The New Sudoku Players' Forum

by **Leren** » Thu Jun 27, 2013 5:52 am

I've tested the first 208 puzzles (numbers 1 - 500) in Champagne's 04c multi_fish rank 0.txt file for MSLS patterns and have provided a summary in the hidden section.

Hidden Text: Show

For the first 6 puzzles I put my solver in survey mode to show the full range of MSLS patterns that I can currently see. For the remainder I've just shown the first (and smallest) pattern that was used in the solution of the puzzle.

I think these results show conclusively that MSLS 16 or 20 cell pattern(s) will provide an equivalent solution wherever 4 or 5 digit Multifish(es) can be seen. It's faster, easier to code than Multifish and there is basically only one pattern to consider. The majority of cases only require a 16 cell pattern - a 20 cell pattern is required when the smallest Multifish pattern contains at least 19 truths. 24-25 cell patterns show up in the surveys but I haven't needed one to solve a puzzle yet. There are a few 19 and 15 link patterns (one cell in the 16 or 20 cell pattern is a given). Overall this method appears to be vastly superior to the Multifish approach - quite frankly I''m stunned :shock:

The one puzzle I didn't see an MSLS pattern in is # 498, but the Multifish pattern in that puzzle is 3 digit and I can't see that either - something to work on this afternoon.

Leren

<Edit> - Based on information provided by Champagne - I've now found an MSLS solution for puzzle 498 - I''m now batting 208/208 - well done Champers!

Leren

by **JC Van Hay** » Thu Jun 27, 2013 6:28 am

Congratulations, Leren. You did an incredible good job !

I will also have a look at #498.
If you have the time, would you mind also looking at #3218, analysed by Danny some time ago, where I got a Rank 0 of 22 Cells, but didn't look for any other one.

Best Regards, JC.

by **JC Van Hay** » Thu Jun 27, 2013 7:16 am

Hi David,

Some not so "trivial" comments.

Concerning basics, I only generalized Steve Kurzhals' basics, as they can be found in his blog on the au site, to include all Rank 0 configurations.
The sk-basics, as I would be tempted to call them, are very important because all the informations collected while doing them combined with an analysis of the distribution of the givens let the puzzle himself show how it can be solved.

I particularly appreciate your detailed informations on the handling of the givens distribution to find multifishes (I too often had to struggle with your use of "promising" pairs, digits, ...

). They are of great help to accelerate the search for Rank 0 of Cells

!

David wrote:You should find that 5x5 and 4x4 grids come in complementary pairs (like simple fish) that will make the same eliminations, when the 4x4 one is easier to notate.

For 4x5 the compliment is another 5x4, but one may use fewer digits than the other.

The idea of "complementary pairs" is very exciting. I did a rapid check on 2 puzzles. Here they are ! You will see a. how their sizes are related and b. they don't give the same "direct" eliminations but well after basics !

First example : 5;elev

12.3.....4.5...6...7.....2.6..1..3....453.........8..9...45.1.........8......2..7;11.90;11.90;2.60;elev;1;5;22
Basics : LC(6C2,8R7) :=> -6r789c3,-8r9c123

Code: Select all: +-------------------------+----------------------+-----------------------+ | 1 2 689 | 3 46789 456-79 | 45789 45-79 45-8 | | 4 (389) 5 | 2789 2789-1 (179) | 6 (1379) (138) | | 389 7 3689 | 689 14689 1456-9 | 4589 2 1345-8 | +-------------------------+----------------------+-----------------------+ | 6 (589) 2789 | 1 279-4 (479) | 3 (457) (2458) | | 2789 (189) 4 | 5 3 (679) | 278 (167) (1268) | | 2357 135 1237 | 267 2467 8 | 2457 1456-7 9 | +-------------------------+----------------------+-----------------------+ | 2789-3 (3689) 2789-3 | 4 5 (3679) | 1 (369) (236) | | 23579 13456-9 12379 | 679 1679 136-79 | 2459 8 3456-2 | | 359 13456-9 139 | 689 1689 2 | 459 3456-9 7 | +-------------------------+----------------------+-----------------------+

All Cells Loop[4x4=16] : {2457N2 2457N6 2457N8 2457N9}
-{1r25 3r27 4r4 5r4 6r57 2c9 7c68 8c29 9c268}
18 Eliminations --> r138c6<>9, r1c68<>7, r7c13<>3, r9c28<>9, r13c9<>8, r1c8<>9, r2c5<>1, r4c5<>4, r6c8<>7, r8c9<>2, r8c6<>7, r8c2<>9

