Chain Links

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Chain Links

Postby mith » Tue Sep 08, 2020 6:23 pm

Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | 1 . . |
| . 2 3 | . . 4 | . 5 . |
+-------+-------+-------+
| . . 2 | . . 6 | . 4 . |
| 7 5 . | . . 3 | . 6 . |
| 8 . . | . 4 . | 9 . . |
+-------+-------+-------+
| 9 . . | . 8 . | 7 . . |
| 2 8 . | . 7 . | . . . |
| . 4 . | . . 5 | . . . |
+-------+-------+-------+
...............1...23..4.5...2..6.4.75...3.6.8...4.9..9...8.7..28..7.....4...5...
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Re: Chain Links

Postby Cenoman » Tue Sep 08, 2020 7:37 pm

Solved with three fishes: JF(1)r3459\c1459, XW(7)r34\c49, SF(9)r359\c459 (presented in a single MSLS step)
Code: Select all
 +--------------------+-----------------------------+-------------------------+
 |  45    167   89    |  2356-179  2356-19  12789   |  2346   2379   2346-79  |
 |  45    67    89    |  2356-79   2356-9   2789    |  1      2379   2346-79  |
 | <16    2     3     | <1679     <169      4       | <68     5     <6789     |68
 +--------------------+-----------------------------+-------------------------+
 | <13    9     2     | <1578     <15       6       | <358    4     <13578    |358
 |  7     5     4     | <1289     <129      3       | <28     6     <128      |28
 |  8     136   16    |  25-17     4        127     |  9      1237   235-17   |
 +--------------------+-----------------------------+-------------------------+
 |  9     136   156   |  2346-1    8        12      |  7      123    23456-1  |
 |  2     8     156   |  346-19    7        19      |  3456   139    3456-19  |
 | <136   4     7     | <12369    <12369    5       | <236    8     <12369    |236
 +--------------------+-----------------------------+-------------------------+
    1                    179       19                                179

MSLS
19 cell truths: r3459 c14579 w/o r1c5; 19 links: 1c1, 179c4, 19c5, 179c9, 68r3, 358r4, 28r5, 236r9
22 eliminations: -179 r1c4, -19 r1c5, -79 r1c9, -79 r2c4, -9 r2c5, -79 r2c9, -17 r4c49, -1 r7c49, -19 r8c49; lclste
{HQ(1789)c4, HQ(1789)c9; NP(19)b8; ste}
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Re: Chain Links

Postby yzfwsf » Tue Sep 08, 2020 11:15 pm

MSLS=>stte
msls.png
msls.png (29.78 KiB) Viewed 193 times
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Re: Chain Links

Postby pjb » Wed Sep 09, 2020 1:53 am

I found same MSLS as Cenoman, but interestingly with slightly different links, although same 22 eliminations:

19 cell Truths: r3459 c14579
19 links: 6r3, 35r4, 2r5, 236r9, 1c1, 1789c4, 19c5, 8c7, 1789c9
22 eliminations

Yet another MSLS does the trick:

24 cell Truths: r12678 c23468
24 links: 1789r1, 789r2, 17r6, 1r7, 19r8, 36c2, 56c3, 23456c4, 2c6, 23c8
18 eliminations: -19 r1c5, -79 r1c9, -9 r2c5, -79 r2c9, -17 r6c9, -1 r7c9, -19 r8c9, -6 r3c4, -5 r4c4, -2 r5c4, -236 r9c4

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Re: Chain Links

Postby denis_berthier » Wed Sep 09, 2020 2:25 am

Code: Select all
(solve-sudoku-grid
   +-------+-------+-------+
   ! . . . ! . . . ! . . . !
   ! . . . ! . . . ! 1 . . !
   ! . 2 3 ! . . 4 ! . 5 . !
   +-------+-------+-------+
   ! . . 2 ! . . 6 ! . 4 . !
   ! 7 5 . ! . . 3 ! . 6 . !
   ! 8 . . ! . 4 . ! 9 . . !
   +-------+-------+-------+
   ! 9 . . ! . 8 . ! 7 . . !
   ! 2 8 . ! . 7 . ! . . . !
   ! . 4 . ! . . 5 ! . . . !
   +-------+-------+-------+
)


