The New Sudoku Players' Forum

by **pjb** » Thu Jul 08, 2021 11:57 pm

Code: Select all: *-----------* |8..|7..|..4| |.5.|...|6..| |...|...|...| |---+---+---| |.3.|97.|..8| |...|.43|..5| |...|.2.|9..| |---+---+---| |..6|...|...| |2..|.6.|..7| |.71|..8|3.2| *-----------* 8..7....4.5....6............3.97...8....43..5....2.9....6......2...6...7.71..83.2

Phil

by **Cenoman** » Fri Jul 09, 2021 9:06 am

Three simple steps.
First, two skyscrapers:

Code: Select all: +---------------------------+---------------------------+-------------------------+ | 8 1269^ 239* | 7 1359* 12569^ | 125 1259 4 | | 1479-3 5 23479 | 134 1389 1249 | 6 12789 139 | | 1479-36 12469 23479 | 13456 13589 124569 | 12578 125789 139 | +---------------------------+---------------------------+-------------------------+ | 156^ 3 25 | 9 7 156^ | 124 124 8 | | 169 1289-6 289 | 168 4 3 | 127 127 5 | | 1457 148 4578 | 158 2 15 | 9 3 6 | +---------------------------+---------------------------+-------------------------+ | 3459* 489 6 | 2 1359* 7 | 1458 14589 19 | | 2 489 34589 | 1345 6 1459 | 1458 14589 7 | | 459 7 1 | 45 59 8 | 3 6 2 | +---------------------------+---------------------------+-------------------------+

1. (3)r1c3 = r1c5 - r7c5 = r7c1 => -3 r23c1, r8c3
2. (6)r1c2 = r1c6 - r4c6 = r4c1 => -6 r3c1, r5c2; two placements & lcls

Code: Select all: +-------------------------+--------------------------+-------------------------+ | 8 1269 239 | 7 1359 12569 | 125 1259 4 | | 1479 5 23479 | c14 1389 1249 | 6 12789 139 | | 1479 12469 23479 | 1456 13589 124569 | 12578 125789 139 | +-------------------------+--------------------------+-------------------------+ | 156 3 25 | 9 7 e156 | 124 124 8 | | 169 1289 289 | d168 4 3 | 127 127 5 | | 1457 148 4578 | d158 2 e15 | 9 3 6 | +-------------------------+--------------------------+-------------------------+ | 3 489 6 | 2 159 7 | 1458 14589 19 | | 2 489 4589 | 3 6 a459-1 | 1458 14589 7 | | 459 7 1 | b45 59 8 | 3 6 2 | +-------------------------+--------------------------+-------------------------+

3. Group S-Wing: (4)r8c6 = r9c4 - (4=1)r2c4 - r56c4 = (1)r46c6 => -1 r8c6; lclste

by **Leren** » Fri Jul 09, 2021 10:30 am

1 & 2 : Same Skyscrapers as Cenoman etc.

Code: Select all: *------------------------------------------------------------* | 8 1269 239 | 7 359-1 12569 | 125 1259 4 | | 1479 5 23479 |a14 389-1 1249 | 6 12789 139 | | 1479 12469 23479 | 1456 3589-1 124569 | 12578 125789 139 | |------------------+----------------------+------------------| | 156 3 25 | 9 7 156 | 124 124 8 | | 169 1289 289 | 168 4 3 | 127 127 5 | | 1457 148 4578 | 158 2 15 | 9 3 6 | |------------------+----------------------+------------------| | 3 489 6 | 2 d159 7 | 1458 14589 19 | | 2 489 4589 | 3 6 c1459 | 1458 14589 7 | | 459 7 1 |b45 59 8 | 3 6 2 | *------------------------------------------------------------*

3. M Wing : (1=4) r2c4 - r9c4 = (4-1) r8c6 = (1) r7c5 => - 1 r123c5; btte

Leren

Website · by **denis_berthier** » Sun Jul 11, 2021 6:50 am

.
SER = 7.1

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 8 1269 239 ! 7 1359 12569 ! 125 1259 4 ! ! 13479 5 23479 ! 134 1389 1249 ! 6 12789 139 ! ! 134679 12469 23479 ! 13456 13589 124569 ! 12578 125789 139 ! +----------------------+----------------------+----------------------+ ! 156 3 25 ! 9 7 156 ! 124 124 8 ! ! 169 12689 289 ! 168 4 3 ! 127 127 5 ! ! 1457 148 4578 ! 158 2 15 ! 9 3 6 ! +----------------------+----------------------+----------------------+ ! 3459 489 6 ! 2 1359 7 ! 1458 14589 19 ! ! 2 489 34589 ! 1345 6 1459 ! 1458 14589 7 ! ! 459 7 1 ! 45 59 8 ! 3 6 2 ! +----------------------+----------------------+----------------------+