Basics : NP(45)r1c89 :=> -45r1c567.r3c79; 9 Singles; LC(6R5) :=> -6r6c8; FSF(9C268) :=> -9r5c1; LC(9C1) :=> -9r789c23

Complementary Rank 0 Logic of cells

Code: Select all: +---------------------------+------------------------+------------------------+ | 1 2 89-6 | 3 789-46 45679 | 789-45 4579 458 | | 4 389 5 | 2789 2789-1 179 | 6 1379 138 | | (389) 7 (3689) | (689) (14689) 1456-9 | (4589) 2 1345-8 | +---------------------------+------------------------+------------------------+ | 6 589 2789 | 1 279-4 479 | 3 457 2458 | | 2789 189 4 | 5 3 679 | 278 167 1268 | | (2357) 135 (1237) | (267) (2467) 8 | (2457) 1456-7 9 | +---------------------------+------------------------+------------------------+ | 2789-3 3689 2789-3 | 4 5 3679 | 1 369 236 | | (23579) 13456-9 (12379) | (679) (1679) 136-79 | (2459) 8 3456-2 | | (359) 13456-9 (139) | (689) (1689) 2 | (459) 3456-9 7 | +---------------------------+------------------------+------------------------+

All Cells Loop[4x5=20] : {3N13457 6N13457 8N13457 9N13457}-{2r68 7r68 8r3 9r389 1c35 3c13 4c57 5c17 6c345 8b8}
18 Eliminations --> r1c57<>4, r1c35<>6, r7c13<>3, r8c26<>9, r9c28<>9, r1c7<>5, r2c5<>1, r3c9<>8, r3c6<>9, r4c5<>4, r6c8<>7, r8c9<>2, r8c6<>7

Basics : 9 Singles; LC(6R5) :=> -6r6c8; HP(45)r1c89; FSF(9C268) :=> -9r5c1; LC(9C1) :=> -9r789c23

The puzzle is then reduced to the same easy SE9.0 puzzle

Code: Select all: +-------------------+----------------+-----------------+ | 1 2 89 | 3 789 6 | 789 45 45 | | 4 89 5 | 2789 2789 1 | 6 379 38 | | 3 7 6 | 89 4 5 | 89 2 1 | +-------------------+----------------+-----------------+ | 6 589 2789 | 1 279 4 | 3 57 258 | | 278 189 4 | 5 3 79 | 278 167 268 | | 257 135 1237 | 267 267 8 | 2457 145 9 | +-------------------+----------------+-----------------+ | 2789 368 278 | 4 5 79 | 1 369 236 | | 2579 1456 127 | 679 1679 3 | 2459 8 456 | | 59 13456 13 | 689 1689 2 | 459 3456 7 | +-------------------+----------------+-----------------+

Solving the Rank 0 R2457xC2689 ...

Code: Select all: #1. r5c6=7->C(S) :=> r5c6=9,r7c6=7; HP(27)r26c4 :=> r6c5=6; FXW(7C48) :=>-7r6c7 #2. r4c8=5->7 Singles NP(59)r9c17 :=> -9r9c45 Chain[4] : (3=6)r9c8-(6=8)r9c4-8r3c4=8r3c7-(8=3)r2c9 :=> r2c9=3 LC(9B8) :=> -9r8c7; NP(89)r24c2 :=> -8r7c2; XYW(25-6)r8c27.r7c9 :=> r7c2=3 C(S) :=> r4c8=7; ste

where C(S)=Contradiction(Singles)

Second example : 21;elev

1.......9.5....2....87...4.2...3......48.5....8.6...7...6..4.5.........1....9.3..;11.80;11.80;7.90;elev;11;21;21
Basics : JF(9C3468) : r4c4=r2c4-r2c3.r23c6=FSF(C368) :=> -9r4c7

Code: Select all: +------------------------+----------------------+------------------------+ | 1 23467 237 | 2345 4568-2 2368 | 5678 368 9 | | 467-39 5 379 | 1349 468-1 13689 | 2 1368 678-3 | | (369) 239-6 8 | 7 (1256) 1239-6 | (156) 4 (356) | +------------------------+----------------------+------------------------+ | 2 1679 1579 | 149 3 179 | 4568-1 1689 4568 | | (3679) 139-67 4 | 8 (127) 5 | (169) 1239-6 (236) | | (359) 8 139-5 | 6 (124) 129 | (1459) 7 (2345) | +------------------------+----------------------+------------------------+ | (3789) 1239-7 6 | 123 (1278) 4 | (789) 5 (278) | | 4578-39 23479 23579 | 235 5678-2 23678 | 4678-9 2689 1 | | 4578 1247 1257 | 125 9 12678 | 3 268 4678-2 | +------------------------+----------------------+------------------------+

