0-rank logic sets in the hardest puzzles

Advanced methods and approaches for solving Sudoku puzzles

0-rank logic sets in the hardest puzzles

Postby ronk » Tue Apr 03, 2012 1:56 pm

Content

This thread is intended to be a collection of 0-rank logic sets, mostly not seen before. It seems reasonable to expect that these logic sets will be quite complex and not likely to be in the toolkit of manual solvers. However, the goal is to find elegant logic sets and present them as clearly as one is able.

An excellent source of puzzles for this collection will (I think) be champagne's shortlist of hardest puzzles without a known sk-loop, almost sk-loop, or other multi-digit fish pattern. He kindly posted this list here.

champagne's "03 NN nothing special hard" puzzles

Hidden Text: Show
Code: Select all
1....6.......8.2....97....5.3.9....4..5....9.....2.1....4.....7.9.3...4.8.....6..;1582;elev;567;11.30;1.20;1.20;914
.2.4.......7.8...6.....3.5...9.6...1.....23.....5...4...1...8..6...1...797.......;243;elev;258;11.40;11.40;11.30;884
..34......5...9...7...2...62...7..1..9...5......3....8..1.6...78......21......4..;4024;elev;L406;11.10;11.10;3.40;881
.......8....1.9..66...2...4.7...8.9.5..........4.3...73.2.....5..5.6.3...1.....7.;3218;elev;997;11.20;1.20;1.20;876
98.7.....7...8.6....5..4...6..3..9...9.....2...4..1..6.3.8..7.......2.1.........5;227;GP;H29;11.50;1.20;1.20;858
98.7.....6.....9....5....7..4..3..2...85..4.......4..1..69..5......2...3.....1.4.;35;GP;H4;11.70;11.70;11.30;852
...45.........9.3.6...375...4....1....8.....29...6..7.3....5.9...2...8...1..7....;620;elev;890;11.30;11.30;10.60;829
..3..6.8.4.....2......3.5....89...3.5...7...4.....1....6.8...9.7...2......1..3...;2780;elev;1126;11.20;1.20;1.20;790
1.......9.5.1...3...8..34...1.5.......9..8..2....6..7.3....4..8..2.......8..7..6.;3411;elev;3174;11.10;11.10;10.80;785
....5...94..1..2.......7...2.8.1.6....62......7......3.3..9..5.8..........28..4..;4971;elev;1943;11.10;1.20;1.20;780
.....6.8.4..7....3.9..3.....1..4...73..1.......8..52...3.9....4......5....2....6.;4891;elev;1905;11.10;1.20;1.20;734
.2.4....9..7......8....2.1...1..5.7..6..9...5...2..........8.5....36...2.3..2.6..;4993;elev;2354;11.10;1.20;1.20;730
.......89.5.1.....6....31...7...16......9..2...8.....4..4.2....7..5..3...6...7...;3329;elev;991;11.20;1.20;1.20;713
.2.4.......7.8...69......5...8...6.15....1.9.....7...3........7.4.2.......1.6.3..;1263;elev;510;11.30;1.20;1.20;670
98.7.....7...6......5..87..5....69....43...6.....2...1.5...48.....6....3....1..2.;12120;GP;kz0;11.70;11.70;11.30;637
........9..71...6.....3.1.42..6...1...5.......8...43..5......2.6.17......9...8...;1690;elev;301;11.30;1.20;1.20;621
1....6....5.........82....4..98..3...6...5.8.........27....2.1...2.4.9.3...3.....;1102;elev;837;11.30;11.30;2.60;619
1.......9..67...2..8....5.......83.....2...64..7.4..1...462....5..8......9...3...;889;elev;L59;11.30;11.30;9.50;607
1..4..7....7.8...6.9.......2..3......4...71....5.4..2..3.9..4......6...8..2....5.;7417;elev;H193;10.80;10.80;10.80;592
98.7.....65....4....3.6....7..5..8......2..5......1..6.4.8..9....9.....3....1..2.;10216;GP;22ky5;10.70;10.70;3.40;580
....5...94..1...3..6.7..1....59......8..7.......5.2..73......6...8.9...2.1....4..;2051;elev;1452;11.20;11.20;9.90;542
1...5.7..........6..83...4...4.....7.3.2....4......92......15..7...9......26....8;3909;elev;2788;11.10;11.10;9.40;529
.2...67..4...8......9.....1..1.....8...2..6...6...3.5......5.2..7.6..3..9...4....;4582;elev;2279;11.10;1.20;1.20;529
98.7.....7...6......5..97..5....69....43...6.....2...1.5...48.....6...3.....1...2;14596;GP;kz1a;11.40;11.40;11.30;525
1...5......7..9..6.983.......67....8.8.......5...4..2.....3.1...3.9....7.....2.4.;3173;elev;1405;11.20;1.20;1.20;519
...4..7..4...8...6..9..2.......3...83..8..4...18....5..9.....1.7..6....3..2..5...;2926;elev;L294;11.20;1.20;1.20;506
..3.5.....5.1....68....7....6..9...57....2.4...5...1........8.......4.2...9.3...1;1362;elev;413;11.30;1.20;1.20;505

