The New Sudoku Players' Forum

by **JC Van Hay** » Sun Jun 30, 2013 7:43 am

champagne wrote:A question to JC :
... what are the extension of specs to do in priority ... assuming we stick to a base (truths) containing exclusively cells ...

Hi Champagne,
I hope this will help you to find answers to your questions. If not let me know

To find all the Rank 0 set of cells, one can do the following, at least as a manual solver :

Select all the unsolved cells in a set of P boxes at the intersection of 2 bands and 2 stacks and all the arrays of NxM unsolved cells at the intersection of N rows and M columns.
Check if they contain Rank 0 subsets.
If not, add unsolved cells until a Rank 0 (sub)set is eventually reached.

In principle, this investigation should be done from the simplest to the most complex cases.

So P=1, N=1 or M=1 for Naked Subsets and P=2, N=2 or M=2 for ALS-XZ Rule, Double Link.
The case P=3, N=3 or M=3 is very exciting as Rank 0 3x4 arrays of unsolved cells not reducible to "simple loops" are unraveled only now ! What about a 3x3
The case P=4, N=4 or M=4 is specially well suited to the study of the Rank 0 configurations of all sorts in this thread.

To avoid redundancy, the nested arrays should be studied in the same time.
Finally, unsolved cells can be added at the condition that they do not increase the Rank of the initial set of cells. So, for example, a set of cells partially covered by the initial cover sets may be added at the condition that the uncovered part is a Naked/valid Rank 0 Subset or empty.

Best Regards, JC.

by **champagne** » Sun Jun 30, 2013 9:19 am

JC Van Hay wrote:I hope this will help you to find answers to your questions. If not let me know

Hi JC

thanks for your explanations

Reading your post, I see on the low side many heavily basic possible r0 logic patterns, which is not so exciting.
I have already many of them with investigations in the 2 digits multi floors and David is requesting a filter to concentrate on "new" patterns.

I don't see clearly the general process to add cells, but, starting from leren's example and using my background, I hope to have a chance to catch most of them (if not all) just optimising the cover.

As I like to work on examples, I took the first puzzle in the list and looked at the rank 0 proposed by my solver.

It is a "X" degenerated form with 2 crossing in r6c2 and r9c2

Can you give me the corresponding cells based rank 0. This should not be to hard for you.

98.7..6..7..6..5......84...6..5..9...35.............2.5...7..69..79....1.....57..4

Code: Select all: A B C |D E F |G H I 9 8 1234 |7 5 123 |6 134 234 7 124 1234 |6 1239 1239 |5 1348 2348 123 5 6 |123 8 4 |123 9 7 ------------------------------------------------------ 6 1247 1248 |5 1234 12378 |9 13478 348 1248 3 5 |1248 1249 12789 |148 1478 6 148 1479 1489 |1348 1346 13678 |1348 2 5 << ------------------------------------------------------ 5 124 12348 |12348 7 1238 |2348 6 9 2348 246 7 |9 2346 2368 |2348 5 1 12348 12469 123489 |12348 12346 5 |7 348 2348 << AA AA

SLG rank 0
9 Truths = {6R69 6C2 7R6 7C28 9R69 9C2 }
9 Links = {6c5 6b7 7b46 9b47 6n26 9n2 }
9 elims 1r6c2 4r6c2 1r6c6 3r6c6 8r6c6 1r9c2 2r9c2 4r9c2 6r8c5

Code: Select all: floors PM 679 X X X |X X X |X X X X X X |X 9+ 9+ |X X X X X X |X X X |X X X X 7+ X |X X 7+ |X 7+ X X X X |X 9+ 79+ |X 7+ X X 79+ 9+ |X 6+ 67+ |X X X << X X X |X X X |X X X X 6+ X |X 6+ 6+ |X X X X 69+ 9+ |X 6+ X |X X X << AA AA

by **JC Van Hay** » Sun Jun 30, 2013 9:46 am

Here it is

Simply looking at the B/B-Plot, one can find the following loop of bilocals :