All Cells Loop[4x4=16] : {3567N1 3567N5 3567N7 3567N9}
-{4r6 5r36 6r35 7r57 8r7 1c57 2c59 3c19 9c17}
18 Eliminations --> r2c19<>3, r3c26<>6, r5c28<>6, r8c17<>9, r57c2<>7, r18c5<>2, r2c5<>1, r2c1<>9, r4c7<>1, r6c3<>5, r8c1<>3, r9c9<>2

Complementary Rank 0 Logic of cells

Code: Select all: +---------------------------+-------------------------+------------------------+ | 1 (23467) (237) | (2345) 4568-2 (2368) | 5678 (368) 9 | | 467-39 5 (379) | (1349) 468-1 (13689) | 2 (1368) 678-3 | | 369 239-6 8 | 7 1256 1239-6 | 156 4 356 | +---------------------------+-------------------------+------------------------+ | 2 (1679) (1579) | (149) 3 (179) | 4568-1 (1689) 4568 | | 3679 139-67 4 | 8 127 5 | 169 1239-6 236 | | 359 8 139-5 | 6 124 129 | 1459 7 2345 | +---------------------------+-------------------------+------------------------+ | 3789 1239-7 6 | 123 1278 4 | 789 5 278 | | 4578-39 (23479) (23579) | (235) 5678-2 (23678) | 4678-9 (2689) 1 | | 4578 (1247) (1257) | (125) 9 (12678) | 3 (268) 4678-2 | +---------------------------+-------------------------+------------------------+

All Cells Loop[5x5-1=24] : {1489N2 12489N3 12489N4 12489N6 12489N8}
-{1r249 2r189 3r128 9r248 4c24 5c34 6c268 7c236 8c68}
18 Eliminations --> r2c19<>3, r3c26<>6, r5c28<>6, r8c17<>9, r57c2<>7, r18c5<>2, r2c5<>1, r2c1<>9, r4c7<>1, r6c3<>5, r8c1<>3, r9c9<>2

Here, the direct eliminations are the same and the puzzle remains among the hardest.

Best Regards, JC.

by **JC Van Hay** » Thu Jun 27, 2013 7:50 am

Puzzle #498

98.7.....76....5....4.6....3..9..7....8.2..4.........1.5.6..3......4..7......1..2;498;GP;H74;2;124;R;C; ; ;;

Code: Select all: +------------------------+---------------------------+--------------------------+ | 9 8 35(12) | 7 35(1) 35(24) | -6(124) 36(12) 36(4) | | 7 6 3(12) | -38(124) 389(1) 389(24) | 5 389(12) 389(4) | | 125 123 4 | 12358 6 3589-2 | 1289 389-12 7 | +------------------------+---------------------------+--------------------------+ | 3 (124) 56(12) | 9 58(1) 568(4) | 7 568(2) 568 | | 156 179 8 | 135 2 3567 | 69 4 3569 | | 2456 2479 5679-2 | 3458 3578 35678-4 | 2689 35689-2 1 | +------------------------+---------------------------+--------------------------+ | -8(124) 5 79(12) | 6 789 789(2) | 3 89(1) 89(4) | | 1268 1239 369-12 | 2358 4 3589-2 | 1689 7 5689 | | 468 3479 3679 | 358 35789 1 | 4689 5689 2 | +------------------------+---------------------------+--------------------------+

All Rows Loop[12] : {1R1247 2R1247 4R1247}-{1c358 2c368 4c69 7n1 4n2 2n4 1n7}
13 Eliminations --> r3c68<>2, r6c38<>2, r8c36<>2, r2c4<>38, r1c7<>6, r3c8<>1, r6c6<>4, r7c1<>8, r8c3<>1

Code: Select all: +---------------------+-------------------------+------------------------+ | 9 8 (1235) | 7 (135) (2345) | 124-6 (1236) (346) | | 7 6 (123) | 124-38 (1389) (23489) | 5 (12389) (3489) | | 125 123 4 | 12358 6 3589-2 | 1289 389-12 7 | +---------------------+-------------------------+------------------------+ | 3 124 (1256) | 9 (158) (4568) | 7 (2568) (568) | | 156 179 8 | 135 2 3567 | 69 4 3569 | | 2456 2479 5679-2 | 3458 3578 35678-4 | 2689 35689-2 1 | +---------------------+-------------------------+------------------------+ | 124-8 5 (1279) | 6 (789) (2789) | 3 (189) (489) | | 1268 1239 369-12 | 2358 4 3589-2 | 1689 7 5689 | | 468 3479 3679 | 358 35789 1 | 4689 5689 2 | +---------------------+-------------------------+------------------------+