If the above puzzles don't ultimately reveal a 0-rank logic set, this thread will be opened up to other ranks. Also, please restrict the logic sets to those steps (or moves) available after the opening moves of SSTS ("Simple Sudoku Technique Set").

Organization

This first post is intended to be a table of contents with links. As such, it will be edited frequently.

Happy hunting!

0-rank logic sets with box covers

#3218; #4993; #7765

Code: Select all
.......8....1.9..66...2...4.7...8.9.5..........4.3...73.2.....5..5.6.3...1.....7. # 3218;elev;997

.2.4....9..7......8....2.1...1..5.7..6..9...5...2..........8.5....36...2.3..2.6.. # 4993;elev;2354

987......65.9..4....4.......4.3..8......6..2......1..5..97..3......2..6......5..1 # 7765;GP;H1604

[edit: 1) add three puzzles with box covers]
Last edited by ronk on Sat Aug 04, 2012 7:26 pm, edited 2 times in total.
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Re: 0-rank logic sets in the hardest puzzles

Postby champagne » Tue Apr 03, 2012 3:56 pm

feel free to transfer (and rearrange if necessary) all the stuff related to GP;H1521 here
it's really a strange animal better located here that is the thread i opened recently, mostly focused on repetitive patterns.

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Re: 0-rank logic sets in the hardest puzzles

Postby ronk » Tue Apr 03, 2012 8:54 pm

here daj95376 wrote:
ronk wrote:each having coincident fins at r58c69 and r69c58.

I don't know the definition of "coincident fins", but my template solver says that these cells contain a candidate from every <3678>-template group, from which it found 224 acceptable combinations.

[edit: The following terminology is partly incorrect. This 0-rank logic set should be viewed as multi-digit fish without fins, as it is the absence of fins that enables a large number of eliminations. The consequence is that the covering cells in this logic set should be regarded as part of the fish body or bodies.]

"Coincident fins" just means there are fins of two or more fish in the same cell. In the GP;H1521 puzzle, as champagne hinted, there are <3678>-jellyfish in r5689 which are covered by 2 columns, 6 boxes and 8 cells (for details see below). In templating, the 8 covering cells show up in the manner you noticed.

I can't see much of anything with all four digits shown in one pencilmark like champagne likes to post, so here are the four single-digit "pencilmarks" instead. Candidates covered by rows, columns and boxes are flagged with "*", those covered by cells with "#". As in the old single-digit fish days, the '#' indicates candidate cells treated as fins.

Code: Select all
98.7.....7.6...8...54......6..8..3......9..2......4..1.3.6..7......5..9......1..4 # GP;H1521

 .  .  3 |  .  3  3 |  .  3  3        .  .  . |  .  6  6 |  6  6  6
 .  .  . |  3  3  3 |  .  3  3        .  .  6 |  .  .  . |  .  .  .
 3  .  . |  3  3  3 |  .  3  3        .  .  . |  .  6  6 |  6  6  6
---------+----------+----------      ---------+----------+----------
 .  .  . |  .  .  . |  3  .  .        6  .  . |  .  .  . |  .  .  .
*3  / *3 | *3  / #3 |  /  / #.        /  /  / |  /  / #6 | *6  / #6
*3  / *3 | *3 #3  / |  / #.  /        /  /  / |  / #6  / | *6 #6  /
---------+----------+----------      ---------+----------+----------
 .  3  . |  .  .  . |  .  .  .        .  .  . |  6  .  . |  .  .  .
 /  /  / | *3  / #3 |  /  / #3        / *6  / |  /  / #. | *6  / #6
 /  /  / | *3 #3  / |  / #3  /        / *6  / |  / #.  / | *6 #6  /
                               