Solved with a good number of Subsets

Code: Select all
***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = SFin
***  Using CLIPS 6.32-r770
***********************************************************************************************
hidden-single-in-a-row ==> r9c3 = 7
hidden-single-in-a-row ==> r5c3 = 4
hidden-single-in-a-block ==> r4c2 = 9
226 candidates, 1599 csp-links and 1599 links. Density = 6.29%
whip[1]: c6n8{r2 .} ==> r3c4 ≠ 8, r1c4 ≠ 8, r2c4 ≠ 8
whip[1]: r3n8{c9 .} ==> r1c7 ≠ 8, r1c8 ≠ 8, r1c9 ≠ 8, r2c8 ≠ 8, r2c9 ≠ 8
hidden-single-in-a-column ==> r9c8 = 8
whip[1]: c1n5{r2 .} ==> r2c3 ≠ 5, r1c3 ≠ 5
hidden-pairs-in-a-column: c3{n8 n9}{r1 r2} ==> r2c3 ≠ 6, r1c3 ≠ 6, r1c3 ≠ 1
hidden-pairs-in-a-column: c1{n4 n5}{r1 r2} ==> r2c1 ≠ 6, r1c1 ≠ 6, r1c1 ≠ 1
x-wing-in-rows: n7{r3 r4}{c4 c9} ==> r6c9 ≠ 7, r6c4 ≠ 7, r2c9 ≠ 7, r2c4 ≠ 7, r1c9 ≠ 7, r1c4 ≠ 7
finned-x-wing-in-columns: n6{c1 c5}{r9 r3} ==> r3c4 ≠ 6
swordfish-in-rows: n9{r3 r5 r9}{c9 c5 c4} ==> r8c9 ≠ 9, r8c4 ≠ 9, r2c9 ≠ 9, r2c5 ≠ 9, r2c4 ≠ 9, r1c9 ≠ 9, r1c5 ≠ 9, r1c4 ≠ 9
jellyfish-in-columns: n1{c2 c6 c3 c8}{r7 r1 r8 r6} ==> r8c9 ≠ 1, r8c4 ≠ 1, r7c9 ≠ 1, r7c4 ≠ 1, r6c9 ≠ 1, r6c4 ≠ 1, r1c5 ≠ 1, r1c4 ≠ 1
naked-quads-in-a-block: b2{r1c4 r1c5 r2c4 r2c5}{n2 n3 n5 n6} ==> r3c5 ≠ 6, r2c6 ≠ 2, r1c6 ≠ 2
hidden-quads-in-a-column: c4{n1 n9 n7 n8}{r5 r9 r3 r4} ==> r9c4 ≠ 6, r9c4 ≠ 3, r9c4 ≠ 2, r5c4 ≠ 2, r4c4 ≠ 5
naked-pairs-in-a-block: b8{r8c6 r9c4}{n1 n9} ==> r9c5 ≠ 9, r9c5 ≠ 1, r7c6 ≠ 1
naked-single ==> r7c6 = 2
hidden-quads-in-a-row: r1{n1 n7 n9 n8}{c6 c2 c8 c3} ==> r1c8 ≠ 3, r1c8 ≠ 2, r1c2 ≠ 6
finned-x-wing-in-columns: n2{c8 c4}{r6 r2} ==> r2c5 ≠ 2
hidden-quads-in-a-column: c9{n1 n9 n7 n8}{r5 r9 r3 r4} ==> r9c9 ≠ 6, r9c9 ≠ 3, r9c9 ≠ 2, r5c9 ≠ 2, r4c9 ≠ 5, r4c9 ≠ 3, r3c9 ≠ 6
stte
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Re: Chain Links

Postby mith » Wed Sep 09, 2020 6:35 pm

This one is pretty similar to Sun, Moon, and Star - the difference is that there is an alternative solve path that gets it a lower SE rating:

Code: Select all
+-------------------------+-------------------------+-------------------------+
| 45      167     *89     | 1235679 123569  *1278-9 | 2346    2379    234679  |
| 45      67      *89     | 235679  23569   *278-9  | 1       2379    234679  |
| 16      2       3       | 1679    169     4       | 68      5       6789    |
+-------------------------+-------------------------+-------------------------+
| 13      9       2       | 1578    15      6       | 358     4       13578   |
| 7       5       4       | 1289    129     3       | 28      6       128     |
| 8       136     16      | 1257    4       127     | 9       1237    12357   |
+-------------------------+-------------------------+-------------------------+
| 9       136     156     | 12346   8       12      | 7       123     123456  |
| 2       8       156     | 13469   7       19      | 3456    139     134569  |
| 136     4       7       | 12369   12369   5       | 236     8       12369   |
+-------------------------+-------------------------+-------------------------+


Unique Rectangle: 8/9 in r1c36,r2c36 => -9r12c6 (still needs an X-Wing, Hidden Triple, and Swordfish before stte)
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Re: Chain Links

Postby denis_berthier » Thu Sep 10, 2020 1:40 am

mith wrote:This one is pretty similar to Sun, Moon, and Star - the difference is that there is an alternative solve path that gets it a lower SE rating:


Yep, right. I usually don't activate uniqueness, as it can be proved by exhibiting the only possible solution.