Code: Select all: +---------------------------+--------------------------+-------------------+ | 9 8 1234 | 7 5 123 | 6 134 234 | | 7 124 1234 | 6 1239 1239 | 5 1348 2348 | | 123 5 6 | 123 8 4 | 123 9 7 | +---------------------------+--------------------------+-------------------+ | 6 1247 1248 | 5 1234 12378 | 9 13478 348 | | 1248 3 5 | 1248 1249 12789 | 148 1478 6 | | 148 -14(79) 148(9) | 1348 134(6) -138(67) | 1348 2 5 | +---------------------------+--------------------------+-------------------+ | 5 124 12348 | 12348 7 1238 | 2348 6 9 | | 2348 246 7 | 9 234-6 2368 | 2348 5 1 | | 12348 -124(69) 12348(9) | 12348 1234(6) 5 | 7 348 2348 | +---------------------------+--------------------------+-------------------+

All Rows Loop[5] : {679R6 69R9}-{6c5 9c3 69n2 6n6} :=> 9 Eliminations --> r6c6<>138, r9c2<>124, r6c2<>14, r8c5<>6

giving rise straightforwardly to :

Code: Select all: +---------------------------+--------------------------+-----------------------+ | 9 8 1234 | 7 5 123 | 6 134 234 | | 7 124 1234 | 6 1239 1239 | 5 1348 2348 | | 123 5 6 | 123 8 4 | 123 9 7 | +---------------------------+--------------------------+-----------------------+ | 6 1247 1248 | 5 1234 12378 | 9 13478 348 | | 1248 3 5 | 1248 1249 12789 | 148 1478 6 | | (148) 79-14 (1489) | (1348) (1346) 67-138 | (1348) 2 5 | +---------------------------+--------------------------+-----------------------+ | 5 124 12348 | 12348 7 1238 | 2348 6 9 | | 2348 246 7 | 9 234-6 2368 | 2348 5 1 | | (12348) 69-124 (123489) | (12348) (12346) 5 | 7 (348) (2348) | +---------------------------+--------------------------+-----------------------+

All Cells Loop[11] : ALS-XZ Rule, Double Link : {6N13457 9N134589}-{1348r6 12348r9 6c5 9c3} :
:=> 9 Eliminations --> r6c6<>138, r9c2<>124, r6c2<>14, r8c5<>6
That is, using "Eureka notation" : 9r6c3=1348r6c13457=6r6c5-6r9c5=12348r9c134589=9r9c3 @

Note : your SLG contains 4 redundant base/cover sets : 6C2-6b7, 7C28-7b46, 9R6-9b4

Best Regards, JC.

by **champagne** » Sun Jun 30, 2013 10:24 am

JC Van Hay wrote:Here it is

I am impressed. :roll:

I can not say I catch the process to do the shift from one r0 to the other, but you got it.

JC Van Hay wrote:All Cells Loop[11] : ALS-XZ Rule, Double Link : {6N13457 9N134589}-{1348r6 12348r9 6c5 9c3} :

this is a 2x7 matrix, with 3 given which put the target very high to find all r0 potential using leren's process.

JC Van Hay wrote:Note : your SLG contains 4 redundant base/cover sets : 6C2-6b7, 7C28-7b46, 9R6-9b4

this is often the case in these degenerated patterns, but it does not affect the result, so I don't try to adjust the count

by **Leren** » Sun Jun 30, 2013 12:42 pm

After getting advice from JCVH I have made some adjustments to my code and came up with a slight variation to JCVH's ''all cells loop"" solution to puzzle 1 of the list of 241

