The New Sudoku Players' Forum

[yzfwsf]

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98.7..6....56...4.....9..85.9...3....5.8.......8.7.5....9.8......6.4.9.........21

[denis_berthier]

SER 10.8; in B2B and therefore not solvable bt whips, braids, g-whips or g-braids.

I'll use a method I rarely use, but that I described in [PBCS], based on intermediate binary contradictions (here bi-whips) and on w*-whips (a generalisation of whips that accepts these intermediate bi-whips in addition to direct links between candidates).
In order to save space, the intermediate binary contradictions are not displayed here.

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(solve "98.7..6....56...4.....9..85.9...3....5.8.......8.7.5....9.8......6.4.9.........21")
***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W
***  Using CLIPS 6.32-r770
***********************************************************************************************
singles ==> r2c9 = 9, r2c6 = 8
232 candidates, 1652 csp-links and 1652 links. Density = 6.17%
whip[1]: r9n6{c6 .} ==> r7c6 ≠ 6
whip[1]: b3n7{r3c7 .} ==> r9c7 ≠ 7, r4c7 ≠ 7, r5c7 ≠ 7, r7c7 ≠ 7
w*-whip[2]: b8n7{r8c6 r9c6} - r9n5{c6 .} ==> r8c1 ≠ 7
w*-whip[3]: c3n2{r5 r1} - r3c6{n4 n1} - c3n1{r5 .} ==> r3c4 ≠ 2
w*-whip[3]: c3n1{r5 r1} - r3c6{n4 n2} - c3n2{r5 .} ==> r3c4 ≠ 1
w*-whip[2]: b5n4{r6c6 r6c4} - b8n3{r8c4 .} ==> r9c6 ≠ 5
w*-whip[3]: b8n6{r9c6 r9c5} - r3c4{n3 n4} - b5n4{r6c4 .} ==> r9c6 ≠ 7
whip[1]: r9n7{c3 .} ==> r7c1 ≠ 7, r7c2 ≠ 7, r8c2 ≠ 7
w*-whip[4]: c7n1{r3 r5} - r2n1{c2 c5} - c5n3{r2 r9} - r9c7{n4 .} ==> r4c9 ≠ 2
w*-whip[4]: r1c9{n3 n2} - c5n2{r5 r2} - r3c6{n2 n1} - c7n1{r5 .} ==> r1c3 ≠ 3
w*-whip[2]: r3c4{n4 n3} - c3n3{r9 .} ==> r5c3 ≠ 4
w*-whip[3]: r3c4{n3 n4} - r3c6{n4 n2} - c3n2{r5 .} ==> r5c3 ≠ 1
w*-whip[3]: r3c4{n3 n4} - r3c6{n4 n1} - c3n1{r4 .} ==> r5c3 ≠ 2
w*-whip[1]: r5c3{n7 .} ==> r3c3 ≠ 3
w*-whip[3]: r1c9{n3 n2} - r3c6{n2 n1} - c7n1{r5 .} ==> r1c5 ≠ 3
whip[1]: r1n3{c9 .} ==> r2c7 ≠ 3, r3c7 ≠ 3
w*-whip[2]: r9c3{n7 n3} - r2c5{n2 .} ==> r3c1 ≠ 7
w*-whip[3]: r1c8{n3 n1} - c5n1{r5 r2} - r7n3{c4 .} ==> r8c8 ≠ 3
w*-whip[3]: r9n5{c4 c1} - c3n3{r9 r5} - r8c9{n3 .} ==> r8c6 ≠ 5
w*-whip[3]: r9n5{c4 c1} - c3n3{r9 r5} - r8c9{n3 .} ==> r8c4 ≠ 5
w*-whip[3]: c8n1{r5 r1} - c5n1{r5 r2} - r8n3{c4 .} ==> r5c8 ≠ 3
w*-whip[3]: r1c9{n3 n2} - c5n2{r5 r2} - r7n3{c4 .} ==> r8c9 ≠ 3
w*-whip[2]: r9n8{c1 c7} - r8n7{c8 .} ==> r7c6 ≠ 5
singles ==> r1c6 = 5, r1c3 = 4
w*-whip[1]: r1n1{c8 .} ==> r5c5 ≠ 1
w*-whip[1]: r1n2{c9 .} ==> r5c5 ≠ 2
singles ==> r5c5 = 6, r9c6 = 6, r9c4 = 9
w*-whip[1]: r9c3{n7 .} ==> r3c3 ≠ 7
w*-whip[1]: r9c3{n7 .} ==> r4c3 ≠ 7
w*-whip[1]: r4c3{n2 .} ==> r3c6 ≠ 2
whip[1]: b2n2{r2c5 .} ==> r4c5 ≠ 2
w*-whip[1]: r4c3{n1 .} ==> r3c6 ≠ 1
stte

