The New Sudoku Players' Forum

by **Yogi** » Tue Apr 12, 2022 7:28 pm

..64.153.3..5.9..1....3..9.2.5...7.313874562967...3.58.6.9.7.8.....5......23.49..

Code: Select all: +---+---+---+ |..6|4.1|53.| |3..|5.9|..1| |...|.3.|.9.| +---+---+---+ |2.5|...|7.3| |138|745|629| |67.|..3|.58| +---+---+---+ |.6.|9.7|.8.| |...|.5.|...| |..2|3.4|9..| +---+---+---+

Website · by **denis_berthier** » Wed Apr 13, 2022 4:24 am

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SER = 8.3

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 789 289 6 ! 4 278 1 ! 5 3 27 ! ! 3 248 47 ! 5 2678 9 ! 248 467 1 ! ! 4578 12458 147 ! 268 3 268 ! 248 9 2467 ! +-------------------+-------------------+-------------------+ ! 2 49 5 ! 168 1689 68 ! 7 14 3 ! ! 1 3 8 ! 7 4 5 ! 6 2 9 ! ! 6 7 49 ! 12 129 3 ! 14 5 8 ! +-------------------+-------------------+-------------------+ ! 45 6 134 ! 9 12 7 ! 1234 8 245 ! ! 4789 1489 13479 ! 1268 5 268 ! 1234 1467 2467 ! ! 578 158 2 ! 3 168 4 ! 9 167 567 ! +-------------------+-------------------+-------------------+ 134 candidates.

1) Simplest-first solution, in W4:

Code: Select all: finned-x-wing-in-rows: n6{r2 r9}{c5 c8} ==> r8c8≠6 biv-chain[3]: r6n4{c7 c3} - c3n9{r6 r8} - r8n3{c3 c7} ==> r8c7≠4 whip[3]: r2c3{n4 n7} - r3n7{c3 c9} - b3n6{r3c9 .} ==> r2c8≠4 finned-x-wing-in-rows: n4{r6 r2}{c7 c3} ==> r3c3≠4 biv-chain[2]: c8n4{r8 r4} - b4n4{r4c2 r6c3} ==> r8c3≠4 z-chain[3]: c1n4{r8 r3} - r2n4{c2 c7} - r6n4{c7 .} ==> r7c3≠4 whip[4]: r2c3{n7 n4} - r6n4{c3 c7} - r3n4{c7 c9} - r3n7{c9 .} ==> r1c1≠7 whip[4]: r6n4{c7 c3} - r2c3{n4 n7} - r3n7{c3 c9} - c9n4{r3 .} ==> r7c7≠4 hidden-pairs-in-a-row: r7{n4 n5}{c1 c9} ==> r7c9≠2 finned-x-wing-in-columns: n2{c6 c9}{r8 r3} ==> r3c7≠2 whip[4]: r6n2{c4 c5} - r7n2{c5 c7} - c7n1{r7 r8} - c7n3{r8 .} ==> r6c4≠1 naked-single ==> r6c4=2 finned-x-wing-in-columns: n1{c4 c8}{r4 r8} ==> r8c7≠1 biv-chain[3]: c3n9{r8 r6} - r6c5{n9 n1} - c4n1{r4 r8} ==> r8c3≠1 biv-chain[4]: r8n3{c7 c3} - c3n9{r8 r6} - r6c5{n9 n1} - c7n1{r6 r7} ==> r7c7≠3 singles ==> r8c7=3, r7c3=3, r3c3=1 x-wing-in-rows: n1{r6 r7}{c5 c7} ==> r9c5≠1, r4c5≠1 finned-x-wing-in-columns: n7{c3 c8}{r2 r8} ==> r8c9≠7 z-chain[3]: r9c5{n8 n6} - r8n6{c4 c9} - r8n2{c9 .} ==> r8c6≠8 z-chain[3]: r3n7{c1 c9} - r1n7{c9 c5} - r1n8{c5 .} ==> r3c1≠8 biv-chain[4]: b5n1{r4c4 r6c5} - r7c5{n1 n2} - r8c6{n2 n6} - r4c6{n6 n8} ==> r4c4≠8 biv-chain[4]: r3c7{n4 n8} - r3c4{n8 n6} - r4c4{n6 n1} - b6n1{r4c8 r6c7} ==> r6c7≠4 stte