3: r5689\c4b4 + r5c6 +(r5c9)+ r6c5 +(r6c8)+ r8c6 + r8c9 + r9c5 + r9c8
6: r5689\c7b7 + r5c6 + r5c9 + r6c5 + r6c8 +(r8c6)+ r8c9 +(r9c5)+ r9c8

 .  .  . |  7  .  . |  .  .  .        .  8  . |  .  .  . |  .  .  .
 7  .  . |  .  .  . |  .  .  .        .  .  . |  .  .  . |  8  .  .
 .  .  . |  .  .  . |  .  7  7        .  .  . |  .  8  8 |  .  .  .
---------+----------+----------      ---------+----------+----------
 .  7  7 |  .  7  7 |  .  7  7        .  .  . |  .  .  . |  .  .  .
 / *7 *7 |  /  / #7 |  /  / #7       *8  / *8 |  /  / #. |  /  / #8
 / *7 *7 |  / #7  / |  / #7  /       *8  / *8 |  / #.  / |  / #8  /
---------+----------+----------      ---------+----------+----------
 .  .  . |  .  .  . |  .  .  .        8  .  8 |  .  8  8 |  .  8  8
 / *7 *7 |  /  / #7 |  /  / #.       *8  / *8 |  /  / #8 |  /  / #8
 / *7 *7 |  / #7  / |  / #.  /       *8  / *8 |  / #8  / |  / #8  /
                               
7: r5689\b47 + r5c6 + r5c9 + r6c5 + r6c8 + r8c6 +(r8c9)+ r9c5 +(r9c8)
8: r5689\b47 +(r5c6)+ r5c9 +(r6c5)+ r6c8 + r8c6 + r8c9 + r9c5 + r9c8

"/" cells must be void of the respective candidate
"(rMcN)" parenthesized cells are cells where candidates could exist without destroying the logic

Code: Select all
 fish bodies  + <----------------- eight fin cells ----------------->
3: r5689\c4b4 + r5c6 +(r5c9)+ r6c5 +(r6c8)+ r8c6 + r8c9 + r9c5 + r9c8
6: r5689\c7b7 + r5c6 + r5c9 + r6c5 + r6c8 +(r8c6)+ r8c9 +(r9c5)+ r9c8
7: r5689\b47  + r5c6 + r5c9 + r6c5 + r6c8 + r8c6 +(r8c9)+ r9c5 +(r9c8)
8: r5689\b47  +(r5c6)+ r5c9 +(r6c5)+ r6c8 + r8c6 + r8c9 + r9c5 + r9c8

Manually preparing the above takes a lot of time, so you're not going to see someone do so very often, especially since an XSUDO image says it all in one swell foop.

____Image

Code: Select all
16 Truths = {3678R5689}
16 Links = {3c4 6c7 69n5 58n6 69n8 58n9 378b4 678b7}
16 Eliminations --> r4c23<>7, r5c69<>5, r7c13<>8, r8c69<>2, r23c4<>3, r69c5<>2, r13c7<>6,
     r69c8<>5

This is not the smallest set of truths for these 16 eliminations.
Last edited by ronk on Wed Apr 04, 2012 11:28 pm, edited 1 time in total.
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Re: 0-rank logic sets in the hardest puzzles

Postby champagne » Wed Apr 04, 2012 5:53 am

ronk wrote:Content

An excellent source of puzzles for this collection will (I think) be champagne's short list of hardest puzzles without a known sk-loop, almost sk-loop or multi-digit fish pattern.
champagne's "03 NN nothing special hard" puzzles


Form




just one remark.

That list is a short list made after the entire list has been filtered by my solver to extract the toughest puzzles seen by my set of rules.