All Cells Loop[20] : {1N35689 2N35689 4N35689 7N35689}-{3r12 5r14 6r4 7r7 8r247 9r27 1c358 2c368 4c69 6b3}
13 Eliminations --> r3c68<>2, r6c38<>2, r8c36<>2, r2c4<>38, r1c7<>6, r3c8<>1, r6c6<>4, r7c1<>8, r8c3<>1

Complementary All Cells Loop :

Code: Select all: +------------------------+-------------------------+-----------------------+ | 9 8 1235 | 7 135 2345 | 124-6 1236 346 | | 7 6 123 | 124-38 1389 23489 | 5 12389 3489 | | (125) (123) 4 | (12358) 6 3589-2 | (1289) 389-12 7 | +------------------------+-------------------------+-----------------------+ | 3 124 1256 | 9 158 4568 | 7 2568 568 | | (156) (179) 8 | (135) 2 3567 | (69) 4 3569 | | (2456) (2479) 5679-2 | (3458) 3578 35678-4 | (2689) 35689-2 1 | +------------------------+-------------------------+-----------------------+ | 124-8 5 1279 | 6 789 2789 | 3 189 489 | | (1268) (1239) 369-12 | (2358) 4 3589-2 | (1689) 7 5689 | | (468) (3479) 3679 | (358) 35789 1 | (4689) 5689 2 | +------------------------+-------------------------+-----------------------+

All Cells Loop[20] : {35689N1 35689N2 35689N4 35689N7}-{1r358 2r368 4r69 56c1 379c2 358c4 689c7 8b7}
13 Eliminations --> r3c68<>2, r6c38<>2, r8c36<>2, r2c4<>38, r1c7<>6, r3c8<>1, r6c6<>4, r7c1<>8, r8c3<>1

by **David P Bird** » Thu Jun 27, 2013 11:38 am

Yes! It looks as if the case for using MSLS is pretty well demonstrated now.

Puzzle #498 is tricky as the 4 digit set that stands out is (1247) because of the SK loop potential, but that only gives a rank 2 pattern.

This is the sort of co-residency grid I was considering where the number of times pairs of givens occur in the same row or column are counted.

`| 1 2 3 4 5 6 7 8 9
1| - 2 0 0 0 0 0 0 0
2| 2 - 0 2 0 1 0 1 0
3| 0 0 - 0 2 1 3 0 2
4| 0 2 0 - 0 0 1 2 0
5| 0 0 2 0 - 3 2 1 0
6| 0 1 1 0 3 - 2 1 1
7| 0 0 3 1 2 2 - 1 3
8| 0 1 0 2 1 1 1 - 1
9| 0 0 2 0 1 1 3 1 –
This shows that (124) looks the most promising subset. But even then there are more row/column options to explore.

Having a further grid where pairs in boxes are counted would also be possible. Together these grids might also give some insight into what makes the more difficult puzzles tougher. I'm not sure whether adding solved cells would make things more or less obvious.

David

by **Leren** » Thu Jun 27, 2013 12:48 pm

MSLS move for puzzle 498 based on information provided to me by Champagne.

Code: Select all: *--------------------------------------------------------------------------------* | 9 8 1235 | 7 135 2345 | 124-6 1236 346 | | 7 6 123 | 124-38 1389 23489 | 5 12389 3489 | |*125 *123 4 |*12358 6 3589-2 |*1289 389-12 7 | |--------------------------+--------------------------+--------------------------| | 3 124 1256 | 9 158 4568 | 7 2568 568 | |*156 *179 8 |*135 2 3567 |*69 4 3569 | |*2456 *2479 5679-2 |*3458 3578 35678-4 |*2689 35689-2 1 | |--------------------------+--------------------------+--------------------------| | 124-8 5 1279 | 6 789 2789 | 3 189 489 | |*1268 *1239 369-12 |*2358 4 3589-2 |*1689 7 5689 | |*468 *3479 3679 |*358 35789 1 |*4689 5689 2 | *--------------------------------------------------------------------------------*

MSLS 1 : Base 124; r35689 c1247: 20 Links; 12r3 1r5 24r6 12r8 4r9; 568c1 379c2 358c4 689c7;

20 Grid cells and 13 eliminations shown on the PM.

There was also MSLS 2 : Base 124; c35689 r1247: 20 Links; 12c3 1c5 24c6 12c8 4c9; 356r1 389r2 568r4 789r7;

Again its late at night so I hope I haven't made any late night blunders.

