Rarity #5

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Rarity #5

Postby m_b_metcalf » Wed Jun 15, 2022 7:52 am

Code: Select all
3 . . 9 . . 6 . .
 . . . . . 1 . . 8
 . . 7 . . . . 2 .
 9 . . 3 . 6 . . .
 . . . . 7 . . . .
 . 4 . 1 . 9 3 . .
 6 . . . . 3 9 . .
 . . 2 . . . . 5 .
 . 5 . . . . . . 2  1to9only

3..9..6.......1..8..7....2.9..3.6.......7.....4.1.93..6....39....2....5..5......2
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Re: Rarity #5

Postby yzfwsf » Wed Jun 15, 2022 8:24 am

MSLS:16 Cells r3589c1467, 16 Links 458r3,2458r5,478r8,478r9,148c1,468c4,48c6,148c7(Digit 48 can be permutated)
39 Eliminations:r4c7<>1,r5c2<>2,r2c147,r38c59,r9c358,r5c89,r1c6,r4c7,r7c4<>4,r3c59,r5c39<>5,r2c4<>6,r8c29,r9c8<>7,r5c238,r38c25,r9c358,r1c6,r4c7,r6c1,r7c4<>8

ALS AIC Type 1: 2r56c1 = r4c2 - (2=57)r24c7 - r89c7 = r7c89 - (7=136892)r123578c2 => r2c1,r4c2<>2, stte
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Re: Rarity #5

Postby denis_berthier » Wed Jun 15, 2022 8:55 am

.
SER = 5.2
Code: Select all
Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 3      128    1458   ! 9      2458   24578  ! 6      147    1457   !
   ! 245    269    4569   ! 24567  23456  1      ! 457    3479   8      !
   ! 1458   1689   7      ! 4568   34568  458    ! 145    2      13459  !
   +----------------------+----------------------+----------------------+
   ! 9      1278   158    ! 3      2458   6      ! 124578 1478   1457   !
   ! 1258   12368  13568  ! 2458   7      2458   ! 12458  14689  14569  !
   ! 2578   4      568    ! 1      258    9      ! 3      678    567    !
   +----------------------+----------------------+----------------------+
   ! 6      178    148    ! 24578  12458  3      ! 9      1478   147    !
   ! 1478   13789  2      ! 4678   14689  478    ! 1478   5      13467  !
   ! 1478   5      13489  ! 4678   14689  478    ! 1478   134678 2      !
   +----------------------+----------------------+----------------------+
240 candidates


Solvable using only Subsets and Finned Fish:
Code: Select all
hidden-pairs-in-a-block: b9{n3 n6}{r8c9 r9c8} ==> r9c8≠8, r9c8≠7, r9c8≠4, r9c8≠1, r8c9≠7, r8c9≠4, r8c9≠1
hidden-pairs-in-a-block: b7{n3 n9}{r8c2 r9c3} ==> r9c3≠8, r9c3≠4, r9c3≠1, r8c2≠8, r8c2≠7, r8c2≠1
hidden-pairs-in-a-row: r7{n2 n5}{c4 c5} ==> r7c5≠8, r7c5≠4, r7c5≠1, r7c4≠8, r7c4≠7, r7c4≠4
hidden-pairs-in-a-block: b8{n1 n9}{r8c5 r9c5} ==> r9c5≠8, r9c5≠6, r9c5≠4, r8c5≠8, r8c5≠6, r8c5≠4
whip[1]: b8n6{r9c4 .} ==> r2c4≠6, r3c4≠6
hidden-pairs-in-a-block: b2{n3 n6}{r2c5 r3c5} ==> r3c5≠8, r3c5≠5, r3c5≠4, r2c5≠5, r2c5≠4, r2c5≠2
hidden-pairs-in-a-block: b3{n3 n9}{r2c8 r3c9} ==> r3c9≠5, r3c9≠4, r3c9≠1, r2c8≠7, r2c8≠4
hidden-triplets-in-a-row: r3{n3 n6 n9}{c9 c5 c2} ==> r3c2≠8, r3c2≠1
swordfish-in-rows: n1{r3 r8 r9}{c7 c1 c5} ==> r5c7≠1, r5c1≠1, r4c7≠1
naked-quads-in-a-row: r5{c1 c7 c4 c6}{n8 n5 n4 n2} ==> r5c9≠5, r5c9≠4, r5c8≠8, r5c8≠4, r5c3≠8, r5c3≠5, r5c2≠8, r5c2≠2
swordfish-in-columns: n4{c5 c8 c9}{r1 r4 r7} ==> r7c3≠4, r4c7≠4, r1c6≠4, r1c3≠4
singles ==> r2c3=4, r9c3=9, r8c2=3, r8c9=6, r9c8=3, r2c8=9, r3c9=3, r3c5=6, r2c5=3, r3c2=9, r9c5=1, r8c5=9, r2c2=6, r5c2=1, r5c8=6, r5c3=3, r5c9=9, r6c3=6, r9c4=6
whip[1]: r7n4{c9 .} ==> r8c7≠4, r9c7≠4
;;; Resolution state RS1
finned-x-wing-in-columns: n5{c3 c9}{r1 r4} ==> r4c7≠5
finned-x-wing-in-columns: n2{c2 c6}{r1 r4} ==> r4c5≠2
finned-x-wing-in-columns: n2{c6 c2}{r1 r5} ==> r5c1≠2
naked-pairs-in-a-block: b4{r4c3 r5c1}{n5 n8} ==> r6c1≠8, r6c1≠5, r4c2≠8
finned-x-wing-in-rows: n2{r2 r6}{c1 c4} ==> r5c4≠2
finned-x-wing-in-rows: n2{r6 r2}{c1 c5} ==> r1c5≠2
hidden-pairs-in-a-block: b2{n2 n7}{r1c6 r2c4} ==> r2c4≠5, r1c6≠8, r1c6≠5
swordfish-in-columns: n5{c1 c6 c7}{r2 r5 r3} ==> r5c4≠5, r3c4≠5
stte


