ; => - 16 r12c3, - 7 r4c8.

The puzzle is completed with singles and just one pointing triple of 1's in Column 2, so with the MSLS the Swordfish is extraneous.

As I said in my previous post, even when MSLS's have different direct eliminations, with follow-on basics they often, if not always, end up at the same position, which, for this relatively easy puzzle, is a complete solution.

Leren
Leren
 
Posts: 2929
Joined: 03 June 2012

Re: 【TECHNIQUE SHARE】ALS NET

Postby borescoper » Thu Jun 16, 2016 7:08 am

Leren wrote:To indicate the essential equivalence of different MSLS patterns in the same puzzle I decided to avoid using the preliminary Swordfish.

The reason being that this is a simple form of Rank 0 pattern albeit of a different shape to the MSLS. This is what came up:

Code: Select all
*--------------------------------------------------------------------------------*
| 268     1468    247-16   | 12568   1567    15678    | 247     3       9        |
| 2689    14689   247-16   | 12689   3       16789    | 247     12467   5        |
| 5       169     3        | 1269    4       1679     | 8       1267    127      |
|--------------------------+--------------------------+--------------------------|
| 23      345     8        | 35      9       357      | 1       24-7    6        |
| 369     7      *456      | 13568   156     2        |*3459   *489    *348      |
| 1       3569   *256      | 4       567     35678    |*23579  *2789   *2378     |
|--------------------------+--------------------------+--------------------------|
| 7       136     9        | 136     8       1346     |*234     5      *1234     |
| 38      2      *15       | 39      15      349      | 6      *4789   *3478     |
| 4       13568  *156      | 7       2       13569    |*39     *189    *138      |
*--------------------------------------------------------------------------------*

MSLS 1 : Base 24; r5689 c3789 & r7c79 : 17 Links; 4r5 2r6 & 2r7 ; 156c3 359c7 89c8 38c9 ; 7b6 174b9 ; => - 16 r12c3, - 7 r4c8.

The puzzle is completed with singles and just one pointing triple of 1's in Column 2, so with the MSLS the Swordfish is extraneous.

As I said in my previous post, even when MSLS's have different direct eliminations, with follow-on basics they often, if not always, end up at the same position, which, for this relatively easy puzzle, is a complete solution.

Leren


thank you very much!
borescoper
 
Posts: 15
Joined: 11 June 2016

Re: 【TECHNIQUE SHARE】ALS NET

Postby eleven » Fri Jun 17, 2016 3:41 pm

For manual (P&P) players MSLS's beyond the swordfish pattern seem to be too hard to spot.
But i guess that for many eliminations an alternative can be found.

E.g. here, when you look at the ALS 12456 in r5689c3:
Since 2 in the ALS implies 345 in r4c125 with 4r3c2, 2 and 4 cannot both be in the ALS, which therefore must contain 156 -> r12c3<>16, r79c2<>1.
And both 2 and 4 in the ALS imply 35 in r4c125 -> r4c6=7.
eleven
 
Posts: 1580
Joined: 10 February 2008

Re: 【TECHNIQUE SHARE】ALS NET

Postby David P Bird » Fri Jun 17, 2016 9:54 pm

eleven wrote:For manual (P&P) players MSLS's beyond the swordfish pattern seem to be too hard to spot.
But i guess that for many eliminations an alternative can be found.

Your observation depends on how you define MSLSs

I have tried but failed to get a consensus on this but no-one was prepared to enter the discussion. JCVH already provided a pointer to the post concerned in the second post in this thread.

As the first one here to use the term I'm therefore sticking to it being a generic term to describe multi-digit, multi-sector locked sets which can be either naked or hidden before the eliminations are made.

Therefore SK-Loops, Multi-fish, and Sue de Coqs are all specific types of MSLS and interacting ALSs are either MSLSs or Almost MSLSs depending on the circumstances (the number of common cells and restricted common digits they have).

As standard fish only use a single digit I never considered them as being included but I have an open mind about that.

David
.
David P Bird
2010 Supporter
 
Posts: 960
Joined: 16 September 2008
Location: Middle England


Return to Advanced solving techniques