Code: Select all: *--------------------------------------------------------------------------------* | 9 8 1234 | 7 5 #123 | 6 #134 234 | | 7 *124 1234 | 6 1239 *1239 | 5 *1348 2348 | | 123 5 6 | 123 8 4 | 123 9 7 | |--------------------------+--------------------------+--------------------------| | 6 *1247 1248 | 5 1234 *12378 | 9 *13478 348 | | 1248 *3 5 | 1248 1249 *12789 | 148 *1478 6 | | 148 79-14 1489 | 1348 1346 67-138 | 1348 2 5 | |--------------------------+--------------------------+--------------------------| | 5 #124 12348 | 12348 7 #1238 | 2348 6 9 | | 2348 *246 7 | 9 234-6 *2368 | 2348 *5 1 | | 12348 69-124 123489 | 12348 12346 5 | 7 #348 2348 | *--------------------------------------------------------------------------------*

MSLS 1 : Base 67; r2458 c268 + r7c2 r1c6 r7c6 r1c8 r9c8 : 15 Links; 7r4 7r5 6r8 ; 124c2 12389c6 1348c8 : Same 9 eliminations as ronk and JCVH.

All I had to do was allow for 2 a digit base and 2 solved/given cells in the basic 4 x 3 grid of cells. One extra trick I've used was to note that 5 is
completely solved in the grid so the complement of the Base 67 is 123489 ie only 8 digits in total need to be considered.

I'll continue testing tomorrow - nice to end the day on a good note - once again congratulations to JCVH - I couldn't have done it without your help.

Leren

by **champagne** » Sun Jun 30, 2013 3:52 pm

Leren wrote:
All I had to do was allow for 2 a digit base
Leren

I added the extra cells and authorised even 1 digit as base.

I have now 172 puzzles appearing solved out of the 241.

I check the result and if it seems ok, I post the fresh list of unsolved puzzles on my side

for the first puzzle, the solver used

17 Truths = {4N235689 6N13457 9N134589 }
17 Links = {1r469 2r49 3r469 4r469 6c5 7r4 8r469 9c3 }
and the same 9 elims

by **ronk** » Sun Jun 30, 2013 5:31 pm

champagne wrote:for the first puzzle, the solver used

17 Truths = {4N235689 6N13457 9N134589 }
17 Links = {1r469 2r49 3r469 4r469 6c5 7r4 8r469 9c3 }
and the same 9 elims

In general, what basic techniques might your program perform before searching for an "all cells loop"?

BTW as JC Van Hay showed, your truths in r4 are superfluous. [edit: add link and correct author]

by **champagne** » Sun Jun 30, 2013 7:01 pm

ronk wrote:In general, what basic techniques might your program perform before searching for an "all cells loop"?

nothing changed

pointing claiming (SE terminology)
pair triplet
XWing swordfish

ronk wrote:BTW as Leren showed, your truths in r4 are superfluous.

as said 2 posts earlier, I don't look for redundancy
my target is to extract if possible any puzzle having a r0 potential

by **Leren** » Mon Jul 01, 2013 3:49 am

Code: Select all: Champagne wrote: I have now 172 puzzles appearing solved out of the 241.

Hi Champagne, I've now gone through all 241 puzzles and have 171 with an all cells Rank 0 logic that produced eliminations ( I am guessing that is what you mean by "solved")

Numerous others produced Rank 0 logics (both all cells and row/column) that did not produce any eliminations. Here is my full list of results.

Hidden Text: Show

Perhaps you can look through them and spot any differences. By that I mean just see if you can spot any puzzles for which you have found an all cells Rank 0 and I have not and vice versa.

Leren

<Edit> I've updated my list to include additional information and numbered each puzzle for easy reference. Added 5 puzzles to solution list - now 176 solved with all cells Rank 0 with eliminations

Leren

by **champagne** » Mon Jul 01, 2013 7:00 am

hi leren,

156 puzzles are in both lists
55 puzzles are in none

Hidden Text: Show

each of us has 15 puzzles not in the other list

yours

Hidden Text: Show

mine

Hidden Text: Show

I have a look to try to understand what is specific in my lot

EDIT the source of deviation can be the point where we start the search.