Leren

by **champagne** » Thu Jun 27, 2013 2:42 pm

JC Van Hay wrote:Hi David,
Try the following, if you want to, in the last Champagne's list : do find if it is possible to extract 16 unsolved cells containing a maximum of 4 candidates at the intersection of 4 rows and 4 columns and check if it gives rise to a Rank 0 Logic! This is a topological problem relatively easy to solve and a' little' more general than your MSLS approach.
Best Regards, JC.

a question to JC Van Hay

looking at examples given by leren I see some crossing with 5 candidates in a 5x5 matrix.

what is exactly the rule for the crossing if any.
If I consider Leren's lay out I got through pm, I see no constraint on the crossing (except that they must be there with a limit of one given, but this seems more a practical limit to speed up the process).

by **ronk** » Thu Jun 27, 2013 3:47 pm

Leren wrote:MSLS move for puzzle 498 based on information provided to me by Champagne.

Code: Select all
*--------------------------------------------------------------------------------* | 9 8 1235 | 7 135 2345 | 124-6 1236 346 | | 7 6 123 | 124-38 1389 23489 | 5 12389 3489 | |*125 *123 4 |*12358 6 3589-2 |*1289 389-12 7 | |--------------------------+--------------------------+--------------------------| | 3 124 1256 | 9 158 4568 | 7 2568 568 | |*156 *179 8 |*135 2 3567 |*69 4 3569 | |*2456 *2479 5679-2 |*3458 3578 35678-4 |*2689 35689-2 1 | |--------------------------+--------------------------+--------------------------| | 124-8 5 1279 | 6 789 2789 | 3 189 489 | |*1268 *1239 369-12 |*2358 4 3589-2 |*1689 7 5689 | |*468 *3479 3679 |*358 35789 1 |*4689 5689 2 | *--------------------------------------------------------------------------------*

MSLS 1 : Base 124; r35689 c1247: 20 Links; 12r3 1r5 24r6 12r8 4r9; 568c1 379c2 358c4 689c7;

20 Grid cells and 13 eliminations shown on the PM.

Using only digits <124> there exists a 0-rank row/col logic set requiring only 12 truths for the same exclusions. There may even be a smaller set of truths.

Code: Select all: +-------------------------+---------------------------+-------------------------+ | 9 8 235(1) | 7 35(1) 2345 | -6(124) 236(1) 346 | | 7 6 23(1) | -38(124) 389(1) 23489 | 5 2389(1) 3489 | | 15(2) 13(2) 4 | 1358(2) 6 3589-2 | 189(2) 389-12 7 | +-------------------------+---------------------------+-------------------------+ | 3 (124) 256(1) | 9 58(1) 568(4) | 7 2568 568 | | 156 179 8 | 135 2 3567 | 69 4 3569 | | 456(2) 479(2) 5679-2 | 358(4) 3578 35678-4 | 689(2) 35689-2 1 | +-------------------------+---------------------------+-------------------------+ | -8(124) 5 279(1) | 6 789 2789 | 3 89(1) 89(4) | | 168(2) 139(2) 369-12 | 358(2) 4 3589-2 | 1689 7 5689 | | 468 3479 3679 | 358 35789 1 | 689(4) 5689 2 | +-------------------------+---------------------------+-------------------------+ 12 Truths = {1R1247 4R47 2C1247 4C47} 17 Links = {2r123468 1c358 7n1 4n2 26n4 1n7 2b7 4b59} 13 Eliminations --> r3c68<>2, r6c38<>2, r8c36<>2, r2c4<>38, r1c7<>6, r3c8<>1, r6c6<>4, r7c1<>8, r8c3<>1

by **champagne** » Thu Jun 27, 2013 4:02 pm

ronk wrote:Using only digits <124> there exists a 0-rank row/col logic set requiring only 12 truths for the same exclusions. There may even be a smaller set of truths.

this is what found my solver (12 truths 12 links with either a row base or a column base), but I think the goal of leren was to see the corresponding cells base logic.

by **ronk** » Thu Jun 27, 2013 8:36 pm

champagne wrote:
ronk wrote:Using only digits <124> there exists a 0-rank row/col logic set requiring only 12 truths for the same exclusions. There may even be a smaller set of truths.
this is what found my solver (12 truths 12 links with either a row base or a column base), but I think the goal of leren was to see the corresponding cells base logic.

OK, as a courtesy to Leren then, I'll wait a couple of days before posting any all cells logic sets.

by **Leren** » Fri Jun 28, 2013 1:54 am

A question to Champagne, do you know of any other puzzles other than # 498 that have 3 digit, but no 4 or 5 digit Multifish ?