The entire list can be easily worked out of the files of the last update of my data base
"01 ..."
"03 TT..."

in the following way

forget all sequence number over 30 000 (not analysed)
take all puzzles in "01 .." not in "03 TT"

I did not include that file in the data base to avoid confusion with the existing "03 NN .." but I can do it starting with the next update

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Re: 0-rank logic sets in the hardest puzzles

Postby ronk » Wed Apr 04, 2012 11:52 am

champagne wrote:The entire list can be easily worked out of the files of the last update of my data base
...
forget all sequence number over 30 000 (not analysed)
take all puzzles in "01 .." not in "03 TT"

Aha, I found 5770 puzzles doing that, definitely not a short list, and it may be too big to include in the opening post. Such a lengthy list should keep even avid fishermen happy for quite a while. Thanks.

champagne wrote:
ronk wrote:An excellent source of puzzles for this collection will (I think) be champagne's short list of hardest puzzles without a known sk-loop, almost sk-loop or multi-digit fish pattern.
champagne's "03 NN nothing special hard" puzzles
That list is a short list made after the entire list has been filtered by my solver to extract the toughest puzzles seen by my set of rules.

I sense short list or shortlist might be an American idiom not known in other countries, so I probably should rephrase.
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Re: 0-rank logic sets in the hardest puzzles

Postby ronk » Wed Apr 04, 2012 2:34 pm

For symmetric puzzles with one 0-rank logic set, there are usually several reasonable alternatives for exactly the same exclusions (eliminations). For puzzle GP-H1521 above, IMO there are five reasonable logic sets, with truths comprised as follows:
  1. 16 truths in 16 cells
  2. 20 truths in 4 lines (2 rows and 2 columns) - ala hidden pair loop
  3. 12 truths in 4 boxes
  4. 16 truths in 4 rows
  5. 16 truths in 4 columns
Each is illustrated below in thumbnail sized images, along with their respective logic sets. Those using XSUDO can paste the puzzle and logic set of interest to see larger images. I can change the thumbnails into clickables, if there are requests to do so, but please use PMs for this.

These five equivalent patterns may be viewed as three pairs of complementary patterns. Figure 1 appears twice because the cell sets can be considered to be in lines (row & cols) or boxes, and these AALSs have complementary AHSs in their respective units.
  1. Fig 1 & Fig 2
  2. Fig 1 & Fig 3
  3. Fig 4 & Fig 5
____Image____Image____Image
Code: Select all
Fig 1: cells      Fig 2: 2 rows & 2 cols   Fig 3: boxes
Code: Select all
Fig 1:
     16 Truths = {5689N4 47N5 47N6 5689N7 47N8 47N9}
     16 Links = {7r4 8r7 3c4 6c7 1b59 2b589 4b68 5b569 9b68}
Fig 2:
     20 Truths = {12459R4 12459R7 12459C4 12459C7}
     20 Links = {7n1 4n2 47n3 23n4 13n7 1b59 2b589 4b68 5b569 9b68}
Fig 3:
     12 Truths = {3B589 6B569 7B568 8B689}
     12 Links = {7r4 8r7 3c4 6c7 69n5 58n6 69n8 58n9}


____Image____Image
Code: Select all
Fig 4: rows          Fig 5: cols
Code: Select all
Fig 4:
     16 Truths = {3R5689 6R5689 7R5689 8R5689}
     16 Links = {3c4 6c7 69n5 58n6 69n8 58n9 378b4 678b7}
Fig 5:
     16 Truths = {3C5689 6C5689 7C5689 8C5689}
     16 Links = {7r4 8r7 69n5 58n6 69n8 58n9 368b2 367b3}
For all images:
     16 Eliminations --> r4c23<>7, r5c69<>5, r7c13<>8, r8c69<>2, r23c4<>3, r69c5<>2, r13c7<>6, r69c8<>5

Besides the above "preferred" interpretations, there is a plethora of other equivalent logic sets. In the below, e.g., only in c4 of Fig 2 is the AHS converted to an AALS.

____Image
Code: Select all
Fig 6: cells & rows & cols mixed
     19 Truths = {12459R4 12459R7 12459C7 5689N4}
     19 Links = {3c4 7n1 4n2 47n3 13n7 1b59 2b589 4b68 5b569 9b68}
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Re: 0-rank logic sets in the hardest puzzles

Postby daj95376 » Thu Apr 05, 2012 2:40 am

Ron,

Thanks for the detailed explanation in your opening post. I'm still studying it, but I now have a better understanding of what's happening in multi-fish logic.
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Re: 0-rank logic sets in the hardest puzzles

Postby champagne » Thu Apr 05, 2012 10:29 am

amazing result,

a new very interesting pattern with 12 truths, but the most important in my view remains the SLG based on cells.