[yzfwsf]

The STTE solution can be activated by using an senior exocet.

[Cenoman]

At a first glance, on the PMs of this puzzle, you can hope to prove Junior Exocets:
JE2(123)r1c89, r2c5, r3c3 or JE2(1234)r3c46, r1c3, r2c7 (potential double JE). They share the same three cross-lines. Unfortunately, in c7, 3 S-cells would contain digit 3. No JE2, nor JE4. So bad !
(Confirmation: an attempt to prove the fundamental exocet property for digit 3, with these target cells, by T&E [+3r1c89, -3r2c5, -3r3c3] leads to a solution, with singles!)
What still can be done is to escape to a Senior exocet.
With the first near missed JE2:

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           b1=CH(123)
 +----------------------------+------------------------+-------------------------+
 |  9        8        1234    |  7      1235   1245    |  6     B13     B23      |
 | <1237    <1237     5       |  6     T123    8       |  1237   4       9       | CL4
 |  123467   123467  <12347   |  1234   9      124     |  1237   8       5       |
 +----------------------------+------------------------+-------------------------+
 |  12467    9       <1247    |  1245  <1256   3       | <1248   167     24678   | CH(12)
 |  123467   5       <12347   |  8     <126    12469   | <1234   13679   23467   | CH(123)
 |  12346    12346    8       |  1249   7      12469   |  5      1369    2346    |
 +----------------------------+------------------------+-------------------------+
 |  123457   12347    9       |  1235   8      1257    | T34     3567    3467    |
 |  123578   1237     6       |  1235   4      1257    |  9      357     378     |
 |  34578    347     <347     |  359   <356    5679    | <348    2       1       | CH(3)
 +----------------------------+------------------------+-------------------------+
                      CL3               CL2               CL1

Senior Exocet (123)r1c89, r2c5, r7c7
S-cells: r459c357, r3c3, r2c12. Cross-lines: c357, r2; cover houses: r45, b1 for digits 1 & 2, r59, b1 for digit 3.
Eliminations: -4 r7c7 (non base digit in target cell); 3 is a true base digit => -3 r2c5 (false in second target cell), -3 r1c5, r23c7 (cells in sight of both base cells); ste

Another choice of "cross-lines"\cover houses, for the same SExocet.

Hidden Text: Show

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                                        b2=CL4
 +----------------------------+------------------------+-------------------------+
 |  9        8        1234    |  7      1235   1245    |  6     B13     B23      |
 |  1237     1237     5       |  6     T123    8       |  1237   4       9       | 
 |  123467   123467  <12347   | <1234   9     <124     |  1237   8       5       | CH(123)
 +----------------------------+------------------------+-------------------------+
 |  12467    9       <1247    |  1245  <1256   3       | <1248   167     24678   | CH(12)
 |  123467   5       <12347   |  8     <126    12469   | <1234   13679   23467   | CH(123)
 |  12346    12346    8       |  1249   7      12469   |  5      1369    2346    |
 +----------------------------+------------------------+-------------------------+
 |  123457   12347    9       |  1235   8      1257    | T34     3567    3467    |
 |  123578   1237     6       |  1235   4      1257    |  9      357     378     |
 |  34578    347     <347     |  359   <356    5679    | <348    2       1       | CH(3)
 +----------------------------+------------------------+-------------------------+
                      CL3               CL2               CL1

