Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

Re: Exotic patterns a resume

Postby JC Van Hay » Sat Dec 05, 2015 5:17 pm

Here is the first(?) 9 cells rank 0 pattern at the intersection of 3 rows and 3 columns I saw here

The puzzle : ....73.6....6..4.96.....3..9.5.8.....1....5..3..4...9..8...2...4..7...3...2.....1
A double exocet solves the cells r1c4=9 and r2c8=7.
Code: Select all
+-----------------------+------------------------+-----------------------+
| 1258   245     148    | 9      7        3      | 128    6      258     |
| 1258   235     138    | 6      125      158    | 4      7      9       |
| 6      24579   14789  | 1258   1245     1458   | 3      1258   258     |
+-----------------------+------------------------+-----------------------+
| 9      2467    5      | 12-3   8        167    | 1267   12-4   23467   |
| (278)  1       467-8  | (23)   369-2    679    | 5      (248)  3467-28 |
| 3      267     678    | 4      1256     1567   | 12678  9      2678    |
+-----------------------+------------------------+-----------------------+
| (157)  8       3679-1 | (135)  3469-15  2      | 679    (45)   467-5   |
| 4      569     169    | 7      1569     15689  | 2689   3      2568    |
| (57)   3679-5  2      | (358)  3469-5   469-58 | 679-8  (458)  1       |
+-----------------------+------------------------+-----------------------+
9 Truths = {579N1 579N4 579N8}
9 Links = {1r7 2r5 5r79 8r59 3c4 4c8 7c1}
15 Eliminations --> 1r7c35, 2r5c59, 5r7c59, 5r9c256, 8r5c38, 8r9c67, 3r4c4, 4r4c8
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Re: Exotic patterns a resume

Postby champagne » Sat Dec 05, 2015 6:43 pm

JC Van Hay wrote:Here is the first(?) 9 cells rank 0 pattern at the intersection of 3 rows and 3 columns I saw here

The puzzle : ....73.6....6..4.96.....3..9.5.8.....1....5..3..4...9..8...2...4..7...3...2.....1
A double exocet solves the cells r1c4=9 and r2c8=7.

[/code]9 Truths = {579N1 579N4 579N8}
9 Links = {1r7 2r5 5r79 8r59 3c4 4c8 7c1}
15 Eliminations --> 1r7c35, 2r5c59, 5r7c59, 5r9c256, 8r5c38, 8r9c67, 3r4c4, 4r4c8



Hi,

nothing to object, remarkable as usual.

That puzzle is rated 10.3 10.3 2.6 by skfr, just below the cut off for the data base of potential hardest.

My solver finds another rank 0 logic

SLG rank 0
18 Truths = {1R68 1C14 2R68 2C14 5R68 5C14 8R68 8C14 1N9 3N9 }
18 Links = {1b578 2c9 2b45 5c9 5b578 8c9 8b48 1n1 2n1 3n4 6n7 8n7 }
19 elims 6r6c7 7r6c7 6r8c7 9r8c7 2r4c2 8r5c3 1r4c6 2r5c5 1r7c3 5r9c2 1r7c5 5r7c5 5r9c5 5r9c6 8r9c6 2r4c9 2r5c9 5r7c9 8r5c9
6r6c7 7r6c7 6r8c7 9r8c7 2r4c2 8r5c3 1r4c6 2r5c5 1r7c3 5r9c2 1r7c5 5r7c5 5r9c5 5r9c6 8r9c6 2r4c9 2r5c9 5r7c9 8r5c9

Once again, the cell rank 0 logic gives the smallest number of "Truths"

Congratulations

champagne
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Re: Exotic patterns a resume

Postby David P Bird » Sat Dec 05, 2015 9:45 pm

JC, it's an interesting puzzle. What you've identified is a rank 0 pattern embedded in an double JExocet pattern.
However if all the JExocet eliminations are made immediately it isn't needed.

Code: Select all
   *-----------------------------*-----------------------------*-----------------------------*
   | 1258  T  2459     1489      | 9-1258   <7>      <3>       | 128 b    <6>      258 b     |
   | 1258-7t  2357     1378      | <6>      125 B    158  B    | <4>      7-1258   <9>       |
   | <6>      79-25    79-18     | 1258-9t  12459    14589     | <3>      1258-7T  2578      |
   *-----------------------------*-----------------------------*-----------------------------*
12 | <9>      467-2    <5>       | 123*     <8>      67-1      | 67-12    1247*    3467-2    |
28 | 278*     <1>      467-8     | 239*     369-2    679       | <5>      2478*    3467-28   |
   | <3>      267      678       | <4>      1256     1567      | 12678    <9>      2678      |
   *-----------------------------*-----------------------------*-----------------------------*
15 | 157*     <8>      3679-1    | 1359*    34569-15 <2>       | 679      457*     467-5     |
   | <4>      569      169       | <7>      1569     15689     | 2689     <3>      2568      |
58 | 57*      3679-5   <2>       | 3589*    3469-5   469-58    | 679-8    4578*    <1>       |
   *-----------------------------*-----------------------------*-----------------------------*
     CL1                           CL2                                    CL3       
                                                  * = 'S' cells

In rows 579 the eliminations from the rank 0 pattern are all non-'S' cell instances of the base digits in their cover houses.
In row 4 the JE eliminations leave (12)r4c48 as a hidden pair.