I was suspecting it should exist as the extension of a locked set, symmetric to a multi fish in the sudoku logic;

I was planning to use as "leading indicator" a band/stack exploration similar to what I am doing with floors.

This reinforce the idea

congratulations to ronk anyway for that first promising example

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Re: 0-rank logic sets in the hardest puzzles

Postby ronk » Thu Apr 05, 2012 12:41 pm

daj95376 wrote:Thanks for the detailed explanation in your opening post. I'm still studying it, but I now have a better understanding of what's happening in multi-fish logic.

Thanks. The opening post doesn't really say much (yet), so you are probably referring to this. I've edited it to withdraw my earlier POV that covering cells in 0-rank logic were equivalent to fish fins.

champagne wrote:a new very interesting pattern with 12 truths, but the most important in my view remains the SLG based on cells.
...
congratulations to ronk anyway for that first promising example

Thanks, but I don't believe it's all that new. I think 'N' truths in 4 boxes has been published before for the usual sk-loop puzzle, but it didn't attract attention because 'N' was 16 rather than 12.
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Re: 0-rank logic sets in the hardest puzzles

Postby daj95376 » Thu Apr 05, 2012 5:57 pm

ronk wrote:
daj95376 wrote:Thanks for the detailed explanation in your opening post. I'm still studying it, but I now have a better understanding of what's happening in multi-fish logic.

Thanks. The opening post doesn't really say much (yet), so you are probably referring to this. I've edited it to withdraw my earlier POV that covering cells in 0-rank logic were equivalent to fish fins.

Yes, I mistook that post as your opening post because it was so significant in opening my eyes to a basic multi-fish pattern.

I also appreciate your dropping the covering cells being viewed as fish fins. That was a major stumbling block for me. I now view the multi-fish pattern as N base sets (houses/units), K cover sets (houses/units), and V*(N-K) cover cells -- where V is the number of values/multi-fish tracked. The base sets and cover cells are static, but the cover sets are dynamic -- an interesting concept. An example using one of the puzzles you listed.

Code: Select all
 +-----------------------+
 | 1 . . | . . 6 | . . . |
 | . . . | . 8 . | 2 . . |
 | . . 9 | 7 . . | . . 5 |
 |-------+-------+-------|
 | . 3 . | 9 . . | . . 4 |
 | . . 5 | . . . | . 9 . |
 | . . . | . 2 . | 1 . . |
 |-------+-------+-------|
 | . . 4 | . . . | . . 7 |
 | . 9 . | 3 . . | . 4 . |
 | 8 . . | . . . | 6 . . |
 +-----------------------+   1582;elev;567;11.30;1.20;1.20;914

 after SSTS
 +--------------------------------------------------------------------------------+
 |  1       24578   2378    |  245     3459    6       |  34789   378     389     |
 |  34567   4567    367     |  145     8       13459   |  2       1367    1369    |
 |  2346    2468    9       |  7       134     1234    |  348     1368    5       |
 |--------------------------+--------------------------+--------------------------|
 |  267     3       12678   |  9       1567    1578    |  578     25678   4       |
 |  2467    124678  5       |  1468    13467   13478   |  378     9       2368    |
 |  9       4678    678     |  4568    2       34578   |  1       35678   368     |
 |--------------------------+--------------------------+--------------------------|
 |  2356    1256    4       |  12568   1569    1258    |  3589    12358   7       |
 |  2567    9       1267    |  3       1567    12578   |  58      4       128     |
 |  8       1257    1237    |  1245    14579   124579  |  6       1235    1239    |
 +--------------------------------------------------------------------------------+
 # 180 eliminations remain

Code: Select all
 +-----------------------------------+
 |  1  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  1  . -1  |  .  1  1  |
 |  . #.  .  |  . *1 *1  |  . #1  .  |
 |-----------+-----------+-----------|
 |  .  . #1  |  . *1 *1  |  . #.  .  |
 |  . #1  .  | #1 *1 *1  |  .  . #.  |
 |  .  .  .  |  .  .  .  |  1  .  .  |
 |-----------+-----------+-----------|
 |  . #1  .  | #1 *1 *1  |  . #1  .  |
 |  .  . #1  |  . *1 *1  |  .  . #1  |
 |  .  1  1  |  1 -1 -1  |  .  1  1  |
 +-----------------------------------+
 r34578\c56 + r3c28,r4c38,r5c249,r7c248,r8c39

