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by **mith** » Tue Apr 13, 2021 9:22 pm

Code: Select all: +-------+-------+-------+ | . . . | . . . | . . . | | . . 9 | 8 . . | . . 7 | | . 6 . | . 5 . | . 4 . | +-------+-------+-------+ | . 5 . | . 3 . | . 6 . | | . . 7 | 9 . . | . . 8 | | . . . | . . 4 | . . . | +-------+-------+-------+ | . . . | . . . | . . . | | . . 8 | 2 . . | . . 9 | | . 4 2 | . 6 . | . 5 . | +-------+-------+-------+ ...........98....7.6..5..4..5..3..6...79....8.....4..............82....9.42.6..5.

by **pjb** » Tue Apr 13, 2021 11:41 pm

There are 11 consecutive fish, but slightly shorter with 5 MSLSs and 4 fish: (basic moves in between not included)

2-3 MSLS at r34c349; Links: 13r3 14r4 7c4 2c9; Eliminations: -1 r3c1, -3 r3c1, -1 r4c1, -4 r4c1, -2 r1c9, -1 r3c6, -3 r3c6, -1 r4c6, -2 r6c9, -1 r3c7, -3 r3c7, -1 r4c7, -4 r4c7, -2 r7c9, -7 r9c4

3-3 MSLS at r258c258; Links: 2r2 2r5 7r8 13c2 14c5 13c8; Eliminations: -2 r2c1, -7 r8c1, -1 r1c2, -3 r1c2, -1 r1c5, -4 r1c5, -1 r1c8, -3 r1c8, -2 r2c6, -7 r8c6, -1 r6c2, -3 r6c2, -1 r6c5, -1 r6c8, -3 r6c8, -2 r2c7, -7 r8c7, -1 r7c2, -3 r7c2, -1 r7c5, -4 r7c5, -1 r7c8, -3 r7c8

3-3 MSLS at r258c258; Links: 12r2 12r5 17r8 3c2 4c5 3c8; Eliminations: -1 r2c1, -1 r8c1, -1 r2c6, -1 r8c6, -1 r2c7, -1 r8c7

3-3 MSLS at r349c349; Links: 3r3 4r4 3r9 1c3 17c4 12c9; Eliminations: -1 r1c3, -1 r1c9, -1 r6c3, -1 r6c9, -1 r7c3, -1 r7c9

3-3 MSLS at r146 c239 +r1c4 r6c4 r7c2 r3c3 r3c9 r9c9; Links: 456r1, 4r4, 56r6, 789c2, 13c3, 123c9; Eliminations: r1c1<>4, r1c1<>5, r1c7<>5, r1c7<>6, r7c3<>3, r7c9<>3

Swordfish of 8s (r349\c167) => -8 r1c1, r1c7, r6c1, r7c6, r7c7

Swordfish of 9s (r349\c167) => -9 r1c67, r6c17, r7c6

Sashimi franken swordfish of 7s (r389\c15b9), fins at r3c46 => -7 r1c5

Finned franken swordfish of 3s (r9b62\c489), fin at r2c6 => -3 r2c8

(1=4)r4c3 - (4=6)r5c1 - (6=5)r5c6 - (5=3)r8c6 - (3=1)r9c4 => -1 r4c4; stte

Phil

by **Leren** » Tue Apr 13, 2021 11:59 pm

I used 1 X Wing, 8 Swordfish, 1 ER and 1 W Wing.

Interestingly the Basic-anti-backdoors list was a big one with 19 possibilities : 5 r1c3, 4 r1c4, 6 r1c9, 4 r2c1, 6 r2c6, 5 r2c7, 1 r3c3, 4 r4c3, 6 r5c1, 5 r5c6, 4 r5c7, 6 r6c4, 5 r6c9, 6 r7c3, 5 r7c4, 4 r7c9, 5 r8c1, 4 r8c5 & 6 r8c7

That many usually indicates an easy OTP solution but mith has tricked us this time

Leren

by **mith** » Wed Apr 14, 2021 1:59 am

Bwahaha

(I'm not aware of an easy one-step solution, no. There are some nasty ones, and maybe someone will find something better than those.)