Your 04c multifish_rank 0.txt file indicated that # 983 and 984 had this property but they also have 4 digit Multifish.

For the academically minded in # 984 I found the following 20 MSLS patterns - the current record holder.

Hidden Text: Show

MSLS 1 : Base 389; r24568 c1379: 20 Links; 89r2 8r5 389r6 39r8 ; 67c1 12c3 12c7 67c9 ; 4b4 5b4 4b6 5b6 ;
MSLS 2 : Base 389; r24568 c13679: 24 Links; 89r2 8r5 389r6 39r8 ; 67c1 12c3 1267c6 12c7 67c9 ; 4b4 5b4 4b6 5b6 ;
MSLS 3 : Base 489; c24568 r1379: 20 Links; 48c2 9c4 489c6 89c8 ; 67r1 12r3 12r7 67r9 ; 3b2 5b2 3b8 5b8 ;
MSLS 4 : Base 489; c24568 r13679: 24 Links; 48c2 9c4 489c6 89c8 ; 67r1 12r3 1267r6 12r7 67r9 ; 3b2 5b2 3b8 5b8 ;
MSLS 5 : Base 1267; r1379 c2458: 16 Links; 67r1 12r3 12r7 67r9 ; 48c2 39c4 35c5 89c8 ;
MSLS 6 : Base 1267; c1379 r2458: 16 Links; 67c1 12c3 12c7 67c9 ; 89r2 45r4 58r5 39r8 ;
MSLS 7 : Base 1267; r1379 c24568: 20 Links; 67r1 12r3 12r7 67r9 ; 48c2 39c4 35c5 4589c6 89c8 ;
MSLS 8 : Base 1267; c1379 r24568: 20 Links; 67c1 12c3 12c7 67c9 ; 89r2 45r4 58r5 3489r6 39r8 ;
MSLS 9 : Base 1267; r13679 c24568: 24 Links; 67r1 12r3 1267r6 12r7 67r9 ; 48c2 39c4 35c5 4589c6 89c8 ;
MSLS 10 : Base 1267; c13679 r24568: 24 Links; 67c1 12c3 1267c6 12c7 67c9 ; 89r2 45r4 58r5 3489r6 39r8 ;
MSLS 11 : Base 3489; r2458 c1379: 16 Links; 89r2 4r4 8r5 39r8 ; 67c1 12c3 12c7 67c9 ; 5b4 5b6 ;
MSLS 12 : Base 3489; r24568 c1379: 20 Links; 89r2 4r4 8r5 3489r6 39r8 ; 67c1 12c3 12c7 67c9 ; 5b4 5b6 ;
MSLS 13 : Base 3489; c24568 r1379: 20 Links; 48c2 39c4 3c5 489c6 89c8 ; 67r1 12r3 12r7 67r9 ; 5b2 5b8 ;
MSLS 14 : Base 3489; r24568 c13679: 24 Links; 89r2 4r4 8r5 3489r6 39r8 ; 67c1 12c3 1267c6 12c7 67c9 ; 5b4 5b6 ;
MSLS 15 : Base 3489; c24568 r13679: 24 Links; 48c2 39c4 3c5 489c6 89c8 ; 67r1 12r3 1267r6 12r7 67r9 ; 5b2 5b8 ;
MSLS 16 : Base 3589; r24568 c1379: 20 Links; 89r2 5r4 58r5 389r6 39r8 ; 67c1 12c3 12c7 67c9 ; 4b4 4b6 ;
MSLS 17 : Base 3589; r24568 c13679: 24 Links; 89r2 5r4 58r5 389r6 39r8 ; 67c1 12c3 1267c6 12c7 67c9 ; 4b4 4b6 ;
MSLS 18 : Base 4589; c2458 r1379: 16 Links; 48c2 9c4 5c5 89c8 ; 67r1 12r3 12r7 67r9 ; 3b2 3b8 ;
MSLS 19 : Base 4589; c24568 r1379: 20 Links; 48c2 9c4 5c5 4589c6 89c8 ; 67r1 12r3 12r7 67r9 ; 3b2 3b8 ;
MSLS 20 : Base 4589; c24568 r13679: 24 Links; 48c2 9c4 5c5 4589c6 89c8 ; 67r1 12r3 1267r6 12r7 67r9 ; 3b2 3b8 ;

Now that I've included 3 digit MSLS patterns they show up in other puzzles - they appear to be subsets of 4 digit patterns and make the same eliminations
as the 4 digit patterns, when follow-on basics are taken into account. What I'm looking for is other puzzles where a 3 digit pattern actually makes a difference.