Code: Select all
 +-----------------------------------+
 |  .  2  2  |  2  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  2  .  .  |
 | *2 #2  .  |  .  . *2  |  . #.  .  |
 |-----------+-----------+-----------|
 | *2  . #2  |  .  .  .  |  . #2  .  |
 | *2 #2  .  | #.  .  .  |  .  . #2  |
 |  .  .  .  |  .  2  .  |  .  .  .  |
 |-----------+-----------+-----------|
 | *2 #2  .  | #2  . *2  |  . #2  .  |
 | *2  . #2  |  .  . *2  |  .  . #2  |
 |  .  2  2  |  2  . -2  |  .  2  2  |
 +-----------------------------------+
 r34578\c16 + r3c28,r4c38,r5c249,r7c248,r8c39

Code: Select all
 +-----------------------------------+
 |  .  .  .  |  .  .  6  |  .  .  .  |
 | -6  6  6  |  .  .  .  |  .  6  6  |
 | *6 #6  .  |  .  .  .  |  . #6  .  |
 |-----------+-----------+-----------|
 | *6  . #6  |  . *6  .  |  . #6  .  |
 | *6 #6  .  | #6 *6  .  |  .  . #6  |
 |  .  6  6  |  6  .  .  |  .  6  6  |
 |-----------+-----------+-----------|
 | *6 #6  .  | #6 *6  .  |  . #.  .  |
 | *6  . #6  |  . *6  .  |  .  . #.  |
 |  .  .  .  |  .  .  .  |  6  .  .  |
 +-----------------------------------+
 r34578\c15 + r3c28,r4c38,r5c249,r7c248,r8c39

Code: Select all
 +-----------------------------------+
 |  .  8  8  |  .  .  .  | -8  8  8  |
 |  .  .  .  |  .  8  .  |  .  .  .  |
 |  . #8  .  |  .  .  .  | *8 #8  .  |
 |-----------+-----------+-----------|
 |  .  . #8  |  .  . *8  | *8 #8  .  |
 |  . #8  .  | #8  . *8  | *8  . #8  |
 |  .  8  8  |  8  . -8  |  .  8  8  |
 |-----------+-----------+-----------|
 |  . #.  .  | #8  . *8  | *8 #8  .  |
 |  .  . #.  |  .  . *8  | *8  . #8  |
 |  8  .  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+
 r34578\c67 + r3c28,r4c38,r5c249,r7c248,r8c39

I would write the multi-fish pattern as:

Code: Select all
 <1268> r34578\c56\c16\c15\c67 + r3c28,r4c38,r5c249,r7c248,r8c39

Eliminations: 21

Code: Select all
 <1268>   <>1  r2c6,r9c56
 <1268>   <>2  r9c6
 <1268>   <>6  r2c1
 <1268>   <>8  r1c7,r6c6

 <1268>   <>3  r37c8,r5c9
 <1268>   <>4  r3c2,r5c24
 <1268>   <>5  r4c8,r7c248
 <1268>   <>7  r4c38,r5c2,r8c3

Regards, Danny

BTW: You might wish to drop the use of "coincidence fins" since you dropped the use of "fin cells". Now, it's just the "conjoined cover cells".
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Re: 0-rank logic sets in the hardest puzzles

Postby David P Bird » Thu Apr 05, 2012 6:47 pm

As a stranger to rank in the truth and link set diagrams, I haven't contributed here, and the last thing I want to do is rain on anyone's parade, but ....

In my spread sheet I have a colouring system for highlighting mini-lines containing 5 digits that intersect on a cell containing a singleton. This identifies if there could be an SK Loop in a puzzle. This shows r47c47 as intersection cells for mini-lines that will probably support a loop in the GP;H1521 puzzle.

Now an SK Loop is a means of finding a multi-sector locked set, and it doesn't really matter how many linking digits there are between terms provided they link coherently.

