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by **Yogi** » Wed Feb 16, 2022 7:29 pm

....1.4......9..7.7......3..41...5.....2...8...........6....1.92..7.8............

Code: Select all: +-------+-------+-------+ | | 1 | 4 | | | 9 | 7 | | 7 | | 3 | +-------+-------+-------+ | 4 1 | | 5 | | | 2 | 8 | | | | | +-------+-------+-------+ | 6 | | 1 9 | | 2 | 7 8 | | | | | | +-------+-------+-------+

by **jco** » Wed Feb 16, 2022 9:04 pm

After basics

Code: Select all: .--------------------------------------------------------------------. | 356 23589 23568 | 356 1 7 | 4 569 568 | | 1 358 34568 | 3456 9 2345 | 268 7 568 | | 7 59 456 | 456 8 245 | 269 3 1 | |----------------------+----------------------+----------------------| | 369 4 1 | 8 7 a36 | 5 9-6 2 | | 3569 7 356 | 2 b345 1 | 369 8 346 | | 356 28 28 | 9 b345 3456 | 367 1 3467 | |----------------------+----------------------+----------------------| | 8 6 7 | 345 2345 345 | 1 245 9 | | 2 1 9 | 7 b456 8 | 36 456 356 | | 4 35 35 | 1 c26 9 | 78 d26 78 | '--------------------------------------------------------------------'

1. (6=3)r4c6 - (3=456)r568c5 - r9c5 = r9c8 => -6 r4c8 [20 placements & lc]
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Code: Select all: .-----------------------------------------------------------. |b36 9 2 | 356 1 7 | 4 c56 8 | | 1 8 346 | 3456 9 345 | 2 7 d56 | | 7 5 46 | 46 8 2 | 9 3 1 | |-------------------+-------------------+-------------------| |a36 4 1 | 8 7 3-6 | 5 9 2 | | 9 7 36 | 2 5 1 | 36 8 4 | | 5 2 8 | 9 34 f346 | 7 1 e36 | |-------------------+-------------------+-------------------| | 8 6 7 | 345 234 345 | 1 24 9 | | 2 1 9 | 7 46 8 | 36 456 356 | | 4 3 5 | 1 26 9 | 8 26 7 | '-----------------------------------------------------------'

2. (6)r4c1 = r1c1 - r1c8 = r2c9 - r6c9 = (6)r6c6 => -6 r4c6; ste

Thanks for the puzzle!

Website · by **denis_berthier** » Thu Feb 17, 2022 7:48 am

.
Starting point:

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 3569 23589 23568 ! 3568 1 7 ! 4 2569 2568 ! ! 1 2358 234568 ! 34568 9 23456 ! 268 7 2568 ! ! 7 2589 24568 ! 4568 2458 2456 ! 2689 3 1 ! +----------------------+----------------------+----------------------+ ! 369 4 1 ! 3689 378 36 ! 5 269 2367 ! ! 3569 3579 356 ! 2 3457 1 ! 3679 8 3467 ! ! 3569 235789 23568 ! 34569 3457 3456 ! 3679 1 3467 ! +----------------------+----------------------+----------------------+ ! 8 6 7 ! 345 2345 2345 ! 1 245 9 ! ! 2 1 9 ! 7 456 8 ! 36 456 356 ! ! 4 35 35 ! 1 26 9 ! 2678 26 2678 ! +----------------------+----------------------+----------------------+ 197 candidates

1) Simplest first solution (in W4)
naked-pairs-in-a-row: r9{c5 c8}{n2 n6} ==> r9c9≠6, r9c9≠2, r9c7≠6, r9c7≠2
whip[1]: b9n2{r9c8 .} ==> r1c8≠2, r4c8≠2
singles ==> r4c9=2, r4c5=7, r4c4=8, r3c5=8, r6c4=9
whip[1]: b5n6{r6c6 .} ==> r2c6≠6, r3c6≠6
whip[1]: c5n2{r9 .} ==> r7c6≠2
whip[1]: r1n2{c3 .} ==> r2c2≠2, r2c3≠2, r3c2≠2, r3c3≠2
hidden-pairs-in-a-row: r6{n2 n8}{c2 c3} ==> r6c3≠6, r6c3≠5, r6c3≠3, r6c2≠7, r6c2≠5, r6c2≠3
hidden-single-in-a-block ==> r5c2=7
whip[1]: c2n9{r3 .} ==> r1c1≠9

Code: Select all: +-------------------+-------------------+-------------------+ ! 356 23589 23568 ! 356 1 7 ! 4 569 568 ! ! 1 358 34568 ! 3456 9 2345 ! 268 7 568 ! ! 7 59 456 ! 456 8 245 ! 269 3 1 ! +-------------------+-------------------+-------------------+ ! 369 4 1 ! 8 7 36 ! 5 69 2 ! ! 3569 7 356 ! 2 345 1 ! 369 8 346 ! ! 356 28 28 ! 9 345 3456 ! 367 1 3467 ! +-------------------+-------------------+-------------------+ ! 8 6 7 ! 345 2345 345 ! 1 245 9 ! ! 2 1 9 ! 7 456 8 ! 36 456 356 ! ! 4 35 35 ! 1 26 9 ! 78 26 78 ! +-------------------+-------------------+-------------------+ 136 candidates

Note the difference in terms of candidates: 61 of them have been eliminated by "Basics" in addition to those eliminated by whips[1] at the start.