Leren

by **champagne** » Fri Jun 28, 2013 5:54 am

Leren wrote:A question to Champagne, do you know of any other puzzles other than # 498 that have 3 digit, but no 4 or 5 digit Multifish ?

Leren

I don't have that in direct access in the potential hardest file, but I have, I think, some corresponding puzzles in my ongoing search in the file with ratings below the potential hardest.

here a sample of such puzzles all should have a row base rank 0 logic using the floors shown at the end of each line

Hidden Text: Show

by **JC Van Hay** » Fri Jun 28, 2013 2:15 pm

champagne wrote:
JC Van Hay wrote:Hi David,
Try the following, if you want to, in the last Champagne's list : do find if it is possible to extract 16 unsolved cells containing a maximum of 4 candidates at the intersection of 4 rows and 4 columns and check if it gives rise to a Rank 0 Logic! This is a topological problem relatively easy to solve and a' little' more general than your MSLS approach.
Best Regards, JC.

a question to JC Van Hay

looking at examples given by leren I see some crossing with 5 candidates in a 5x5 matrix.

what is exactly the rule for the crossing if any.
If I consider Leren's lay out I got through pm, I see no constraint on the crossing (except that they must be there with a limit of one given, but this seems more a practical limit to speed up the process).

I will suppose that by crossing you mean overlapping cover sets (OCS). As with the case of overlapping base sets (OBS), as long as the number of OBS is equal to the number of OCS, the Rank 0 Logic applies. So no rules, great Rank 0 Logic

.

I looked more closely at puzzles #12, 13, 14 and 17. You certainly have noticed, and Leren as well, that in these puzzles, each Rank 0 array of 24 cells is equivalent to a Rank 0 sub-array of 20 cells [making eliminations in one of its rows (cannibalism -> an assignment could follow as in # 14 and 17). However, to someone who doesn't notice that, the cannibalism will not be seen directly, but only after basics follow-on.] Therefore , shortly said, adding 4 cells to get a Rank 0 of cells from another one only requires 4 more overlaping or not cover sets.

by **champagne** » Fri Jun 28, 2013 3:58 pm

JC Van Hay wrote: do find if it is possible to extract 16 unsolved cells containing a maximum of 4 candidates at the intersection of 4 rows and 4 columns
...
I will suppose that by crossing you mean overlapping cover sets (OCS). ...

Hi,

thanks for the answer (BTW, I doubled the question through pm)

The post shows that I was not clear enough.

I refer strictly to your following wording 16 unsolved cells containing a maximum of 4 candidates at the intersection of 4 rows and 4 columns

I understand here that in a 4x4 cells matrix having a chance to produce a rank 0 SLG, the cells must not contain more than 4 candidates. If this is correct, it can speed up the search substantially, but I don't see what is the logic behind.

sorry to come back with the same question

by **Leren** » Sat Jun 29, 2013 12:48 am

Code: Select all: Champagne wrote: I refer strictly to your following wording 16 unsolved cells containing a maximum of 4 candidates at the intersection of 4 rows and 4 columns

Hi Champagne, I'm not sure what this statement means either, I'll just explain how I've implemented the MSLS search process.

Pick any 4 digits. Call these the Row digits (in practice they are the Floor or Base digits of the corresponding Multifish). Call the remaining 5 digits the Column digits (these are the non-base or Roof digits of the Multifish).

Pick a 4 x 4 grid of unsolved cells. These cells must hold exactly 16 truths.

The idea behind a 4 x 4 MSLS is to (1) eliminate the Row digits in the 4 rows but not in the 4 columns of the grid and (2) eliminate the 5 Column digits in the 4 columns but not in the 4 rows of the grid. (Take a good look at any Multifish solution - that's what actually happens - the base digits get eliminated in 4 or 5 rows but not in 4 or 5 columns and the non-base digits get eliminated in 4 or 5 columns but avoid 4 or 5 rows. Sometimes this pattern is hard to see but it's always there if you look hard enough.)

For these eliminations to be valid the counts of the 4 row digits in the 4 rows of the grid plus the count of the column digits in the 4 columns of the grid must be exactly 16.

Now it looks like this search process may take a long time unless you "know'' beforehand what the likely grid locations and base digits are. In practice this simply isn't true. The base digits and grid cells almost "magically" pick themselves quite quickly.

Why is that ? Good question - glad you asked

Well, look first at the grid cells. In practice there aren't all that many 4 x grids of unsolved cells. What I do is pick any row as the first row, any column as the first column, any other row as the second row etc etc. As you add each row and column to build up the grid look at the newly created intersections. If any of them are solved or given then the potential grid is already invalid. So in practice you don't end up building most grids very far before they are proved invalid.