Here are boxes 5,6,8,9:
Code: Select all
        (3)c4                  (6)c7
         v                      v 
       *----------------------*----------------------*
(7)r4> | 8      127    257    | 3      457    579    |     
       | 135    .      .      | 456    .      .      |  (125)b5   (459)b6   
       | 235    .      .      | 569    .      .      |
       *----------------------*----------------------*     
(8)r8> | 6      248    289    | 7      158    258    |  (459)b8   (125)b9   
       | 234    .      .      | 126    .      .      |
       | 239    .      .      | 256    .      .      |
       *----------------------*----------------------*

As a loop it's cumbersome:
(125#2=3)r56c4 - (3=249#2)r89c4 - (249#2=8)r7c56 - (8=125#2)r7c89 - (125#2=6)r89c7 - (6=459#2)r56c7
= (459#2=7)r4c89 - (7=125#2)r4c56 – Loop

But as a locked set it's easier:
Multi-Sector Locked Set: (3)c4,(249)b8,(8)r7,(125)b9,(6)c7,(459)b6,(7)r4,(125)b5
(16 digits, 16 available intersection cells)

This makes all the exclusions from the various rank 0 diagrams.

Interpreting the loop isn't so straightforward. In the rows and columns the external eliminations are obvious but in the boxes they're not.

ronk wrote: .... but I don't believe it's all that new. I think 'N' truths in 4 boxes has been published before for the usual sk-loop puzzle, but it didn't attract attention because 'N' was 16 rather than 12.

Is this the approach you were hinting at?
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Re: 0-rank logic sets in the hardest puzzles

Postby ronk » Thu Apr 05, 2012 8:17 pm

daj95376 wrote:An example using one of the puzzles you listed.

Code: Select all
 +-----------------------+
 | 1 . . | . . 6 | . . . |
 | . . . | . 8 . | 2 . . |
 | . . 9 | 7 . . | . . 5 |
 |-------+-------+-------|
 | . 3 . | 9 . . | . . 4 |
 | . . 5 | . . . | . 9 . |
 | . . . | . 2 . | 1 . . |
 |-------+-------+-------|
 | . . 4 | . . . | . . 7 |
 | . 9 . | 3 . . | . 4 . |
 | 8 . . | . . . | 6 . . |
 +-----------------------+   1582;elev;567;11.30;1.20;1.20;914

Code: Select all
 after SSTS
1: r34578\c56 + r3c28,r4c38,r5c249,r7c248,r8c39
2: r34578\c16 + r3c28,r4c38,r5c249,r7c248,r8c39
6: r34578\c15 + r3c28,r4c38,r5c249,r7c248,r8c39
8: r34578\c67 + r3c28,r4c38,r5c249,r7c248,r8c39

Eliminations: 21
 <1268>   <>1  r2c6,r9c56
 <1268>   <>2  r9c6
 <1268>   <>6  r2c1
 <1268>   <>8  r1c7,r6c6

 <1268>   <>3  r37c8,r5c9
 <1268>   <>4  r3c2,r5c24
 <1268>   <>5  r4c8,r7c248
 <1268>   <>7  r4c38,r5c2,r8c3

That looks correct to me, great job. A couple of comments:

  • This is a set of 4-digit 5-fish entirely in rows. IMO champagne's program should have found this as one of his "03 G1" fish and been excluded from the "03 NN" list, but it's a good warmup for us before the more difficult ones later,
  • We need to reserve the '#' symbol for candidates that will actually be fins in R-rank logic when R > 0. Any suggestions for a different symbol, one that doesn't conflict with single-digit fish practices?
daj95376 wrote:I would write the multi-fish pattern as: <1268> r34578\c56\c16\c15\c67 + r3c28,r4c38,r5c249,r7c248,r8c39

I'm willing to go with that, at least for now, and I understand that "c56" is for <1>, "c16" for <2>, etc. Did you note that all other fish digits in those columns are big numbers (givens and possibly placements in other puzzles). If that were always true or when it's true as here, your suggestion might be shortened even further to ... <1268> r34578\c1567 + r3c28,r4c38,r5c249,r7c248,r8c39, but let's see what else pops up first.

daj95376 wrote:I now view the multi-fish pattern as N base sets (houses/units), K cover sets (houses/units), and V*(N-K) cover cells -- where V is the number of values/multi-fish tracked. The base sets and cover cells are static, but the cover sets are dynamic -- an interesting concept.