So the hunt must be on to find your rank 0 pattern in isolation!

DPB
.
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Re: Exotic patterns a resume

Postby StrmCkr » Fri Jul 22, 2016 10:01 am

http://forum.enjoysudoku.com/post220194.html#p220194

based on the above link for a "muti sector locked set" als-xy ring /generalized als-xy ring example
isn't it possible as the following idea: {if i'm reading/understanding it correctly}

a 2x2 muti fish has 4 digits potentially locked into 4 cells. {base x cover = intersection count ==>> # of digits locked into position }
there is exactly 9 digits known thus 5 free floating digits.

{USING THE ALS-XYRING {GENERALIZED OR NOT example}

formulate a base search sector for digts 56789 on Rows 25
{where
1 indicates a cell that contains these digits
0 indicates a cells that do not contain these digits}
Code: Select all
.1.|.1.|...
.0.|.0.|...
.1.|.1.|...
----------------
.1.|.1.|...
.0.|.0.|...
.1.|.1.|...
----------------
.1.|.1.|...
.1.|.1.|...
.1.|.1.|...


formulate a base search sector for digts 56789 on Cols 25

Code: Select all
...|...|...
101|101|111
...|...|...
----------------
...|...|...
101|101|111
...|...|...
----------------
...|...|...
...|...|...
...|...|...

when
base x cover = [empty]
there is exactly zero intersections in the cover/base set containing the digit set 56789
indicating directly that there is exactly 4 cells holding digits [1234 ]
all peer cells containing digits 1234 that can see all copies of each digit [1,2,3,4] in the intersection cells <> [1,2,3,4]
Some do, some teach, the rest look it up.
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Re: Exotic patterns a resume

Postby David P Bird » Fri Jul 22, 2016 1:01 pm

Chris, what you seem to describe (I haven't the time to study it deeply) seems to be a special case of the way I use complementary digit sets in what I call 'truth balancing'.

Here is the SK loop from the <Domino Loops thread> using (1259) for the rows and (34678) for the columns.

1.....9...3...7.4...5.....2.....6.7.....1.....4.3.8...9.......5.7.8...3...2...1..#8668;tax
Code: Select all
    *-------------------------*-------------------------*-------------------------*
25  | <1>     268     47      | 2456    3468-25 2345    | <9>     568     37      |
    | 268     <3>     689     | 1259-6  25689   <7>     | 568     <4>     168     |
19  | 47      689     <5>     | 1469    3468-9  1349    | 37      168     <2>     |
    *-------------------------*-------------------------*-------------------------*
    | 2358    1259-8  1389    | 259-4   2459    <6>     | 23458   <7>     13489   |
259 | 3678-25 25689   3678-9  | 24579   <1>     2459    | 3468-25 25689   3468-9  |
    | 2567    <4>     1679    | <3>     2579    <8>     | 256     1259-6  169     |
    *-------------------------*-------------------------*-------------------------*
12  | <9>     168     3468-1  | 12467   3467-2  1234    | 4678-2  268     <5>     |
    | 456     <7>     146     | <8>     24569   1259-4  | 246     <3>     469     |
59  | 3468-5  568     <2>     | 45679   3467-59 3459    | <1>     689     4678-9  |
    *-------------------------*-------------------------*-------------------------*
              68                467             34                68

MS-NS:(25)r1,(19)r3,(259)r5,(12)r7,(59)r9,(68)c2,(467)c4,(34)c6,(68)c8 (20 digit instances, 20 fully covered cells)
=> 21 Elims: 25r1c5, 6r2c4, 9r3c5, 8r4c2, 4r4c4, 25r5c1, 9r5c3, 25r5c7, 9r5c9, 6r6c8, 1r7c3, 2r7c5, 2r7c7, 4r8c6, 5r9c1, 59r9c5, 9r9c9

I call the different digit sets the 'home' and 'away' sets as they are either both cover sets or both base sets <described here>

The cover sets shown above are a transformation (one of many possible) of those shown in the original post using using Obi-Wahn's fish transformations <repeated here>.

For SK loops identifying the set members to use is simple but for other puzzles I build a list of givens in each row and column. I then look for what appears to be locked sets or almost locked sets in the givens by row or by column.

Hope this helps - a real world example of your approach would be a great help in any further discussions.

David
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