Rarity #31 - That pattern again!

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Rarity #31 - That pattern again!

Postby m_b_metcalf » Tue Jul 19, 2022 2:45 pm

Code: Select all
 . . . . . . . . .
 . . 5 8 . 1 7 . .
 . 9 4 2 . 7 3 8 .
 . 5 3 . . . 9 2 .
 . . . . . . . . .
 . 4 7 . . . 1 3 .
 . 8 9 7 . 3 4 1 .
 . . 1 9 . 8 2 . .
 . . . . . . . . .  m_b_metcalf, PG 30
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Re: Rarity #31 - That pattern again!

Postby Cenoman » Tue Jul 19, 2022 4:55 pm

Krakenless solution:
Code: Select all
 +-------------------------+------------------------------+------------------------+
 |  1278     127     28    |  3456    34569       4569    |  56    4569   12       |
 |  23-6     236     5     |  8       469         1       |  7     469    2469     |
 | a16       9       4     |  2       56          7       |  3     8     b156      |
 +-------------------------+------------------------------+------------------------+
 | f168      5       3     |  146     14678       46      |  9     2    Cc4678     |
 | e129-6   e126   Ee268   |  13456   123456789   24569   |Dd568 Dd4567 Dd45678    |
 | f2689     4       7     |  56      25689       2569    |  1     3    Cc568      |
 +-------------------------+------------------------------+------------------------+
 | A25-6     8       9     |  7       256         3       |  4     1    Bb56       |
 |  3457-6   37-6    1     |  9       456         8       |  2     567    3567     |
 |  23457-6  237-6 FA26    |  1456    12456       2456    |  568   5679   356789   |
 +-------------------------+------------------------------+------------------------+

1. (6=1)r3c1 - (1=56)r37c9 - r46c9 = r5c789 - r5c123 = (6)r46c1 => -6 r25789c1
2. (6=25)b7p19 - (5=6)r7c9 - r46c9 = r5c789 - r5c3 = (6)r9c3 => -6 r89c2; lclste
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Re: Rarity #31 - That pattern again!

Postby P.O. » Tue Jul 19, 2022 6:11 pm

this pattern has a fine morph:
Code: Select all
                . . . . . . . . .         . . . . X X X X .
                . . X X . X X . .         . . . . . . . . .
                . X X X . X X X .         . . . . X X X X .
                . X X . . . X X .         . . . . . . . . .
                . . . . . . . . .         X . X . X X X X .
                . X X . . . X X .         X . X . X . . X .
                . X X X . X X X .         X . X . X . . X .
                . . X X . X X . .         X . X . X X X X .
                . . . . . . . . .         . . . . . . . . .
               
this puzzle morphed:
....9253..............1347..........7.3.4189.9.8.2..1.8.1.7..5.2.7.3894..........

Code: Select all
QUINTE ROW: ((1 4 2) (3 4 5 6)) ((1 5 2) (3 4 5 6 9)) ((1 6 2) (4 5 6 9)) ((1 7 3) (5 6)) ((1 8 3) (4 5 6 9))
(((1 1 1) (1 2 3 6 7 8)) ((1 2 1) (1 2 3 6 7)) ((1 3 1) (2 6 8)) ((1 9 3) (1 2 4 5 6 9)))
intersection:
((((3 0) (2 1 1) (2 3 6)) ((3 0) (2 2 1) (2 3 6))))

26r9c3 => r3c1 r7c9 <> 6
 r9c3=2 - r1c3{n2 n8} - r5c3{n28 n6} - b6n6{r5c789 r46c9} - r7c9{n6 n5} - r7c1{n25 n6}
 r9c3=6 - b8n6{r9c456 r78c5} - b2n6{r123c5 r1c46} - c7n6{r1 r5} - c2n6{r5 r2} - r3n6{c1 c9}
 
ste.

there is also a solution using the Pattern Overlay Method: these cells are not in any valid template for the values considered:
Code: Select all
   r5c5 <> 2
   r5c5 r9c9 <> 5
   r1c1 r1c2 r1c5 r1c8 r1c9 r2c1 r2c5 r2c9 r4c5 r5c1
   r5c2 r5c4 r5c5 r5c6 r5c8 r5c9 r6c5 r8c1 r8c5 r8c9
   r9c1 r9c2 r9c5 r9c8 r9c9  <> 6
   
 r1c7{n5 n6} - c8n6{r2 r8} - r7c9{n6 n5} => r13c9 r9c7 <> 5
 bte.
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Re: Rarity #31 - That pattern again!

Postby DEFISE » Wed Jul 20, 2022 9:25 am

Hidden quads: 1278r1c1239 => -3r1c1 -6r1c1 -3r1c2 -6r1c2 -6r1c3 -4r1c9 -5r1c9 -6r1c9 -9r1c9
Box/Line: 3r1b2 => -3r2c5
g-whip[6]: c3n6{r9 r5}- b6n6{r5c7 r456c9}- r7c9{n6 n5}- r3c9{n5 n1} - r3c1{n1 n6}- r7c1{n6 .} => -2r9c3
Singles + Box/Lines to the end.

Another solution with one z-chain and one AIC
(unlike a whip, a z-chain only requires the memorization of candidates that see the target z (called z-candidates)):

Hidden Text: Show
Hidden quads: 1278r1c1239 => -3r1c1 -6r1c1 -3r1c2 -6r1c2 -6r1c3 -4r1c9 -5r1c9 -6r1c9 -9r1c9
Box/Line: 3r1b2 => -3r2c5
g-z-chain[5]: b6n6{r4c9 r5c78}- c3n6{r5 r9}- r8n6{c1 c5}- r3n6{c5 c1}- c2n6{r2 .} => -6r7c9
Single(s): 5r7c9, 5r3c5, 5r8c1, 4r8c5, 4r9c1, 3r2c1, 7r1c1, 8r1c3
Box/Line: 4r2b3 => -4r1c8
Box/Line: 5r6b5 => -5r5c4 -5r5c6
Box/Line: 2b1c2 => -2r5c2 -2r9c2
Naked pairs: 26b7p19 => -6r8c2 -6r9c2
Box/Line: 6r8b9 => -6r9c7 -6r9c8 -6r9c9
Single: 8r9c7
AIC : 6r7c5 = 6r7c1 – 6r3c1 = 6r2c2 => -6r2c5
STTE
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