I don't think your formula works in every case. See the 5-digit 4-fish below for a counter example. Also, I don't understand what you see as "dynamic."

Left: your 4-digit 5-fish
Right: a 5-digit 4-fish
____Image____Image
Thumbnail images are clickable.
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Re: 0-rank logic sets in the hardest puzzles

Postby daj95376 » Thu Apr 05, 2012 10:57 pm

you wrote:That looks correct to me, great job. A couple of comments:

  • This is a set of 4-digit 5-fish entirely in rows. IMO champagne's program should have found this as one of his "03 G1" fish and been excluded from the "03 NN" list, but it's a good warmup for us before the more difficult ones later,
  • We need to reserve the '#' symbol for candidates that will actually be fins in R-rank logic when R > 0. Any suggestions for a different symbol, one that doesn't conflict with single-digit fish practices?

I performed what I call "template reduction" at the 2-template and 3-template level before reaching the <1268>-template scenario. As such, seven templates for <8> were removed at the 3-template level. It's possible that these templates corrupted champagne's logic. I'm all for keeping the use of (#) consistent for fin cells. I'm flexible on what might replace it for cover cells -- say (%). I don't have any idea what "SLG" and "R-rank logic" mean. I just examine a puzzle based on what my template solver finds and what I observe in the solutions of others.

you wrote:
daj95376 wrote:I would write the multi-fish pattern as: <1268> r34578\c56\c16\c15\c67 + r3c28,r4c38,r5c249,r7c248,r8c39

I'm willing to go with that, at least temporarily, and I understand that "c56" is for <1>, "c16" for <2>, etc. Did you note that all other fish digits in those columns are big numbers (givens and possibly placements in other puzzles). If that were always true or when it's true as here, your suggestion might be shortened even further to ... <1268> r34578\c1567 + r3c28,r4c38,r5c249,r7c248,r8c39, but let's see what else pops up first.

I'm making suggestions and observations based on an extremely limited exposure to basic multi-fish patterns. As I learn more, hopefully, I'll improve my contributions. As for reducing the cover sets to "\c1567", I can see how the presence of given/solved cells remove any ambiguity in this puzzle. I'm not sure if that would be true in other puzzles. However, I'm okay with using the shorter format -- until I run into a case where it becomes confusing.

you wrote:
daj95376 wrote:I now view the multi-fish pattern as N base sets (houses/units), K cover sets (houses/units), and V*(N-K) cover cells -- where V is the number of values/multi-fish tracked. The base sets and cover cells are static, but the cover sets are dynamic -- an interesting concept.

I don't think your formula works in every case. See the 5-digit 4-fish below for a counter example. Also, I don't understand what you see as "dynamic."

In the fish patterns that I presented above, the base sets and the (conjoined) cover cells were the same for all four values; i.e., static. On the other hand, the pairs of cover sets changed for each value; i.e., dynamic.

you wrote:Left: your 4-digit 5-fish
Right: a 5-digit 4-fish

I don't understand the graphic output from XSUDO. So, I'll just wait to examine future puzzles and their eliminations. I should note that I only produce results for one level at a time. The 4-template results blocked the reporting of any concurrent 5-template results.
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Re: 0-rank logic sets in the hardest puzzles

Postby ronk » Fri Apr 06, 2012 4:11 am

David P Bird wrote:
ronk wrote: .... but I don't believe it's all that new. I think 'N' truths in 4 boxes has been published before for the usual sk-loop puzzle, but it didn't attract attention because 'N' was 16 rather than 12.

Is this the approach you were hinting at?

Correct boxes, but I was referring to hidden sets rather than naked sets.
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Re: 0-rank logic sets in the hardest puzzles

Postby champagne » Fri Apr 06, 2012 8:39 am

May I suggest a challenging search

........3..1..56...9..4..7......9.5.7.......8.5.4.2....8..2..9...35..1..6........ fata morgana


fata morgana shows a high potential in floors 136
It has an Exocet pattern r5c46 r4c2 r6c8 that leads to a direct elimination <24>r4c2.

Up to now, I have not seen any rank 0 logic proposed for more eliminations

It would not be surprising to have one, may be after the first clearing

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