Senior Exocet (123)r1c89, r2c5, r7c7
S-cells: r459c357, r3c346. Cross-lines: c357, b2; cover houses: r345 for digits 1 & 2, r359 for digit 3.
Same eliminations.

A senior exocet can also be found, starting from the second near missed JE2 (with the same alternative choice of "cross-lines"\cover houses):

Hidden Text: Show

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            b1=CL4
 +----------------------------+------------------------+-------------------------+
 |  9        8       T1234    |  7      1235   1245    |  6      13      23      |
 | <1237    <1237     5       |  6      123    8       | <1237   4       9       | CH(123)
 |  123467   123467   12347   | B1234   9     B124     |  1237   8       5       |
 +----------------------------+------------------------+-------------------------+
 |  12467    9       <1247    |  1245  <1256   3       | <1248   167     24678   | CH(12)
 |  123467   5       <12347   |  8     <126    12469   | <1234   13679   23467   | CH(123)
 |  12346    12346    8       |  1249   7      12469   |  5      1369    2346    |
 +----------------------------+------------------------+-------------------------+
 |  123457   12347    9       |  1235   8      1257    | T34     3567    3467    |
 |  123578   1237     6       |  1235   4      1257    |  9      357     378     |
 |  34578    347     <347     |  359   <356    5679    | <348    2       1       | CH(3)
 +----------------------------+------------------------+-------------------------+
                      CL3               CL2               CL1

Senior Exocet (1234)r3c46, r1c3, r7c7
+4r3c46 => +4r1c3; no check of cover houses for digit 4.
S-cells: r459c357, r2c127. Cross-lines: c357, b1; cover houses: r245 for digits 1 & 2, r259 for digit 3.
Eliminations: -4 r7c7 (base digit can't be true in target cell r7c7); 3 is a true base digit => -3 r1c3 (false in second target cell), -3 r3c1237, b2p235 (cells in sight of both base cells); ste
Alternatively:

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                                                          b3=CH(123)           
 +----------------------------+------------------------+-------------------------+
 |  9        8       T1234    |  7      1235   1245    |  6     <13     <23      | CL4
 |  1237     1237     5       |  6      123    8       | <1237   4       9       |
 |  123467   123467   12347   | B1234   9     B124     |  1237   8       5       |
 +----------------------------+------------------------+-------------------------+
 |  12467    9       <1247    |  1245  <1256   3       | <1248   167     24678   | CH(12)
 |  123467   5       <12347   |  8     <126    12469   | <1234   13679   23467   | CH(123)
 |  12346    12346    8       |  1249   7      12469   |  5      1369    2346    |
 +----------------------------+------------------------+-------------------------+
 |  123457   12347    9       |  1235   8      1257    | T34     3567    3467    |
 |  123578   1237     6       |  1235   4      1257    |  9      357     378     |
 |  34578    347     <347     |  359   <356    5679    | <348    2       1       | CH(3)
 +----------------------------+------------------------+-------------------------+
                      CL3               CL2               CL1

Senior Exocet (1234)r3c46, r1c3, r7c7
+4r3c46 => +4r1c3; no check of cover houses for digit 4.
S-cells: r459c357, r2c7, r1c89. Cross-lines: c357, r1; cover houses: r45, b3 for digits 1 & 2, r59, b3 for digit 3.
Same eliminations.

[SpAce]

I found something a bit different. Hoping it's correct.