EDIT 2
the first one in my list should not be there with the solution proposed by my solver.
My code as of yesterday still has a window that I did not have the time to filter.

by **JC Van Hay** » Mon Jul 01, 2013 8:28 am

Both list contains 4 Rank 0 3x4 arrays of cells but no 3x3 w/o added cells

.

Here are the analysis of 3 puzzles where no Rank 0 of cells has yet been found by Leren's and/or Champagne's code.

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;

Code: Select all: +-------------------+-----------------------+---------------------------+ | 9 8 1234 | 7 6 1234 | 5 234 1234 | | 7 5 1234 | 123 1248 9 | 1234 -234(68) 12346 | | 123 134 6 | 1235 12458 12345 | 12349 -234(789) 123479 | +-------------------+-----------------------+---------------------------+ | 4 16 125 | 8 3 1256 | 129 -25(79) 12579 | | 12356 9 7 | 4 125 1256 | 8 235 1235 | | 1235 13 8 | 1259 1259 7 | 6 2345 12345 | +-------------------+-----------------------+---------------------------+ | 8 2 345 | -35(69) 7 345 | 34(9) 1 345(69) | | 1356 1346 9 | 12356 1245 8 | 7 2345(6) 2345-6 | | 1356 7 1345 | 123569 12459 12345 | 234-9 2345(69) 8 | +-------------------+-----------------------+---------------------------+

Multifish[6] : 9r7c4=9r7c79-9r9c8=HT(789-6)r234c8=6r89c8-6r7c9=6r7c4 @
6 Truths = {69R7 6789C8}
6 Links = {7n4 234n8 69b9}
12 Eliminations --> r234c8<>2, r23c8<>3, r23c8<>4, r7c4<>35, r4c8<>5, r8c9<>6, r9c7<>9
or
ALS-XZ Rule, Double Link[9] : 6r7c9=345r7c3679=9r7c79-9r9c8=2345r15689c8=6r89c8 @
9 Truths = {7N3679 15689N8 }
9 Links = {345r7 2345c8 69b9}
12 Eliminations --> r234c8<>2, r23c8<>3, r23c8<>4, r7c4<>35, r4c8<>5, r8c9<>6, r9c7<>9

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;

Code: Select all: +---------------------+-----------------------+------------------------+ | 9 8 1234 | 7 1234 1345 | 6 1234 1245 | | 7 5 1234 | 1234 123468 13468 | 2348 9 1248 | | 1234 123 6 | 12345 123489 134589 | 234578 12348 124578 | +---------------------+-----------------------+------------------------+ | 128(6) 4 12(7) | 12 5 -1(69) | -28(79) 128 3 | | 123 79 5 | 8 12349 1349 | 2479 6 1247 | | 1238-6 69 123 | 1234 123469 7 | 24589 1248 12458 | +---------------------+-----------------------+------------------------+ | 1234 123 9 | 6 7 1348 | 2348 5 248 | | 12345 123 8 | 9 134 1345 | 234 7 6 | | 345(6) (67) 34(7) | 345 348 2 | 1 348 9 | +---------------------+-----------------------+------------------------+

Loop[5] : 6r4c1=(6-9)r4c6=(9-7)r4c7=7r4c3-7r9c3=(7-6)r9c2=6r9c1 @
5 Truths = {679R4 7R9 6B7}
5 Links = {6c1 7c3 4n67 9n2}
4 Eliminations --> r4c7<>28, r4c6<>1, r6c1<>6
or
Sue de Coq : 7r4c3=128r4c1348=6r4c1-(6=9)r6c2-(9=7)r5c2 @
6 Truths = {4N1348 56N2}
6 Links = {128r4 679b4}
4 Eliminations --> r4c7<>28, r4c6<>1, r6c1<>6

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;

