## 0-rank logic sets in the hardest puzzles

Advanced methods and approaches for solving Sudoku puzzles

### Re: 0-rank logic sets in the hardest puzzles

champagne wrote:May I suggest a challenging search ... fata morgana

Searching for gold where many have already been doesn't seem promising to me.
ronk
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### Re: 0-rank logic sets in the hardest puzzles

daj95376 wrote:
ronk wrote: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.

Looking at the graphic reveals seven cover cells, a prime number. Therefore, in this case your expression below won't work.

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

I didn't search for a 5-templates (subset) either, but made an educated guess at a <34579>-template complementary to your <1268>-template.
ronk
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### Re: 0-rank logic sets in the hardest puzzles

ronk wrote: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

ronk I have a problem with that post.

I had a look to the number 3.
It does not fit with the GP;H1521 puzzle.

EDIT : wrong interpretation on my side of the truths, it's ok.

After my last run, I worked out a list of puzzles having very high chances to produce some rank 0 logic not in the basic forms seen by my code.

The last 2 items in the list are

a rough estimate the number (divided by ten) of potential eliminations
the digits having given that number

But most of the puzzles in that list should give a rank 0 logic with 4 digits.

Hidden Text: Show
98.7.....7...6......5..97..5....84...9.6...3...4.2...1.5....8.....3....6....1..2.;12177;GP;kz0;11;12346;
98.7..6..5...6......6....7.8..4....3.4...2.1...5.9......8.5.7.....3...4......1..2;12742;GP;kz0;11;12347;
98.7.....6...9.7....7..5...5...4..3..4...2..1..98.......65..9......3...4.....1.2.;14518;GP;kz1a;11;12348;
..34..7...5...9..6..9.2.....1..97.6....2..1..8.....9...7..156......3..7........5.;2447;elev;1652;10;23478;
1...5......7.....6.897.......89....3.7.......5...3.4...3.6....8.....21......4..2.;5586;elev;L550;10;12456;
98.7..6..7...9..85..4......8...7.3....5.....4.....2.1.6..9...2..9..3.8.......1...;13227;GP;kz0;10;12345;
98.7..6....5.6........9..4.3......2..2...97....12....4.6..2.8....38..........7.5.;19896;GP;KZ1C;10;13459;
.....6.8...71..2.....32...1..1.4...7.6.....5.9.........9.........42....38....5.7.;2325;elev;L206;9;45689;
1....6....5.1...3...9.2..............7...5.1.....3.4.8..8...9.4..2.9....7....3.6.;5233;elev;2544;9;13567;
98.7..6......96..........5.7....94...3.4.......287....6...8.7...2.....3...1.....5;9470;GP;cy4;9;12358;
98.7.....6...8.7....7..5...5...4..3..4...2..1..96.......85..9......3..4......1..2;11747;GP;kz0;9;12347;
98.7..6..5...6......6.98...4..3...5...2.....1....7.9..1......2..3...78....5.....4;12758;GP;kz0;9;12345;
98.7.....7...6......5..87..5....98...7.6...4...3.2...1.5....3.....4...2.....1...6;16434;GP;Kz1 b;9;12346;
98.76....54....7.......5.8.8......4....3....2....1.6..7..6....3.5...9.7....2..1..;23722;GP;KZ1C;9;12367;
98.76....54....7.......5.8.8......4....3..6......2...17..6....2.5...9.7....1..3..;29918;GP;2011_12;9;12367;
..34..7...5...9.2.....1....23.....5...1.6.3..8..........46..........8.9....17.6..;5416;elev;2183;8;23589;
98.7.....6...5.8....5....7..4......3..98.........42.1...65..7......1..4......3..2;10031;GP;22ky5;8;12346;
98.7.....6...5.9....5....7..4......3..89.........42.1...65..7......1..4......3..2;10067;GP;22ky5;8;12346;
98.7..6..7...9..5...4......6..3....2.7..8.9.......1...3...6.8....5....4......2..1;10686;GP;22ky5;8;12345;
98.7..6....5.9.........4.3.5...2...1.18....2...2...7...5..1...8...3..4.......6.7.;12529;GP;kz0;8;23467;
98.7..6..5...6......6....7.8..4....3.4...2.1...9.8......8.5.7.....3...4......1..2;12743;GP;kz0;8;12347;
98.7..6..5...9......4..3...3....5.4...9.4...6...6..2...1......8...1...62.....71..;16977;GP;Kz1 b;8;34579;
98.7.....6...8.7....7..5.8.4....3..2..68.........4..1...96..5......12.4.........3;19062;GP;KZ1C;8;12348;
98.7..6..75.....8...6......4...3......8....9......24.1.6..4...3..75...6......12..;22565;GP;KZ1C;8;12346;
98.7.....6...8.7....7..5.8.4....3.2...98.........4...1..69..5......2...3.....1.4.;28047;GP;2011_12;8;12347;
.2...6..94......3...8...5.........7....61...2.7..92....6..7...1.....1.9....5..3..;2706;elev;1228;7;12679;
1....67...5.........92........3...5......48.67...6...1..29...3.8....3..4......1..;3060;elev;L314;7;23579;
1....6..9.......3...9.3.5...4..7.3....5...42.9.......8...8.....6....1.....2.4..7.;3158;elev;L313;7;16789;
12..5......7..9...6..3...1.........7.....48...3..6..2...9..84..5...9..3..6.......;3308;elev;L316;7;45789;
98.7..6....5.9.........8.4.5...3...2.21....3...3...7...5..2...1...4...7......68..;12533;GP;kz0;7;46789;
98.7..6..5...6......6.89...4..3...5...2.....1....7.3..1......2..6...79....5.....4;12756;GP;kz0;7;12345;
98.7..6..5...9......4..3...3....5.4...9.4...6...6..2...1.....62...1....8.....71..;12858;GP;kz0;7;34579;
98.7.....6...9.7....7..5...4....3.2..9..4...1..68.......96..5......1...3.....2.4.;19227;GP;KZ1C;7;12348;
98.7..6....5.64.......9..3.8....67...5......9...8...2.7...8.4...2......3..1..7...;19954;GP;KZ1C;7;12359;
98.7..6..5...6......6..9...8....4.3...7.9.5.....2....1.3......2..9.8.7.......1.4.;20590;GP;KZ1C;7;12348;
98.7..6..7..5.......4.8..7.8..39..4..43..............2.7..3..9....6....5.....12..;22146;GP;KZ1C;7;12569;
98.7..6..75..6......6......4....3.2..9.4....1..5.7......9.5.8.....1...4......2..3;23250;GP;KZ1C;7;12347;
98.7..6....5.9......4..3...3....5.4...9.4...6...2..8...1.....68...1....2.....71..;28327;GP;2011_12;7;34579;
champagne
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### Re: 0-rank logic sets in the hardest puzzles