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                      *123               *123             *1237     *b3:123
.------------------------------.------------------------.------------------------.
|  9         8        e12'4-3  | m7     ms123'5  m12'45 |  6      Ms13   Ms23    | \123_
| b1237     b1237      5       |  6      e12-3    8     | e127-3    4      9     | \___7
|  12467-3   12467-3  e127'4-3 | M3-124   9      M124   | t127-3    8      5     |
:------------------------------+------------------------+------------------------:
|  12467     9        s12'47   |  1245   s12'56   3     | s12'48    167    24678 | \12__
|  123467    5        s123'47  |  8      s12'6    12469 | s123'4    13679  23467 | \123_
|  12346     12346     8       |  1249    7       12469 |  5        1369   2346  |
:------------------------------+------------------------+------------------------:
|  123457    12347     9       |  1235    8       1257  | T3-4      3567   3467  |
|  123578    1237      6       |  1235    4       1257  |  9        357    378   |
|  34578     347      s3'47    |  359    s3'56    5679  | s3'48     2      1     | \__3_
'------------------------------'------------------------'------------------------'

3s-SExocet (1237)r2c12,r3c7,r7c7 : 12r145,3r159,7r2 =>

-4 r7c7 (non-base-digit in target)
+3 r2c12 (true base-digit; only possibility in target r7c7) (btte)
-3 r3c7 (true base-digit in the other target)
+3 r1c89, +3 r3c4 (true base-digit in the double-mirror); stte

[yzfwsf]

I found something a bit different. Hoping it's correct.

My solver can find 3 SExocets, the first one is basically the same as yours.

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Senior Exocet:Base Cells-r2c1,r2c2;Target Cells-r3c7,r7c7;Cross Cells-r13456789c5,r45689c37,r1c7,r7c3
7r3 locked in target Cell;"S" Cells Need Include:1r3,2r3,3r3,
Non BaseCands In Target Cells: r7c7<>4
True BaseCands False In Another Target:r3c7<>3
True BaseCands False In Base Cells Constraint:r3c123,r2c57,r1c3<>3

[SpAce]

Hi yzfwsf,

My solver can find 3 SExocets, the first one is basically the same as yours.

Thanks for confirming it! It seemed weird with both targets lined up in the same column, but why not.

Btw, have you looked at David's JE1 (single target) example? Would you agree that it could (and probably should) be expressed as a Senior Exocet instead? I think it's wrong by definition to talk about an Exocet that has only one target and a non-base-digit true in the base cells. As a Senior Exocet it can have two targets, and no special "wildcard" rules needed:

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                 *2456     *2456                    *245
.------------------------.------------------------.------------------------.
| b456   b246     1      | e245689  235689  34589 | e245'3   7       2356  |
|  3      9      e24567  | t2456    2567    457   |  8       124     1256  |
|  8      2467   e24567  |  1       23567   3457  |  9      m24'3   m256'3 |
:------------------------+------------------------+------------------------:
|  1456   1468    9      |  3       568     158   |  7       128     1258  |
|  157    1378   s5'78   | s5'89    4^      2^    | s5'13    6^      13589 | \__5_
|  2^     1368   s56'8   | s56'89   56789   15789 | s5'13    1389    4^    | \__56
:------------------------+------------------------+------------------------:
|  149    1248    3      |  7       2589    4589  | s6^      12489   1289  | \___6
|  4679   24678  t246'78 | s24'89   1       3489  | s24'3    5^      2389  | \24__
|  149    5^     s24'8   | s24'89   2389    6^    | s24'13   123489  7     | \24__
'------------------------'------------------------'------------------------'

SExocet (2456)r1c12,r2c4,r8c3 : 2r89,4r89,5r56,6r67 =>

+6 r8c3,r1c12; -6 r2c4 (all the other base-digits must go to the other target r2c4)

Isn't that correct?

[yzfwsf]

Same

SExocet1.png (50.01 KiB) Viewed 546 times

[SpAce]

Ah, yet another way to see it! Thanks. So I guess mine with the live target (r8c3) is ok too?