Now for the choice of row and column (Floor and Roof) digits. When you have built a valid grid then if you make bad choice of row and column digits the total link count will be about twice the required value, so you can move on to a new choice of digits without much processing. If the Link count is 16 you are lucky and you've got yourself a basic (or vanilla ) Rank 0 MSLS - again without much processing required.

If the Link count is slightly more than 16 you can reduce it by substituting box covers for row or column covers, where there are 2 or 3 rows in the same Tier or columns in the same Stack and one or more boxes in those rows or columns don't contain the digit of interest in any of the grid cells. I think this is where most of the processing effort takes place, there are a lot of cases to consider, so in practice I limit the initial Link count to <= the number of grid cells + 5. Above that I don't think there is much chance of achieving a Truth/Link balance.

One other trick is to allow for up to 1 cell in the grid to be given or solved. This reduces the Truth requirement to 15 but increases the number of valid grids but does catch a few extra MSLSs. if you allow the number of solved/given cells to be > 1 then the processing time will go up a lot and I doubt that you will catch many more valid cases.

Of course in everything I've said above you can interchange row/columns and you can have 4 x 5, 5 x 4 or even 5 x 5 grids. You can also have 3 row digits and 6 column digits. This is how I found the MSLS for puzzle 498.

Take a look at the MSLS survey results for the following puzzle:

1.......2..94...5..6....7.....89..4....3.6.....8.4.....2....1..7.......6..5.8..3.;12;tax;gsf-2007-05-24-003 64879;3;1267;R;C;X; ;;

MSLS 1 : Base 1267; r1378 c3458: 16 Links; 67r1 12r3 67r7 12r8 ; 34c3 59c4 35c5 89c8 ;
MSLS 2 : Base 1267; r1378 c34568: 20 Links; 67r1 12r3 67r7 12r8 ; 34c3 9c4 3c5 3489c6 89c8 ; 5b2 5b8 ;
MSLS 3 : Base 1267; c1279 r24569: 20 Links; 26c1 17c2 26c7 17c9 ; 38r2 3r4 489r5 39r6 49r9 ; 5b4 5b6 ;
MSLS 4 : Base 1267; r13578 c3458: 19 Links; 67r1 12r3 127r5 67r7 12r8 ; 34c3 59c4 35c5 89c8 ;
MSLS 5 : Base 1267; c12679 r2469: 20 Links; 26c1 17c2 127c6 26c7 17c9 ; 38r2 35r4 359r6 49r9 ;
MSLS 6 : Base 1267; c12679 r24569: 24 Links; 26c1 17c2 127c6 26c7 17c9 ; 38r2 35r4 4589r5 359r6 49r9 ;
MSLS 7 : Base 3489; c3458 r1378: 16 Links; 34c3 9c4 3c5 89c8 ; 67r1 12r3 67r7 12r8 ; 5b2 5b8 ;
MSLS 8 : Base 3489; r24569 c1279: 20 Links; 38r2 3r4 489r5 39r6 49r9 ; 26c1 17c2 26c7 17c9 ; 5b4 5b6 ;
MSLS 9 : Base 3489; c34568 r1378: 20 Links; 34c3 9c4 3c5 3489c6 89c8 ; 67r1 12r3 67r7 12r8 ; 5b2 5b8 ;
MSLS 10 : Base 3489; r24569 c12679: 24 Links; 38r2 3r4 489r5 39r6 49r9 ; 26c1 17c2 1257c6 26c7 17c9 ; 5b4 5b6 ;

MSLS 1 - vanilla 4 x 4 grid case (no box link substitutions)
MSLS 2 - 4 x 5 grid with 2 box substitutions
MSLS 3 - similar to 2 with - rows/columns interchanged
MSLS 4 - vanilla 5 x 4 grid with one given/solved cell
MSLS 5 - vanilla 5 x 4 grid - rows/columns interchanged
MSLS 6 - vanilla 5 x 5 grid - 1 one given/solved cell - rows/columns interchanged
MSLS 7 - 4 x 4 grid - box link substitutions - rows/columns interchanged
MSLS 8 - 5 x 4 grid - box link substitutions
MSLS 9 - similar to MSLS 8 rows/columns interchanged
MSLS 10 - 5 x 5 grid - 1 one given/solved cell - box link substitutions

Thus endeth the lesson !!

Leren

The New Sudoku Players' Forum

Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume

Re: Exotic patterns a resume