champagne wrote:After my last run, I worked out a list of puzzles having very high chances to produce some rank 0 logic not in the basic forms seen by my code.
...
But most of the puzzles in that list should give a rank 0 logic with 4 digits.

98.7.....7...6......5..97..5....84...9.6...3...4.2...1.5....8.....3....6....1..2.;12177;GP;kz0;11;12346;
98.7..6..5...6......6....7.8..4....3.4...2.1...5.9......8.5.7.....3...4......1..2;12742;GP;kz0;11;12347;
...

Thanks for filtering and posting these puzzles. For the two listed above, <12346>-templates and <12347>-templates, respectively, certainly destroy the puzzles. Indeed, they are both reduced to a cascade of singles. We know that all puzzles are solved with 9-templates, so it's not a surprise that k-templates become more effective with increasing k.

Using subsets of the truths contained in the 5-templates above, an overlay of Xsudo-like logic subsets can certainly make the same exclusions. Whether any of these logic subsets are 0-rank, I don't know, but I'll certainly take a long look.

BTW I think it's more likely that 0-rank logic sets would be found where the number of exclusions due to templating is in the 10 to 40 range, rather than near 100.
ronk
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Joined: 02 November 2005
Location: Southeastern USA

### Re: 0-rank logic sets in the hardest puzzles

For quite a while I have wondered how to implement XSUDO type logic into my own solver, fearing it as simply too difficult. David Bird's recent posts made me realise that some modest progress in this area might be possible. I have modified the method David posted to detect rank 0 logic with the truths in the rows as follows: Take 4 base set digits and determine the rows and columns not containing these as givens/solved. Therefore, if there are 4 rows found there are 16 truths, or if 5 rows then 20 truths, etc. The unsolved cells at the intersections of the rows and columns constitute cell links, and the columns passing through the base set digits contain the column links which are easily computed as (total number of base set digits)-(number of base set digits in column). When the truths = cell links + column links, then the rank 0 pattern is established. This was easily extended to base sets of 5 digits, and also to the situation where one of the base set digits is allowed to be in a row containing the truths, leading to patterns with 19 truths. I tested this methodology with the first 100 of Champagne's "03 G multi fish seen.txt" file. Only 7 of them did not yield a rank 0 logic pattern. The number of truths, if there is a SK loop, and if there is an exocet is indicated.