Website · by **denis_berthier** » Wed Apr 14, 2021 2:47 am

.
Resolution state after Singles:

Code: Select all: +-------------------------+-------------------------+-------------------------+ ! 1234578 12378 1345 ! 13467 12479 123679 ! 1235689 12389 12356 ! ! 12345 123 9 ! 8 124 1236 ! 12356 123 7 ! ! 12378 6 13 ! 137 5 12379 ! 12389 4 123 ! +-------------------------+-------------------------+-------------------------+ ! 12489 5 14 ! 17 3 1278 ! 12479 6 124 ! ! 12346 123 7 ! 9 12 1256 ! 12345 123 8 ! ! 123689 12389 136 ! 1567 1278 4 ! 123579 12379 1235 ! +-------------------------+-------------------------+-------------------------+ ! 135679 1379 1356 ! 13457 14789 135789 ! 1234678 12378 12346 ! ! 13567 137 8 ! 2 147 1357 ! 13467 137 9 ! ! 1379 4 2 ! 137 6 13789 ! 1378 5 13 ! +-------------------------+-------------------------+-------------------------+ 263 candidates, 2099 csp-links and 2099 links. Density = 6.09%

First trying to find as many Subsets as possible (25 found, including 10 fish):
hidden-pairs-in-a-block: b5{n5 n6}{r5c6 r6c4} ==> r6c4 ≠ 7, r6c4 ≠ 1, r5c6 ≠ 2, r5c6 ≠ 1
naked-triplets-in-a-row: r5{c2 c5 c8}{n3 n2 n1} ==> r5c7 ≠ 3, r5c7 ≠ 2, r5c7 ≠ 1, r5c1 ≠ 3, r5c1 ≠ 2, r5c1 ≠ 1
naked-triplets-in-a-column: c4{r3 r4 r9}{n3 n7 n1} ==> r7c4 ≠ 7, r7c4 ≠ 3, r7c4 ≠ 1, r1c4 ≠ 7, r1c4 ≠ 3, r1c4 ≠ 1
swordfish-in-columns: n6{c3 c4 c9}{r7 r6 r1} ==> r7c7 ≠ 6, r7c1 ≠ 6, r6c1 ≠ 6, r1c7 ≠ 6, r1c6 ≠ 6
swordfish-in-columns: n9{c2 c5 c8}{r6 r7 r1} ==> r7c6 ≠ 9, r7c1 ≠ 9, r6c7 ≠ 9, r6c1 ≠ 9, r1c7 ≠ 9, r1c6 ≠ 9
swordfish-in-columns: n4{c3 c4 c9}{r4 r1 r7} ==> r7c7 ≠ 4, r7c5 ≠ 4, r4c7 ≠ 4, r4c1 ≠ 4, r1c5 ≠ 4, r1c1 ≠ 4
hidden-pairs-in-a-block: b9{n4 n6}{r7c9 r8c7} ==> r8c7 ≠ 7, r8c7 ≠ 3, r8c7 ≠ 1, r7c9 ≠ 3, r7c9 ≠ 2, r7c9 ≠ 1
swordfish-in-rows: n8{r3 r4 r9}{c7 c1 c6} ==> r7c7 ≠ 8, r7c6 ≠ 8, r6c1 ≠ 8, r1c7 ≠ 8, r1c1 ≠ 8
hidden-pairs-in-a-block: b3{n8 n9}{r1c8 r3c7} ==> r3c7 ≠ 3, r3c7 ≠ 2, r3c7 ≠ 1, r1c8 ≠ 3, r1c8 ≠ 2, r1c8 ≠ 1
hidden-pairs-in-a-block: b4{n8 n9}{r4c1 r6c2} ==> r6c2 ≠ 3, r6c2 ≠ 2, r6c2 ≠ 1, r4c1 ≠ 2, r4c1 ≠ 1
hidden-pairs-in-a-block: b8{n8 n9}{r7c5 r9c6} ==> r9c6 ≠ 7, r9c6 ≠ 3, r9c6 ≠ 1, r7c5 ≠ 7, r7c5 ≠ 1
swordfish-in-rows: n5{r2 r5 r8}{c1 c7 c6} ==> r7c6 ≠ 5, r7c1 ≠ 5, r6c7 ≠ 5, r1c7 ≠ 5, r1c1 ≠ 5
hidden-pairs-in-a-block: b1{n4 n5}{r1c3 r2c1} ==> r2c1 ≠ 3, r2c1 ≠ 2, r2c1 ≠ 1, r1c3 ≠ 3, r1c3 ≠ 1
hidden-pairs-in-a-block: b3{n5 n6}{r1c9 r2c7} ==> r2c7 ≠ 3, r2c7 ≠ 2, r2c7 ≠ 1, r1c9 ≠ 3, r1c9 ≠ 2, r1c9 ≠ 1
hidden-pairs-in-a-block: b7{n5 n6}{r7c3 r8c1} ==> r8c1 ≠ 7, r8c1 ≠ 3, r8c1 ≠ 1, r7c3 ≠ 3, r7c3 ≠ 1
swordfish-in-columns: n3{c3 c4 c9}{r6 r3 r9} ==> r9c7 ≠ 3, r9c1 ≠ 3, r6c8 ≠ 3, r6c7 ≠ 3, r6c1 ≠ 3, r3c6 ≠ 3, r3c1 ≠ 3
x-wing-in-columns: n3{c1 c7}{r1 r7} ==> r7c8 ≠ 3, r7c6 ≠ 3, r7c2 ≠ 3, r1c6 ≠ 3, r1c2 ≠ 3
hidden-triplets-in-a-column: c6{n3 n5 n6}{r2 r8 r5} ==> r8c6 ≠ 7, r8c6 ≠ 1, r2c6 ≠ 2, r2c6 ≠ 1
hidden-triplets-in-a-row: r6{n3 n5 n6}{c3 c9 c4} ==> r6c9 ≠ 2, r6c9 ≠ 1, r6c3 ≠ 1
swordfish-in-columns: n1{c3 c4 c9}{r4 r3 r9} ==> r9c7 ≠ 1, r9c1 ≠ 1, r4c7 ≠ 1, r4c6 ≠ 1, r3c6 ≠ 1, r3c1 ≠ 1
hidden-pairs-in-a-row: r9{n1 n3}{c4 c9} ==> r9c4 ≠ 7
swordfish-in-columns: n1{c1 c6 c7}{r6 r7 r1} ==> r7c8 ≠ 1, r7c2 ≠ 1, r6c8 ≠ 1, r6c5 ≠ 1, r1c5 ≠ 1, r1c2 ≠ 1
naked-pairs-in-a-block: b7{r7c2 r9c1}{n7 n9} ==> r8c2 ≠ 7, r7c1 ≠ 7
naked-triplets-in-a-column: c2{r2 r5 r8}{n1 n2 n3} ==> r1c2 ≠ 2
finned-jellyfish-in-rows: n7{r9 r6 r8 r3}{c1 c7 c8 c5} ==> r1c5 ≠ 7
PUZZLE 0 IS NOT SOLVED. 61 VALUES MISSING.