Code: Select all
***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = S
***  Using CLIPS 6.32-r770
***********************************************************************************************
hidden-single-in-a-row ==> r9c3 = 7
hidden-single-in-a-row ==> r5c3 = 4
hidden-single-in-a-block ==> r4c2 = 9
226 candidates, 1599 csp-links and 1599 links. Density = 6.29%
whip[1]: c6n8{r2 .} ==> r3c4 ≠ 8, r1c4 ≠ 8, r2c4 ≠ 8
whip[1]: r3n8{c9 .} ==> r1c7 ≠ 8, r1c8 ≠ 8, r1c9 ≠ 8, r2c8 ≠ 8, r2c9 ≠ 8
hidden-single-in-a-column ==> r9c8 = 8
whip[1]: c1n5{r2 .} ==> r2c3 ≠ 5, r1c3 ≠ 5
hidden-pairs-in-a-column: c3{n8 n9}{r1 r2} ==> r2c3 ≠ 6, r1c3 ≠ 6, r1c3 ≠ 1
************ UNIQUENESS RULE UR4-H APPLIED ******************
horizontal unique rectangle type 4 in cells r1c3, r1c6, r2c3 and r2c6 ==> n9 eliminated from the candidates for r1c6 and r2c6
hidden-single-in-a-column ==> r8c6 = 9
hidden-single-in-a-block ==> r9c9 = 9
whip[1]: r3n9{c5 .} ==> r1c4 ≠ 9, r1c5 ≠ 9, r2c4 ≠ 9, r2c5 ≠ 9
hidden-pairs-in-a-column: c1{n4 n5}{r1 r2} ==> r2c1 ≠ 6, r1c1 ≠ 6, r1c1 ≠ 1
x-wing-in-rows: n7{r3 r4}{c4 c9} ==> r6c9 ≠ 7, r6c4 ≠ 7, r2c9 ≠ 7, r2c4 ≠ 7, r1c9 ≠ 7, r1c4 ≠ 7
hidden-triplets-in-a-column: c4{n7 n8 n9}{r3 r4 r5} ==> r5c4 ≠ 2, r5c4 ≠ 1, r4c4 ≠ 5, r4c4 ≠ 1, r3c4 ≠ 6, r3c4 ≠ 1
swordfish-in-rows: n1{r3 r4 r5}{c5 c1 c9} ==> r9c5 ≠ 1, r9c1 ≠ 1, r8c9 ≠ 1, r7c9 ≠ 1, r6c9 ≠ 1, r1c5 ≠ 1
stte

(I haven't touched the rules for uniqueness for a very long time and their eliminations still appear in an old, verbose style. I must update this.)
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Re: Chain Links

Postby Cenoman » Thu Sep 10, 2020 10:33 pm

ysfwsf wrote:MSLS=>stte

Very interesting solution.
This solution is a shorter MSLS than mine, and moreover, yields ste finish.
But most interesting to me, the pattern is an example of the "generalised Sue de Coq" already discussed.
To me, SDC is the pattern of an AALS doubly linked twice, to two ALS's (each with with different restricted commons)
Doubts were stated, whether it could be seen in more than two sectors.
Here we have even four ! (with a definition a little further extended)

Code: Select all
+-------------------------+-------------------------+-------------------------+
| 45      167     89      | 1235679 123569  12789   | 346-2   2379    234679  |
| 45      67      89      | 235679  23569   2789    | 1       2379    234679  |
|c16      2       3       | 179-6   19-6    4       |c68      5       789-6   |
+-------------------------+-------------------------+-------------------------+
| 3-1     9       2       | 1578    15      6       | 35-8    4       13578   |
| 7       5       4       | 1289    129     3       |c28      6       128     |
| 8       136     16      | 1257    4       127     | 9       1237    12357   |
+-------------------------+-------------------------+-------------------------+
| 9       136     156     | 346-12  8      b12      | 7       123     123456  |
| 2       8       156     | 346-19  7      b19      | 3456    139     134569  |
|a136     4       7       |b12369  b12369   5       |a236     8       129-36  |
+-------------------------+-------------------------+-------------------------+

