The New Sudoku Players' Forum

by **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

by **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..

by **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

by **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!

by **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

by **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.

by **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!

by **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

Leren

by **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

by **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

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

by **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

by **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!

by **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.

by **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
.

by **AnotherLife** » Sun Feb 13, 2022 10:21 am

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.

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.

Hi Eleven,
Actually, your solution can be explained in MSLS language. As David pointed out,

David P Bird wrote:...interacting ALSs are either MSLSs or Almost MSLSs depending on the circumstances...

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 7-35 | 1 247 6 | | 369 7 456* | 13568 156 2 | 3459 489 348 | | 1 3569 256* | 4 567 35678 | 23579 2789 2378 | :----------------------+--------------------+---------------------: | 7 36-1 9 | 136 8 1346 | 234 5 1234 | | 38 2 15* | 1359 15 13459 | 6 14789 13478 | | 4 3568-1 156* | 7 2 13569 | 39 189 138 | '----------------------'--------------------'---------------------' * - cell truths

This is the case of doubly linked ALS's: (2=345)r4c124 - (4=1256)r5689c3 loop => -16 r12c3, -35 r4c6, -1 r79c2; ste
Such structures can be always interpreted as MSLS's. In this example,
MSLS: 7 cell truths r4c124, r5689c3; 7 links 35r4, 24b4, 56c3, 1c3 (or 1b7) => 8 eliminations -16 r12c3, -35 r4c6, -1 r79c2; ste

So, here we don't need Leren's monster MSLS 17x17 but a simpler MSLS 7x7 will do.

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Re: 【TECHNIQUE SHARE】ALS NET

Re: 【TECHNIQUE SHARE】ALS NET

Re: 【TECHNIQUE SHARE】ALS NET

Re: 【TECHNIQUE SHARE】ALS NET

Re: 【TECHNIQUE SHARE】ALS NET

Re: 【TECHNIQUE SHARE】ALS NET

Re: 【TECHNIQUE SHARE】ALS NET

Re: 【TECHNIQUE SHARE】ALS NET

Re: 【TECHNIQUE SHARE】ALS NET