first 100 of champagnes 03 G multi-fish: Show
Code: Select all
`12.3.....4.5...6...7.....2.6..1..3....453.........8..9...45.1.........8......2..7;5;elev;1;G1              16T   -   -2.......6.5..8..1...4...9...7.3.1......82.......7.5.3...9...4...8..1..5.6.......2;10;tax;tarek-ultra-0203;G13                          19T   SK   -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;G123                       16T   SK   -6.......2.9.4...5...1...7...5..84.......2.......3.5.4.2.....6...3...9.8...7.....1;13;tax;coloin-04-10;G13             16T   SK   -1.......2.9.4...5...6...7...5.3.4.......6........58.4...2...6...3...9.8.7.......1;14;tax;coloin-04-10;G13             16T   SK   -1.......2.3.4...5...6...7...5.8.4.......29......3...9...7.....1.9...8.4.2.....6..;17;Hp54;4;G123                16T   SK   -1.......2.3.4...5...6...7...5.9.4.......23......8...9...2...6...9...8.4.7.......1;18;Hp54;1;G123               16T   SK   -.2.4..7....6.....17...3......5....6..4.2..9.......5..8..1..8....9..7.......92.3..;20;elev;10;G2                20T   -   -1.......9.5....2....87...4.2...3......48.5....8.6...7...6..4.5.........1....9.3..;21;elev;11;G1                16T   -   -5.......9.2.1...7...8...3...4.6.........5.......2.7.1...3...8...6...4.2.9.......5;22;tax;m_b_metcalf;G13             16T   SK   -..3.8....7..2......6...9.1.........3.....596..9.....54.1...45..8...3......27.....;23;tax;tarek071223170000-;G13          16T   SK   -1.......6.5.7...8...3...4.....5.8.9.....3.....8.92....6.....3...7...5.2...4.....1;24;col;H1;G13                16T   SK   -98.7.....6..89......5..4...7...3.9....6...7....2....41.6..8.3.......1..5.......2.;25;GP;H2;G1                20T   -   -98.7.....6..89......5..4...7...3.9....6...7....2....51.6..8.3.......1.4.........2;26;GP;H3;G1                20T   -   -1......8......92....6.3...52....8.....5.7.....6.5....4..47...........91..3..6...7;28;elev;14;G1                20T   -   -.2....78.4.......6.9..7..1....5....3.....1.......9.12..7..1.8..5....4.....67.3...;29;elev;7;G12                20T   -   -.....6..94...8.2.....7...1.2.9...8....4.3.9...6.....5.3.8.4.......5......7...1...;31;elev;4;G1                16T   -   -1....6.......8.2...9.7....5.7.3...5......16....4....73..59....48...2.....3.......;32;elev;L1;G1                20T   -   -1.......9.4...3.8...2...6...7..58.......2.......7.4.5...6...2...3.8...7.9.......1;38;tax;tarek-2803;G13             16T   SK   -1.......2.9.4...5...6...7...5.3.4......96.........8.4...2...6...3...9.8.7.......1;39;tax;coloin-04-10;G123             16T   SK   -1.......2.3.4...5...6...7...5.8.3.......7.......95..8.7.....6...9...8.3...2.....1;40;tax;jpf-04/08;G13             16T   SK   -..34..7.......9..2....1..5.2.........38...6..6.43.........2..9......5..1.6.8..3..;41;tarekdb;pearly6000-4268;G13          16T   SK   -..34..7.......9..2....1..5.27........38...6....43.........2..9......5..1.6.8..3..;42;tarekdb;pearly6000-3802;G123         16T   SK   -..345........89......2..4...1......7..4.2.8..9......6...28..5..6......9..7......1;45;tarekdb;pearly6000-3112;G123          16T   SK   -.2...6......1...3...9.7...5..5....78.3.....1.8...4.5....4.9.8...6...2...9.......7;47;elev;H1;G1                20T   -   -...4...8...6..91......3...42....56...7..4..3...5........1..2...5.....9...8..6...7;49;elev;29;G2                20T   -   -...4....9....8.1...8..13........8..7.3..6.2....75......1...26....4.....59......7.;50;elev;L4;G12            16T   -   -1.......2..34...5..6....7.....85..9....3.6.....8.9.....2....1..7.......6..9.8..3.;51;tax;jpf-04/14/B4;G123         16T   SK   -1.......2.3.4...5...6...7...5.8.4.......73......9...8.7.....6...4...8.9...2.....1;52;tax;jpf-04/14/01;G123         16T   SK   -..1...5...2.4...6.3....7....6.28........9..2.......4.65.....1...9.8...4...7.....3;54;col;H2;G13            -   -   -....56.8...71.....6.....4.......85...3......29...4..6..1.7.......2.....38...9..5.;55;elev;30;G1            20T   -   -98.7.....7..6..8....5.4....37....6...6.........2....31...3..98.....1...2.....5..4;57;GP;H8;G12            20T   -   -12...6....5...92....8.3........7...3...8....49....15....4....7.56....9..........1;58;elev;L5;G12            20T   -   -1.......2..34...5..6....7......3..4....8.6.....954.....2....1..7.......6..5.9..8.;60;tax;jpf-04-10;G123         16T   SK   -..34....9.5...9.......2.1..2...7.....84........98....3.9.5....86......7.....1.6..;62;elev;21;G2            20T   -   -.2...6......18......8.3.4....49....3....4.8..5......7.7......2...13..9...6...5...;63;elev;23;G2            20T   -   -.2....7..4....9..3....1..6....3.5..88.......5.6....2...1..7....5..9.4.....98.....;65;elev;22;G2            19T   -   -1.....7.9.57....3..8.7.....2...4......68......38....5......1..4....9...2...3..56.;68;elev;25;G2            20T   -   -1.....7.9.57....3..8.7.....2...4......68......38....5......1..2....9...4...3..56.;71;elev;26;G2            20T   -   -1....6.8.4......36....7.5...4...1..3....2......97......3...8.6...25..9...1.......;72;elev;27;G1            20T   -   -1.......2.3.4...5...6...7...5.8.3.......74......9...8.7.....6...9...8.3...2.....1;74;tax;jpf-04/14/02;G123         16T   SK   -..34...8..5....1..7.......6.1....5....8.9..2.6.......7..294........3..4....8.5...;75;tarekdb;pearly6000-4143;G123      16T   SK   -3.......8.7.5...1...6...4...9.2.1.......4.......97..2.4.....3...5...2.7...8.....6;76;tax;tarek-ultra-0313;G13         16T   SK   -3.......1.4...2.7...5...8......76.4.....5.....6.2.9...1.....5...7.6...9...8.....3;77;tax;tarek-1847;G13         16T   SK   -1.......2.9.4...5...6...7...5.9.3.......7.......85..4.7.....6...3...9.8...2.....1;78;tax;Easter-Monster;G13         16T   Sk   -..3.5....4....9....8.7....1..5.3.....1.6...2.9....4......8...72.6......8......41.;80;tarekdb;pearly6000-3978;G123      16T   SK   -...1....9.......85..9.5..6...5.3...6.7...2...1..4.......3.8..9..2...73..4........;82;col;H3;G13            -   -.......35.....2.6...3.5..8...5.9...6.7....9..1..4.......6.8..9..2.1.....4....7...;83;col;H4;G13            -   -   EX..345.........9......2.34...1......7..4.2.8..9......6...28..5..6......9..7......1;86;tarekdb;pearly6000-3238;G13      16T   SK   -...4......5..8...3..9..2....9..6.3.......4.1...47...2..6....8..8...9...5..1....7.;88;elev;43;G1            16T   -   -....5.7.....1.9.6.........52....8.16.......2..3....4.7.7..4......19.2...9.86.....;89;elev;42;G1            20T   -   -1...5..8...7.....6.9.2.........13....7.9..4..8..5......4.6..9.......5.3...2...6.7;90;elev;45;G1            20T   -   -   (BS 5)1....6.8....7....3.9....5....5.4.....4....2..6....1.3...2.9....8....3.7....8....6;91;elev;44;G1            20T   -   -....5..8...67..1.......3..426.9.............19.7...2...3..4..1......8..5..21..6..;92;elev;41;G13            -   -   EX..3.5...9...1..........2....7...1.6.5........9.8.3.4.....2...7...5...8.48...4...3;96;elev;49;G1            20T   -   -....5..8.4....9..3...2..1...6...3.....18...3.93......7..2...5...7...4..66..5.....;98;elev;L8;G12            16T   -   -.......8...6...12....2..6.5..15..9..8....3....4..7....3....8.....21....6.7..4....;99;col;H5;G13            16T   SK   -3....97...6..4......18.....5......93.....327.........8..4.1....2....7.5..8.6.....;100;tax;tarek071223170000-;G13      16T   SK   -1......8......913.......5.6..7.4....3....1.5..6.2.....5....89...4..7......26.....;101;tax;col-201107-M3-3;G123         16T   SK   -987......65.........49..8..5..8..7......3..4......2..1.6.7..5......4...3.....1.2.;102;GP;H10;G23            19T   SK   -5.......9.2.1...7...8...3...4...2.......5.......7.6.1...3...8...6...4.2.9.......5;103;tax;StrmCkr;G13         16T   SK   -98.7..6....5.4.......9...8.6.....3.937......8..2....1..3.6..8......5.........1.4.;105;GP;H14;G1            20T   -   -....5.7.......9.32...1.2.6...4......8...4.....3.2.1....1.6...9.5.7...8...9....3..;107;elev;51;G12            20T   -   -.23..6...4...8......93.7.......6..7..769...2.5.......1........5.3.6...9.....1.8..;108;elev;54;G1            20T   -   -.23...7..4.......66......1....5.8.....57.....97..6.......8.23....2..58......1...4;109;elev;53;G2            20T   -   -98.7.....7..8..6....5.4....63....9...7.........2....31...3..89.....2...5.....4..2;111;GP;H12;G12            