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[mith]

Code: Select all

+-------+-------+-------+
| . . . | 8 . . | . . 1 |
| . . 9 | . 7 . | . 2 . |
| . 1 . | . . 5 | . . 4 |
+-------+-------+-------+
| . . 2 | . 4 . | . 5 . |
| 9 . . | 3 . . | 6 . . |
| . 8 . | . . . | . 7 . |
+-------+-------+-------+
| 7 . . | . . . | . . 8 |
| . 6 . | 4 . 1 | . 9 . |
| . . 5 | . 2 . | . . . |
+-------+-------+-------+
...8....1..9.7..2..1...5..4..2.4..5.9..3..6...8.....7.7.......8.6.4.1.9...5.2....

[SpAce]

Quick and dirty.

Code: Select all

.----------------------.---------------------.---------------.
|   23456  23457  3467 | 8     h369    23469 |  79   36   1  |
| fg3468   34     9    | 1      7     h346   | e38   2    5  |
|   2368   1      3678 | 269   h369    5     |  79   368  4  |
:----------------------+---------------------+---------------:
|   136    37     2    | 679    4     c6789  | d18   5    39 |
|   9      457    147  | 3     b158    7-8   |  6    148  2  |
|   13456  8      1346 | 2569   1569   269   |  14   7    39 |
:----------------------+---------------------+---------------:
|   7      2349   134  | 569    3569   369   |  25   134  8  |
|   238    6      38   | 4     a58-3   1     |  25   9    7  |
|  g1348   349    5    | 79     2     h3789  |  134  134  6  |
'----------------------'---------------------'---------------'

(8)r8c5 = r5c5 - @(8)r4c6 = r4c7 - r2c7 = r2c1 - 6r2c1|8r9c1 = (6,93)b2p628,(8)r9c6 => -3 r8c5, -8 r5c6; btte

[denis_berthier]

There's a solution with Subsets and nothing more complex than Typed bivalue-chains[3], but I also found one with an oddagon[7]:

(solve "...8....1..9.7..2..1...5..4..2.4..5.9..3..6...8.....7.7.......8.6.4.1.9...5.2....")
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = O+S
*** Using CLIPS 6.32-r770
***********************************************************************************************
singles ==> r5c9 = 2, r2c4 = 1
193 candidates, 1098 csp-links and 1098 links. Density = 5.93%
whip[1]: c9n7{r9 .} ==> r9c7 ≠ 7, r8c7 ≠ 7
singles ==> r8c9 = 7, r2c9 = 5, r9c9 = 6
whip[1]: c9n3{r6 .} ==> r4c7 ≠ 3, r6c7 ≠ 3
whip[1]: c9n9{r6 .} ==> r6c7 ≠ 9, r4c7 ≠ 9
hidden-pairs-in-a-column: c7{n2 n5}{r7 r8} ==> r8c7 ≠ 3, r7c7 ≠ 4, r7c7 ≠ 3, r7c7 ≠ 1
hidden-pairs-in-a-column: c7{n7 n9}{r1 r3} ==> r3c7 ≠ 8, r3c7 ≠ 3, r1c7 ≠ 3
swordfish-in-columns: n8{c3 c5 c8}{r3 r8 r5} ==> r8c1 ≠ 8, r5c6 ≠ 8, r3c1 ≠ 8
singles ==> r5c6 = 7, r9c4 = 7, r4c2 = 7
oddagon[7]: r4n1{c1 c7},r4c7{n1 n8},r4n8{c7 c6},c6n8{r4 r9},r9n8{c6 c1},r9c1{n8 n1},c1n1{r9 r4} ==> r9c1 ≠ 1
singles ==> r7c3 = 1, r5c3 = 4, r5c2 = 5, r1c1 = 5, r6c7 = 4
hidden-pairs-in-a-row: r1{n2 n4}{c2 c6} ==> r1c6 ≠ 9, r1c6 ≠ 6, r1c6 ≠ 3, r1c2 ≠ 3
hidden-pairs-in-a-column: c1{n4 n8}{r2 r9} ==> r9c1 ≠ 3, r2c1 ≠ 6, r2c1 ≠ 3
singles and whips[1] to the end

[mith]

Nice. I found something very different, there are lots of ways to go in this one.

The swordfish here is similar to the 3x3 patterns found in some of my other puzzles. Here r249c358 nearly forms a complete 3x3, with no given in r9c8. However, the 8 in box 9 covers this cell, so the three given 8s again force a swordfish (in either r249 or c358).

[pjb]

1) Swordfish of 8s (r249\c167) => -8 r3c1, r5c6, r8c1 (same eliminations as continuous loop on 8 as in SpAce's chain), =>

Code: Select all

 45-236  2345    3467   | 8      369    23469  | 79     36     1     
 48-36   34      9      | 1      7      346    | 38     2      5     
a236     1       3678   | 269    369    5      | 79     368    4     
------------------------+----------------------+---------------------
b136     7       2      | 69     4      689    | 18     5      39     
 9      b45     b14     | 3      158    7      | 6      148    2     
b13456   8       36-14  | 2569   1569   269    | 14     7      39     
------------------------+----------------------+---------------------
 7       2349    134    | 569    3569   369    | 25     134    8     
a23      6       38     | 4      358    1      | 25     9      7     
 148-3   349     5      | 7      2      389    | 134    134    6     


2) double ALS:
Double ALS at r38c1 and r4c1, r5c23, r6c1, with X-Z values 6 and 3 => -236 r1c1, -36 r2c1, -3 r9c1, -14 r6c3 => btte

Phil

[SpAce]

1) Swordfish of 8s (r249\c167) => -8 r3c1, r5c6, r8c1 (same eliminations as continuous loop on 8 as in SpAce's chain)

Good point that my subchain actually contains a loop with the 8s. Technically it could have eliminated 8r38c1 as well, but it might have been a bit confusing in an already complex subchain + split-node environment.

2) double ALS

Nice! Btw, it's also a (non-basic) Sue-de-Coq.