1) Solved using nothing more complicated than a bivalue-chain[3]:

Code: Select all: finned-x-wing-in-rows: n3{r8 r1}{c3 c4} ==> r3c4 ≠ 3, r2c4 ≠ 3 singles ==> r8c4 = 3, r7c1 = 3 finned-x-wing-in-columns: n6{c4 c2}{r5 r3} ==> r3c1 ≠ 6 whip[1]: c1n6{r5 .} ==> r5c2 ≠ 6 biv-chain[3]: b8n1{r7c5 r8c6} - b8n4{r8c6 r9c4} - r2c4{n4 n1} ==> r1c5 ≠ 1, r2c5 ≠ 1, r3c5 ≠ 1 hidden-single-in-a-column ==> r7c5 = 1 naked-single ==> r7c9 = 9 whip[1]: r7n5{c8 .} ==> r8c7 ≠ 5, r8c8 ≠ 5 whip[1]: c9n1{r3 .} ==> r1c7 ≠ 1, r1c8 ≠ 1, r2c8 ≠ 1, r3c7 ≠ 1, r3c8 ≠ 1 hidden-pairs-in-a-row: r1{n1 n6}{c2 c6} ==> r1c6 ≠ 9, r1c6 ≠ 5, r1c6 ≠ 2, r1c2 ≠ 9, r1c2 ≠ 2 finned-x-wing-in-rows: n5{r8 r4}{c6 c3} ==> r6c3 ≠ 5 naked-triplets-in-a-column: c6{r1 r4 r6}{n1 n6 n5} ==> r8c6 ≠ 5, r3c6 ≠ 6, r3c6 ≠ 5, r3c6 ≠ 1, r2c6 ≠ 1 stte

2) A 4-step solution using nothing more complicated than a whip[4]:

Code: Select all: step 1: biv-chain-rn[2]: r1n3{c5 c3} - r8n3{c3 c4} ==> r7c5 ≠ 3, r2c4 ≠ 3, r3c4 ≠ 3 hidden-single-in-a-column ==> r8c4 = 3 hidden-single-in-a-block ==> r7c1 = 3 step 2: whip[3]: b8n4{r8c6 r9c4} - r2c4{n4 n1} - b5n1{r5c4 .} ==> r8c6 ≠ 1 singles ==> r7c5 = 1, r7c9 = 9 whip[1]: r7n5{c8 .} ==> r8c7 ≠ 5, r8c8 ≠ 5 whip[1]: c9n1{r3 .} ==> r1c7 ≠ 1, r1c8 ≠ 1, r2c8 ≠ 1, r3c7 ≠ 1, r3c8 ≠ 1 step 3: whip[4]: r6c6{n5 n1} - r4c6{n1 n6} - r1n6{c6 c2} - r1n1{c2 .} ==> r6c4 ≠ 5 whip[1]: b5n5{r6c6 .} ==> r1c6 ≠ 5, r3c6 ≠ 5, r8c6 ≠ 5 singles ==> r8c3 = 5, r4c3 = 2 whip[1]: c3n8{r6 .} ==> r5c2 ≠ 8, r6c2 ≠ 8 step 4: z-chain[4]: r1n6{c2 c6} - r4n6{c6 c1} - c2n6{r5 r3} - c2n2{r3 .} ==> r1c2 ≠ 1 stte

3) A 3-step solution using an excessively long chain for such a simple puzzle:

Code: Select all: step 1: biv-chain-rn[2]: r1n3{c3 c5} - r7n3{c5 c1} ==> r8c3 ≠ 3, r2c1 ≠ 3, r3c1 ≠ 3 singles ==> r7c1 = 3, r8c4 = 3 step 2: whip[3]: b8n4{r8c6 r9c4} - r2c4{n4 n1} - b5n1{r5c4 .} ==> r8c6 ≠ 1 singles ==> r7c5 = 1, r7c9 = 9 whip[1]: r7n5{c8 .} ==> r8c7 ≠ 5, r8c8 ≠ 5 whip[1]: c9n1{r3 .} ==> r1c7 ≠ 1, r1c8 ≠ 1, r2c8 ≠ 1, r3c7 ≠ 1, r3c8 ≠ 1 step3: whip[8]: r1n6{c2 c6} - c4n6{r3 r5} - c2n6{r5 r3} - c2n2{r3 r5} - r4c3{n2 n5} - r8n5{c3 c6} - r6c6{n5 n1} - r4c6{n1 .} ==> r1c2 ≠ 1 stte

PS: the last two solutions are based on an experimental "fewer-steps" strategy inspired by DEFISE's.

Phil's tenth