20T   -   -98.7.....6..89......5..4...7...3.9....6...7....2....41.6..8.3.......1.5.........2;112;GP;H15;G1            20T   -   -12.....8..5....13...9.....421...3.......7......76........94...6.....5..38....2.5.;113;elev;57;G12            20T   -   -1......8..5......68.9..21..............57...2..4..8.9.....6...3..1..4.2..7.3.....;114;elev;L9;G1            -   -   -1....67......8...6.9.2........9...5.3...1.8........6.1..2....4.7...3...8..45.....;115;elev;55;G2            20T   -   -1.3....8..5......6..9.2.1.......4..78...9..1....5....23..6......4...7.....1.3..2.;116;elev;56;G1            16T   -   -1.......2..34...5..6....7......3..4....5.6.....894.....2....1..7.......6..5.8..9.;117;tax;jpf-04/14/14;G123         16T   SK   -..3.....9...1...63.....75....196.....4.......7....5......6...21..92...3.8.....4..;119;elev;L10;G2            20T   -   -....56..94......3...9...5.12..........6..81...4.7...........9....8.6...5.3.2...7.;122;elev;36;G1            20T   -   -1.3.......5...9...6...3.1..2.....3....4.1...2.8.....7..7...5......8...9...6.2.4..;124;elev;40;G2            20T   -   -1.....7.9.57....3..8.7.....2....4.....68......38....5......1..2....9...4...3..56.;125;elev;38;G2            -   -   -1.......7.2.4...6...3...5...4.2.9.......46.9....5.......7...1...8.9...2.5.......3;133;col;H6;G13            25T   SK   -   (BS 5).2...6......1...3...9.7...5..5....78.3.....1.8...4.5....4.9.8...6.2.....9.......7;135;elev;H3;G1            20T   -   -5.......8.3...2.4...9...1......27.3....5.4....7.63....8.....9...4.7...6...1.....5;140;tax;tarek-2228;G13         19T   SK   -6.......2.9.4...5...1...7...5.34........6.......8.5.4.2.....6...3...9.8...7.....1;141;tax;coloin-04-10;G13         16T   SK   -9.......7.1...8.3...2...5.......6.1....32.....6.1.4...7.....2...3.6...4...5.....9;142;tax;tarek-2164;G123         16T   SK   -1.......2.3.4...5...6...7...8.5.9.......7.......83..4.7.....6...5...8.9...2.....1;144;tax;jpf-04/05;G13         16T   SK   -1......89.....91.2......4....76......3..4....9....2..5..4.7....5....8.1..6.3.....;148;tax;tarek-4/08;G13         16T   SK   -9876.....65....7...........5...4..3..2......1..68..5....59..8......3..2......1..4;153;GP;H21;G1            -   -   -98.7.....76....5....5.......9..4..3...85..6.......2..1..98..7......3..2......1..4;160;GP;H22;G13            20T   SK   EX2.......3.1.7...6...4...5...8.6.9.......2.......81..9.5.....2...7...6.1...3.....4;162;tax;tarek-3033;G13         16T   SK   -.2...6.....71....6....3..5...86......1...8..75...4......1..2..8....9..4.9..8..3..;166;elev;L11;G2            20T   -   -....5.....5.1....3..9..7.5..3....8..6.......1..5.2..4......5.7...2.94....8.6..4..;168;elev;133;G2            20T   -   -.2.4.......7..9...6...3.5.............4..1.9.8.....3.15...6...3....1.6.8..67...2.;172;elev;100;G12            20T   -   -98.7.....7..........6.5.7..4..8...7..3....89......2..1.9.4...3...2.6.........1..5;174;GP;H26;G12            20T   -   -....5....4....9.3..8.1....6.1.8....5.....24....756....3......2.......9...68.....7;175;elev;L12;G1            20T   -   -....5...9..67......8...2.4.23....8....79......4...3.1.....6...5......2.......143.;176;elev;101;G12            20T   -   -4....91...2..3......75.....8......9......461.......8.5..3.7....6....1.8..5.2.....;177;tax;tarek071223170000-;G123      16T   SK   -........94..7...3...9..15..2...6..7..9....8..........16..37......8..5....3..2..4.;178;elev;L13;G1            16T   -   -..7..1...6...9.2...3.5.....9.....6.8.......3.....8..922...4...9..13......5...7...;179;tax;tarek071223170000-;G13      16T   SK   -1...56..9...7.........3.56...8...4...7.2.....6....3.1.3...9..5...2.......4....8..;183;elev;104;G1            16T   -   -...4....9....8.12.....135..2...3.8...4.........96.....3...21.5.5.........6......7;185;elev;105;G1            20T   -   -1...5...9..7...2...6.2.......83..6...7.......5....4..3....4...1....9..4..3.7..8..;186;elev;108;G2            20T   -   -..34..........9..6.9..7..1...4...8...7..6..2.5.....3......9...28..5.7....1...2.7.;191;elev;H7;G2            20T   -   -`
ronk-moderator edit: hide data]