Code: Select all: +----------------------------+----------------------+-----------------------+ | 9 8 13 | 7 1234 1234 | 6 124 5 | | 7 1236 136 | 5 123468 12346 | 9 1248 248 | | 15 1256 4 | 168 12689 1269 | 128 3 7 | +----------------------------+----------------------+-----------------------+ | 6 134 138 | 1348 7 1349 | 12348 5 23489 | | 13458 9 2 | 13468 13468 13456 | 7 148 348 | | 13458 1345(7) -138(57) | 2 13489 13459 | 1348 6 3489 | +----------------------------+----------------------+-----------------------+ | 2 1346-7 13678 | 9 1346 13467 | 5 478 3468 | | 348 346-7 36789 | 346 5 23467 | 2348 24789 1 | | 1345 13456(7) -136(579) | 1346 12346 8 | 234 -24(79) 2346 | +----------------------------+----------------------+-----------------------+

Loop[4] : HP(79)r9c38=7r9c2-7r6c2=(7-5)r6c3=5r9c3 @
4 Truths = {7R69 9R9 5C3}
4 Links = {7c2 69n3 9n8}
10 Eliminations --> r6c3<>138, r9c3<>136, r78c2<>7, r9c8<>24
or
Rank 0 of cells[16] : [7r9c2=12346r9c124579=5r912 and 12356B1]-5r56c12=1348r4c23.r56c12=7r6c2 @
16 Truths = {1N3 2N23 3N12 4N23 5N1 6N12 9N124579}
16 Links = {12346r9 5c12 7c2 1236b1 1348b4}
10 Eliminations --> r6c3<>138, r9c3<>136, r78c2<>7, r9c8<>24

OR ...

Code: Select all: +--------------------------+------------------------+-----------------------+ | 9 8 13 | 7 1234 1234 | 6 124 5 | | 7 1236 136 | 5 123468 12346 | 9 1248 248 | | 15 1256 4 | 168 12689 1269 | 128 3 7 | +--------------------------+------------------------+-----------------------+ | 6 134 138 | 1348 7 1349 | 12348 5 23489 | | 13458 9 2 | 13468 13468 13456 | 7 148 348 | | 13458 13457 -138(57) | 2 13489 13459 | 1348 6 3489 | +--------------------------+------------------------+-----------------------+ | 2 1346-7 1368(7) | 9 1346 1346(7) | 5 48(7) 3468 | | 348 346-7 368(79) | 346 5 2346(7) | 2348 248(79) 1 | | 1345 134567 -136(579) | 1346 12346 8 | 234 -24(79) 2346 | +--------------------------+------------------------+-----------------------+

Multifish[6] : 9r8c8=(9-7)r9c8=XW(7C68)-7r78c3=HP(57)r69c3-9r9c3=9r8c3 @
6 Truths = {5C3 7C368 9C38}
6 Links = {7r78 9r8 69n3 9n8}
10 Eliminations --> r6c3<>138, r9c3<>136, r78c2<>7, r9c8<>24
or
Rank 0 3x6cells+2cells [18] :
18 Truths = {12478N3 12345678N6 12578N8}
18 Links = {7r78 9r8 1368c3 123469c6 1248c8 5b5}
10 Eliminations --> r6c3<>138, r9c3<>136, r78c2<>7, r9c8<>24

by **champagne** » Mon Jul 01, 2013 9:52 am

Hi JC

the 2 first examples are IMO out of the scope of leren's process. The first one has not a clear "base" for digits The second one has a special cells pattern

for leren, the second in my list should be ok

98.7..6..75.4.......3.8..7.8...7..3....29.1.......4...3..1....6.7..3..9.......2..;