Code: Select all: CURRENT RESOLUTION STATE: 1237 78 45 46 29 127 123 89 56 45 123 9 8 124 36 56 123 7 278 6 13 137 5 279 89 4 123 89 5 14 17 3 278 279 6 124 46 123 7 9 12 56 45 123 8 12 89 36 56 278 4 127 279 35 13 79 56 45 89 17 1237 278 46 56 13 8 2 147 35 46 137 9 79 4 2 13 6 89 78 5 13

From this point on, there are many possibilities:
- either with the standard simplest-first strategy, requiring no more than Subsets[3] and bivalue-chains[3]:

Code: Select all: biv-chain[3]: r3c3{n1 n3} - c4n3{r3 r9} - r9n1{c4 c9} ==> r3c9 ≠ 1 biv-chain[3]: r3c9{n2 n3} - c7n3{r1 r7} - b9n2{r7c7 r7c8} ==> r2c8 ≠ 2 biv-chain[2]: r2n2{c5 c2} - b4n2{r5c2 r6c1} ==> r6c5 ≠ 2 biv-chain[3]: r2c8{n1 n3} - r1n3{c7 c1} - r3c3{n3 n1} ==> r2c2 ≠ 1 biv-chain[3]: r2c2{n2 n3} - r1n3{c1 c7} - b3n2{r1c7 r3c9} ==> r3c1 ≠ 2 naked-pairs-in-a-block: b1{r1c2 r3c1}{n7 n8} ==> r1c1 ≠ 7 biv-chain[3]: c4n7{r4 r3} - r3c1{n7 n8} - r4n8{c1 c6} ==> r4c6 ≠ 7 biv-chain[3]: r4c6{n2 n8} - r6c5{n8 n7} - r4n7{c4 c7} ==> r4c7 ≠ 2 x-wing-in-rows: n2{r3 r4}{c6 c9} ==> r1c6 ≠ 2 naked-pairs-in-a-column: c6{r1 r7}{n1 n7} ==> r3c6 ≠ 7 naked-pairs-in-a-block: b2{r1c5 r3c6}{n2 n9} ==> r2c5 ≠ 2 stte