The interesting points were that with rare exceptions the SK loop puzzles have a 4 row 16 truth counterpart, and end up with same eliminations after the subsequent naked triples and quads. One puzzle in the group had 20 truth logic, an SK loop and an exocet, and two had an SK loop with 19 truth logic. I hope to extend the truths to include boxes to widen the detection rate sometime soon. The nice thing about this approach is that it is very quick, even in my web based javascript.

Phil Beeby
pjb
2014 Supporter

Posts: 2041
Joined: 11 September 2011
Location: Sydney, Australia

### Re: 0-rank logic sets in the hardest puzzles

pjb wrote:I hope to extend the truths to include boxes to widen the detection rate sometime soon.

I'll be interested to see how you get on with that.

Deleted material that didn't stand up to later verification

How are you determining the combinations of the digits in the base set to check? I feel there must be a way to do this without needing to resort to brute force.

[Added] When I compared this method against the Shark one, I found that I had a misunderstanding somewhere. I can certainly get eliminations for puzzle 54 which I thought your method should find too - but it doesn't.

DPB
David P Bird
2010 Supporter

Posts: 1040
Joined: 16 September 2008
Location: Middle England

### Re: 0-rank logic sets in the hardest puzzles

pjb, picking though your description again I think your wording could be improved in places. As I now have it, you have one set of columns with cells that are covered by individual cell links, and a second set of columns where column links are used. I'm not sure how you handle cells where one or other of the base digits must be true, but perhaps that's not critical.

If your check sums balance you then get the equivalent of a simple Shark balance.
When they don't, if a row contains a single truth you can add it to the original row set that has no truths and get an equivalent to one type of a Shark adjusted balance.

As you say, this must be very quick to run in a computer solver, but you are not getting other forms of adjusted balance that are possible, which would slow your code down. If you re-run cases where there is a misbalance swapping over the rows and columns, you may then find you pick up some missed cases when you add the optional column.

I have disliked the aspect of the Shark approach where various options for the ninth line must be evaluated, and have given an example where 3 alternative are needed to make all the eliminations. However, spurred on by you post, I'm getting the feeling that in these circumstances quickly trying the complementary digit set may be simpler. Perhaps you could test that out on your 19 truth solutions as I'm on my way to bed now.

DPB
David P Bird
2010 Supporter

Posts: 1040
Joined: 16 September 2008
Location: Middle England

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