z-chain[3]: r8c7{n6 n3} - r5c7{n3 n9} - r4c8{n9 .} ==> r6c7≠6
t-whip[4]: r4c6{n6 n3} - c5n3{r6 r7} - r7n2{c5 c8} - r9c8{n2 .} ==> r4c8≠6
singles ==> r4c8=9, r3c7=9, r3c2=5, r9c2=3, r2c2=8, r6c2=2, r1c2=9, r6c3=8, r9c3=5, r1c3=2, r1c9=8, r9c9=7, r9c7=8, r6c7=7, r2c7=2, r3c6=2, r5c1=9, r6c1=5, r5c5=5, r5c9=4, r7c8≠5
finned-x-wing-in-rows: n3{r4 r1}{c1 c6} ==> r2c6≠3
whip[1]: b2n3{r2c4 .} ==> r7c4≠3
finned-swordfish-in-rows: n6{r3 r2 r5}{c3 c4 c9} ==> r6c9≠6
stte

2) Fewer step solution (3-steps), also in W4, from the starting point.
naked-pairs-in-a-row: r9{c5 c8}{n2 n6} ==> r9c9≠6, r9c9≠2, r9c7≠6, r9c7≠2
whip[1]: b9n2{r9c8 .} ==> r1c8≠2, r4c8≠2
singles ==> r4c9=2, r4c5=7, r4c4=8, r3c5=8, r6c4=9
whip[1]: b5n6{r6c6 .} ==> r2c6≠6, r3c6≠6
whip[1]: c5n2{r9 .} ==> r7c6≠2
whip[1]: r1n2{c3 .} ==> r2c2≠2, r2c3≠2, r3c2≠2, r3c3≠2
whip[4]: r4c6{n6 n3} - c5n3{r6 r7} - r7n2{c5 c8} - r9c8{n2 .} ==> r4c8≠6
singles ==> r4c8=9, r3c7=9, r3c2=5, r9c2=3, r2c2=8, r9c3=5, r1c9=8, r9c9=7, r9c7=8, r6c3=8, r6c2=2, r1c2=9, r5c2=7, r6c7=7, r5c1=9, r6c1=5, r5c5=5, r5c9=4, r1c3=2, r2c7=2, r3c6=2
whip[1]: r8n5{c9 .} ==> r7c8≠5
biv-chain[3]: r4n6{c1 c6} - r6n6{c6 c9} - b3n6{r2c9 r1c8} ==> r1c1≠6
stte

by **P.O.** » Thu Feb 17, 2022 8:31 am

Code: Select all: after singles et intersections: 3569 23589 23568 3568 1 7 4 ×2569 2568 1 2358 234568 34568 9 23456 268 7 2568 7 2589 24568 4568 2458 2456 2689 3 1 369 4 1 3689 378 36 5 ×269 2367 3569 3579 356 2 3457 1 3679 8 3467 3569 235789 23568 34569 3457 3456 3679 1 3467 8 6 7 345 c-2345 c-2345 1 c+245 9 2 1 9 7 456 8 36 456 356 4 35 35 1 b+26 9 ×2678 a±2+6 ×2678 r9c8{n2 n6} - r9c5{n6 n2} - r7n2{r5r6 r8} => r1c8 r4c8 r9c7 r9c9 <> 2 singles: ( r6c4b5 n9 r4c4b5 n8 r3c5b2 n8 r4c5b5 n7 r4c9b6 n2 ) intersections: r1n2{c2c3} => r2c2 r2c3 r3c2 r3c3 <> 2 c5n2{r7r9} => r7c6 <> 2 c6n6{r4r6} => r2c6 r3c6 <> 6 3569 23589 23568 356 1 7 4 569 568 1 358 34568 3456 9 2345 268 7 568 7 59 456 456 8 245 269 3 1 ea±3+6×9 4 1 8 7 a+36 5 e-69 2 3569 3579 356 2 b-345 1 3679 8 3467 356 23578 23568 9 b-345 3456 367 1 3467 8 6 7 345 b2+345 345 1 245 9 2 1 9 7 456 8 36 456 356 4 35 35 1 c+26 9 678 d2+6 678 r4n3{c1 c6} - c5n3{r5r6 r7} - r7n2{c5 c8} - r9c8{n2 n6} - r4n6{c8 c1} => r4c1 <> 9 singles: ( r5c9b6 n4 r6c7b6 n7 r6c1b4 n5 r5c5b5 n5 r1c2b1 n9 r5c1b4 n9 r5c2b4 n7 r9c9b9 n7 r1c3b1 n2 r6c2b4 n2 r1c9b3 n8 r6c3b4 n8 r9c7b9 n8 r3c6b2 n2 r2c7b3 n2 r2c2b1 n8 r9c3b7 n5 r9c2b7 n3 r3c2b1 n5 r3c7b3 n9 r4c8b6 n9 ) intersection: r7n5{c4c6} => r7c8 <> 5 a3+6 9 2 356 1 7 4 b5-6 8 1 8 346 3456 9 345 2 7 b5+6 7 5 46 46 8 2 9 3 1 a3±6 4 1 8 7 3×6 5 9 2 9 7 36 2 5 1 36 8 4 5 2 8 9 34 c34+6 7 1 c3-6 8 6 7 345 234 345 1 24 9 2 1 9 7 46 8 36 456 356 4 3 5 1 26 9 8 26 7 c1n6{r4 r1} - b3n6{r1c8 r2c9} - r6n6{c9 c6} => r4c6 <> 6 ste.

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