Code: Select all: A B C |D E F |G H I 9 8 124 |7 125 3 |6 1245 1245* 89 7 5 126 |4 126 1269 |3 128 1289 1246 1246 3 |569 8 12569 |459 7 12459 << -------------------------------------------------- 8 12469 124569 |56 7 156 |459 3 2459 << 456 3 4567 |2 9 8 |1 456 457 * 1256 1269 125679 |3 156 4 |589 2568 25789 << -------------------------------------------------- 3 249 24589 |1 245 259 |7 458 6 12456 7 124568 |568 3 256 |458 9 1458 << 1456 1469 145689 |5689 456 7 |2 1458 3 124567 AA AA AA 56 45 12457

Code: Select all: SLG rank 0 13 Truths = {1N9 3N479 4N479 5N9 6N79 8N479 } 13 Links = {1c9 2c9 4c79 5c479 6c4 7c9 8r68 9r3 9b6 } 7 elims 1r2c9 2r2c9 5r9c4 6r9c4 8r6c8 8r8c3 9r3c6

this looks as a 3x4 matrix with a box cover for digit 9

by **Leren** » Mon Jul 01, 2013 12:28 pm

Hi Champagne and JC

Here is an update of my status re the 241 puzzles. Note that in my previous post I have provided numbers for each puzzle, to avoid confusion.

Hidden Text: Show

I fixed a bug this afternoon that resolved puzzle numbers 9, 32, 41, 70 and 84 within the bounds of my test process, which is : 3 x 3, 3 x 4, 3 x 5, 4 x 3, 4 x 4, 4 x 5 or 5 x 5 starting grid, 2 given/solved cells allowed in the grid, Truth Margin of 6 (ie up to 6 row/column -> box Truth reductions or extra cell Truth increases allowed.) . So I had already resolved 4 of the puzzles in Champagne's list. To further test his list I increased the solved/given cells to 3 and the Truth margin to 10. This enabled me to resolve a further 8 but 3 remained unresolved (despite finding literally 100s of Rank 0 constructions that gave no eliminations in 3 puzzles - the record stands at a massive 717 !)

So I've now resolved 184 of the 241 puzzles, although the test settings are far beyond what I would consider practical.

Champagne, could you provide your solution to puzzles 187, 236 and 238 - they are either outside the scope of my code or I might have a bug.

A brief look at JC's solutions indicated that they are outside the scope of my current code, but I will give them more thought tomorrow. Have a pleasant evening gents, it's getting late here in Sydney.

Leren

by **ronk** » Mon Jul 01, 2013 1:23 pm

champagne wrote:Hi JC

the 2 first examples are IMO out of the scope of leren's process. The first one has not a clear "base" for digits The second one has a special cells pattern

Looking at hidden sets in just rows or just columns, there is a "clear base" <6789> for the first. As is obvious by greatly increased truth counts, the translations to cell-only has inelegant results.

Code: Select all: 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; Rows: 9 Truths = {6R27 7R34 8R23 9R347} Cells: 21 Truths = {2N34579 3N1245679 4N23679 7N3679} OR Cols: 9 Truths = {6C1248 78C8 9C458} Cells: 25 Truths = {35689N1 3468N2 23689N4 235689N5 15689N8} For any 12 Eliminations --> r234c8<>2, r23c8<>3, r23c8<>4, r7c4<>35, r4c8<>5, r8c9<>6, r9c7<>9

Oops, did the wrong "2nd" puzzle: Show

by **champagne** » Mon Jul 01, 2013 3:41 pm

ronk wrote:Looking at hidden sets in just rows and just columns, there is a "clear base" <6789> Like many others here, the translations to just cells has inelegant, even ugly results.
Cells: 21 Truths = {2N34579 3N1245679 4N23679 7N3679}

This is in the scope of leren's process, if I take a 4x5 matrix as start, all is ok except that we have 3 given where we both have a limit to 2 given.

It seems that if we open widely the limits we have a good chance to catch nearly all puzzles identified with the other process, but the runtime has to be severely optimised. With the current code, I'll be better off keeping the existing extraction

We have still an untouched limit with no matrix "2 x n" as start

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