Even in W6, there's no 2-step solution.
2) 3-step solution in W6:

Code: Select all: whip[6]: r2n6{c8 c5} - c5n7{r2 r1} - b3n7{r1c9 r2c8} - r2c3{n7 n4} - r3n4{c3 c7} - r6n4{c7 .} ==> r3c9≠6 hidden-single-in-a-block ==> r2c8=6 whip[1]: c8n7{r9 .} ==> r8c9≠7, r9c9≠7 z-chain[3]: b4n4{r6c3 r4c2} - r2n4{c2 c7} - r6n4{c7 .} ==> r7c3≠4, r8c3≠4, r3c3≠4 whip[6]: r4c2{n9 n4} - c8n4{r4 r8} - r7n4{c9 c1} - r7n5{c1 c9} - r9c9{n5 n6} - c5n6{r9 .} ==> r4c5≠9 stte

3) 1-step solution using the nukes:

Code: Select all: FORCING[3]-T&E(W1) applied to trivalue candidates n7r3c1, n7r3c3 and n7r3c9 : ===> 7 values decided in the three cases: n4r7c1 n5r7c9 n6r2c8 n6r9c9 n8r4c6 n9r1c1 n2r6c4 ===> 49 candidates eliminated in the three cases: n7r1c1 n8r1c1 n9r1c2 n2r1c5 n2r2c2 n6r2c5 n8r2c5 n4r2c7 n4r2c8 n7r2c8 n4r3c1 n8r3c1 n4r3c2 n8r3c2 n4r3c3 n2r3c4 n8r3c6 n2r3c7 n2r3c9 n6r3c9 n8r4c4 n1r4c5 n8r4c5 n6r4c6 n1r6c4 n2r6c5 n5r7c1 n4r7c3 n4r7c7 n2r7c9 n4r7c9 n4r8c1 n9r8c1 n4r8c2 n8r8c2 n4r8c3 n2r8c4 n8r8c6 n2r8c7 n4r8c7 n1r8c8 n6r8c8 n6r8c9 n7r8c9 n8r9c2 n6r9c5 n6r9c8 n5r9c9 n7r9c9 stte

by **P.O.** » Wed Apr 13, 2022 11:51 am

Code: Select all: 789 289 6 4 278 1 5 3 27 3 248 47 5 2678 9 248 467 1 4578 ×12458 147 268 3 268 248 9 2467 2 49 5 168 1689 68 7 14 3 1 3 8 7 4 5 6 2 9 6 7 49 12 129 3 14 5 8 45 6 134 9 12 7 1234 8 245 ×4789 1489 13479 1268 5 268 1234 1467 2467 ×578 158 2 3 168 4 9 167 567 r6c3n49 => r3c2 <> 1 r8c1 <> 4 r9c1 <> 5 r3c2 <> 1 : r6c3=4 - r2c3{n4 n7} - r3c3{n47 n1} r6c3=9 - [ r4c2{n9 n4} - r4c8{n4 n1} & c5{r67}{n12} ] - r9n1{c58 c2} r8c1 <> 4 : r6c3=4 - r2c3{n4 n7} - c5n7{r2 r1} - r1n8{c5 c12} - c1{r37}{n45} r6c3=9 - r6n4{c3 c7} - r3{c467}{n268} - c9n6{r3 r89} - c8{r489}{n147} r9c1 <> 5 : r6c3=4 - r2c3{n4 n7} - c5n7{r2 r1} - r1n8{c5 c12} - c1{r37}{n45} r6c3=9 - r6n4{c3 c7} - c7{r23}{n28} - r1c9{n2 n7} - c5{r167}{n128} - r9c5{n18 n6} - r9c9{n67 n5} bte.

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