AALS: (1236)r9c17
ALS1: (12369)b8p3678, restricted commons 3, 6
ALS2: (1268)r3c17,r5c7, restricted commons 1, 2 (OK, this is an ALS-chain rather than a single ALS, it works the same)
=> rank 0 logic. Eliminations: -2 r1c7, -6r3c459, -1 r4c1, -8r4c7, -12r7c4, -19r8c4, -36r9c9; ste
PM 9x9, symmetric
Hidden Text: Show
Code: Select all
 1r7c6   2r7c6
 1r8c6           9r8c6
 1r9c4   2r9c4   9r9c4   3r9c4   6r9c4
 1r9c5   2r9c5   9r9c5   3r9c5   6r9c5
                         3r9c1   6r9c1   1r9c1
                         3r9c7   6r9c7           2r9c7
                                                 2r5c7   8r5c7
                                                         8r3c7   6r3c7
                                         1r3c1                   6r3c1
----------------------------------------------------------------------
-1r78c4 -2r7c4  -9r8c46 -3r9c9  -6r9c9  -1r4c1  -2r1c7  -8r4c7  -6r3c459

Any taker to write it as an AIC (loop) ?
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Re: Chain Links

Postby SpAce » Thu Sep 10, 2020 11:53 pm

Cenoman wrote:Any taker to write it as an AIC (loop) ?

I can't see any easy way to do it without a two-sector locked set.

Code: Select all
.----------------.--------------------------.-----------------------.
|  45   167  89  |  1235679  123569   12789 |   346-2  2379  234679 |
|  45   67   89  |  235679   23569    2789  |   1      2379  234679 |
| a16   2    3   |  179-6    19-6     4     |  b68     5     789-6  |
:----------------+--------------------------+-----------------------:
|  3-1  9    2   |  1578     15       6     |   35-8   4     13578  |
|  7    5    4   |  1289     129      3     |  c28     6     128    |
|  8    136  16  |  1257     4        127   |   9      1237  12357  |
:----------------+--------------------------+-----------------------:
|  9    136  156 |  346-12   8       e12    |   7      123   123456 |
|  2    8    156 |  346-19   7       e19    |   3456   139   134569 |
| f136  4    7   | e129'36  e129'36   5     | de2'36   8     129-36 |
'----------------'--------------------------'-----------------------'

(1=6)r3c1 - (6=8)r3c7 - (8=2)r5c7 - r9c7 = (129'36)r78c6,r9c457 - (3|6=1)r9c1 - loop => 12 elims

--
Edit. Added missing elimination (6r3c9) to the grid. (It was already counted in the tally.)
Last edited by SpAce on Fri Sep 11, 2020 10:26 am, edited 1 time in total.
-SpAce-: Show
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."
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Re: Chain Links

Postby Cenoman » Fri Sep 11, 2020 9:14 am

SpAce wrote:I can't see any easy way to do it without a two-sector locked set.

Yes. That's why I raised the question. The best I found was:
(DP129 = 3|6)b8p3678 - (36)r9c17 = [(6=1)r3c1 - (1=2)r9c17 - (2=8)r5c7 - (8=6)r3c7 loop] => -1 r4c1, -8r4c7, -6r3c45; ste
As the DP is False, the embedded loop is True.
These four eliminations solve the puzzle (ste). I guess the other eights are not demonstrated by this chain.
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Re: Chain Links

Postby SpAce » Fri Sep 11, 2020 10:55 am

Cenoman wrote:=> -1 r4c1, -8r4c7, -6r3c45; ste
These four eliminations solve the puzzle (ste). I guess the other eights are not demonstrated by this chain.

You could add two more: -2r1c7, -6r3c9 (I also forgot to mark that one), but I agree that the other six aren't proved by that chain.

Strictly speaking I'm not sure if my loop proves -36r9c9 either. It's the eternal question about AALS-loops where one side of a strong link is an ORed node (as in SK-Loops). In my experience those eliminations are always valid, but the normal loop interpretation (all the left terms true XOR all the right terms true) doesn't necessarily agree, because an ORed node can't eliminate anything external.

I think someone should investigate that and define the exact conditions when those eliminations are valid (or not). If it could be added as a special loop rule, then SK-Loops could be written as normal AIC-loops, too. There's no question about their validity if the logic is written as set logic (Rank 0), but how to make the loop reflect that?
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