Alternatively, if ordinary Subsets are given a preference over Finned Fish, after resolution state RS1 the resolution path continues as follows, making a Jellyfish appear:
Code: Select all
swordfish-in-columns: n2{c2 c6 c7}{r4 r1 r5} ==> r5c4≠2, r5c1≠2, r4c5≠2, r1c5≠2
naked-pairs-in-a-block: b4{r4c3 r5c1}{n5 n8} ==> r6c1≠8, r6c1≠5, r4c2≠8
hidden-pairs-in-a-block: b2{n2 n7}{r1c6 r2c4} ==> r2c4≠5, r1c6≠8, r1c6≠5
jellyfish-in-columns: n8{c2 c3 c5 c8}{r7 r1 r4 r6} ==> r4c7≠8
finned-x-wing-in-columns: n5{c3 c9}{r1 r4} ==> r4c7≠5
naked-pairs-in-a-row: r4{c2 c7}{n2 n7} ==> r4c9≠7, r4c8≠7
finned-x-wing-in-rows: n7{r4 r7}{c2 c7} ==> r9c7≠7, r8c7≠7
stte
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Re: Rarity #5

Postby Cenoman » Wed Jun 15, 2022 8:24 pm

Code: Select all
 +-------------------------+------------------------+---------------------------+
 |  3      128     1458    |  9      2458   257-48  |  6        147     1457    |
 |  25-4   269     4569    |  257-4  36     1       |  57-4     39      8       |
 | <1458   69      7       | <458    36    <458     | <145      2       39      | 5
 +-------------------------+------------------------+---------------------------+
 |  9      1278    158     |  3      2458   6       |  257-148  1478    1457    |
 | <1258   1368-2  1368-5  | <2458   7     <2458    | <12458    14689   1469-5  |25
 |  257-8  4       568     |  1      258    9       |  3        678     567     |
 +-------------------------+------------------------+---------------------------+
 |  6      178     148     |  25     25     3       |  9        1478    147     |
 | <1478   39      2       | <4678   19    <478     | <1478     5       36      |  7
 | <1478   5       39      | <4678   19    <478     | <1478     36      2       |  7
 +-------------------------+------------------------+---------------------------+
    148                       468           48         148

1. MSLS 16 cells r3589c1467, 16 links: 48c1467, 1c17, 6c4, 5r35, 2r5, 7r89
10 eliminations: -4 r2c147, -148 r4c7, -8 r6c1, -2 r5c2, -5 r5c39; 18 placements

Code: Select all
 +----------------------+------------------------+------------------------+
 |  3      128   b158   |  9      2458   24578   |  6       147   c1457   |
 |  25     6      4     |  257    3      1       |  57      9      8      |
 |  158    9      7     |  458    6      458     |  145     2      3      |
 +----------------------+------------------------+------------------------+
 |  9     D1278  a158   |  3      2458   6       |  2-57    1478  d1457   |
 |  1258   18     3     |  2458   7      2458    |  12458   6      9      |
 |  2578   4      6     |  1      258    9       |  3       78    d57     |
 +----------------------+------------------------+------------------------+
 |  6     C178    18    |  25     25     3       |  9      B1478  B147    |
 |  1478   3      2     |  478    9      478     | A1478    5      6      |
 |  478    5      9     |  6      1      478     | A478     3      2      |
 +----------------------+------------------------+------------------------+

2. Finned X-Wing: (5)r4c3 = r1c3 - r1c9 = r46c9 => -5 r4c7
3. ER b9: (7)r89c7 = r7c89 - r7c2 = r4c2 => -7 r4c7; ste
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