- or with a single step. There are many possibilities.
There are 18 W1-anti-backdoors: n6r8c7 n4r8c5 n5r8c1 n4r7c9 n5r7c4 n6r7c3 n5r6c9 n6r6c4 n4r5c7 n5r5c6 n6r5c1 n4r4c3 n5r2c7 n6r2c6 n4r2c1 n6r1c9 n4r1c4 n5r1c3, all of which give rise to a single-step solution (after the initial Subsets).
Here are the simplest solutions:
1) Using a bivalue-chain [5]

Code: Select all: biv-chain[5]: r2n6{c7 c6} - b2n3{r2c6 r3c4} - c4n7{r3 r4} - c5n7{r6 r8} - r8n4{c5 c7} ==> r8c7 ≠ 6 stte

Code: Select all: biv-chain[5]: r8c6{n5 n3} - b2n3{r2c6 r3c4} - c4n7{r3 r4} - c5n7{r6 r8} - b8n4{r8c5 r7c4} ==> r7c4 ≠ 5 stte

Code: Select all: biv-chain[5]: c5n4{r2 r8} - c5n7{r8 r6} - c4n7{r4 r3} - b2n3{r3c4 r2c6} - b2n6{r2c6 r1c4} ==> r1c4 ≠ 4 stte

2) Using a z-chain[4]:

Code: Select all: z-chain[4]: b8n7{r8c5 r7c6} - b8n1{r7c6 r9c4} - r4c4{n1 n7} - c5n7{r6 .} ==> r8c5 ≠ 4 stte

Website · by **denis_berthier** » Wed Apr 14, 2021 2:54 am

mith wrote:(I'm not aware of an easy one-step solution, no. There are some nasty ones, and maybe someone will find something better than those.)

If you want a dirty one starting with the original puzzle, forcing-T&E(S) (or, for that matter, conjugated tracks) will provide it:
FORCING-T&E(S) applied to bivalue candidates n2r7c7 and n2r7c8 :
===> 8 values decided in both cases: n1r6c7 n2r6c1 n2r2c2 n1r2c8 n3r2c6 n1r9c9 n3r9c4 n4r2c5
===> 36 candidates eliminated in both cases: n2r1c1 n7r1c1 n4r1c4 n7r1c5 n2r1c6 n1r1c7 n4r2c1 n1r2c2 n3r2c2 n1r2c5 n2r2c5 n6r2c6 n2r2c8 n3r2c8 n2r3c1 n3r3c4 n7r3c6 n1r3c9 n7r4c6 n2r4c7 n1r4c9 n2r5c2 n1r5c8 n1r6c1 n2r6c5 n2r6c7 n7r6c7 n2r6c8 n1r7c7 n7r7c7 n7r7c8 n4r8c5 n3r8c6 n1r8c8 n1r9c4 n3r9c9

Code: Select all: CURRENT RESOLUTION STATE: 13 78 45 6 29 17 23 89 56 5 2 9 8 4 3 56 1 7 78 6 13 17 5 29 89 4 23 89 5 14 17 3 28 79 6 24 46 13 7 9 12 56 45 23 8 2 89 36 56 78 4 1 79 35 13 79 56 45 89 17 23 28 46 56 13 8 2 17 5 46 37 9 79 4 2 3 6 89 78 5 1

stte

Website · by **denis_berthier** » Wed Apr 14, 2021 5:37 am

.
On second thoughts, considering the large number of Subsets, I wondered if there would be a simple whips solution using no Subset. (Rare types of Subset eliminations cannot be obtained by whips.)

There are indeed much simpler solutions than I thought, starting with the same bivalue-chains[≤3]

start: Show

Code: Select all: ;;; Resolution state RS1 1237 12378 45 46 1279 1237 123 89 56 45 123 9 8 124 1236 56 123 7 12378 6 13 137 5 12379 89 4 23 89 5 14 17 3 1278 1279 6 124 46 123 7 9 12 56 45 123 8 123 89 136 56 1278 4 1237 12379 1235 137 1379 56 45 89 137 1237 12378 46 56 137 8 2 147 1357 46 137 9 1379 4 2 137 6 89 1378 5 13

and requiring only:

- either z-chains of max length 5: Show

- or bivalue-chains + t-whips of max length 3: Show

This turns this puzzle into an excellent example for training on bivalue chains and z-chains or t-whips (in addition to training on Subsets).

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