The New Sudoku Players' Forum

by **mith** » Mon Oct 26, 2020 2:17 pm

Code: Select all: +-------+-------+-------+ | . 3 . | . 1 . | . . . | | . 4 1 | 5 . . | . 9 . | | 2 . . | 6 . . | 5 . 3 | +-------+-------+-------+ | . 5 . | . . . | 8 . 9 | | . . . | . 7 . | . . . | | 9 . 3 | . . . | . 2 . | +-------+-------+-------+ | 3 . 8 | . . 4 | . . 6 | | . 2 . | . . 6 | 4 3 . | | . . . | . 3 . | . 8 . | +-------+-------+-------+ .3..1.....415...9.2..6..5.3.5....8.9....7....9.3....2.3.8..4..6.2...643.....3..8.

Website · by **denis_berthier** » Mon Oct 26, 2020 3:25 pm

SER = 9.0, W = 7, TyW = 13

Code: Select all: (solve-sudoku-grid +-------+-------+-------+ ! . 3 . ! . 1 . ! . . . ! ! . 4 1 ! 5 . . ! . 9 . ! ! 2 . . ! 6 . . ! 5 . 3 ! +-------+-------+-------+ ! . 5 . ! . . . ! 8 . 9 ! ! . . . ! . 7 . ! . . . ! ! 9 . 3 ! . . . ! . 2 . ! +-------+-------+-------+ ! 3 . 8 ! . . 4 ! . . 6 ! ! . 2 . ! . . 6 ! 4 3 . ! ! . . . ! . 3 . ! . 8 . ! +-------+-------+-------+ )

Code: Select all: *********************************************************************************************** *** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin *** Using CLIPS 6.32-r774 *********************************************************************************************** singles ==> r5c7 = 3, r4c4 = 3, r2c6 = 3, r3c8 = 1, r3c5 = 4 174 candidates, 929 csp-links and 929 links. Density = 6.17% whip[1]: c5n9{r8 .} ==> r9c6 ≠ 9, r7c4 ≠ 9, r8c4 ≠ 9, r9c4 ≠ 9 finned-x-wing-in-rows: n8{r3 r6}{c2 c6} ==> r5c6 ≠ 8 z-chain[3]: b6n1{r6c9 r5c9} - r8n1{c9 c1} - r4n1{c1 .} ==> r6c4 ≠ 1 t-whip[4]: r8n8{c4 c5} - r8n9{c5 c3} - c2n9{r9 r3} - r3n8{c2 .} ==> r1c4 ≠ 8 whip[6]: b1n6{r2c1 r1c3} - r1n5{c3 c1} - c1n8{r1 r2} - r2c5{n8 n2} - r4c5{n2 n6} - c8n6{r4 .} ==> r5c1 ≠ 6 whip[7]: r8n8{c4 c5} - c5n9{r8 r7} - b8n5{r7c5 r9c6} - r6c6{n5 n1} - b6n1{r6c9 r5c9} - r5n5{c9 c8} - r7n5{c8 .} ==> r5c4 ≠ 8 whip[1]: b5n8{r6c6 .} ==> r6c2 ≠ 8 whip[7]: r7c8{n5 n7} - r8c9{n7 n1} - c7n1{r9 r6} - b6n7{r6c7 r6c9} - r6c2{n7 n6} - r5n6{c2 c8} - c8n5{r5 .} ==> r9c9 ≠ 5 whip[7]: r8n8{c4 c5} - c5n9{r8 r7} - c5n5{r7 r6} - r6c6{n5 n1} - b6n1{r6c9 r5c9} - c9n5{r5 r8} - r7n5{c8 .} ==> r6c4 ≠ 8 singles ==> r6c4 = 4, r8c4 = 8 z-chain[3]: r4n1{c6 c1} - r8n1{c1 c9} - b6n1{r5c9 .} ==> r6c6 ≠ 1 z-chain[5]: c2n9{r9 r3} - r3n8{c2 c6} - r6c6{n8 n5} - r9n5{c6 c1} - r9n4{c1 .} ==> r9c3 ≠ 9 z-chain[5]: c5n8{r6 r2} - c9n8{r2 r1} - c9n4{r1 r5} - c9n5{r5 r8} - r7n5{c8 .} ==> r6c5 ≠ 5 whip[1]: c5n5{r8 .} ==> r9c6 ≠ 5 whip[1]: r9n5{c3 .} ==> r8c1 ≠ 5, r8c3 ≠ 5 naked-pairs-in-a-column: c3{r3 r8}{n7 n9} ==> r9c3 ≠ 7, r4c3 ≠ 7, r1c3 ≠ 9, r1c3 ≠ 7 whip[1]: r1n9{c6 .} ==> r3c6 ≠ 9 hidden-pairs-in-a-block: b7{r9c1 r9c3}{n4 n5} ==> r9c3 ≠ 6, r9c1 ≠ 7, r9c1 ≠ 6, r9c1 ≠ 1 singles ==> r9c2 = 6, r9c7 = 9 hidden-pairs-in-a-block: b8{r7c5 r8c5}{n5 n9} ==> r7c5 ≠ 2 finned-x-wing-in-rows: n7{r4 r2}{c1 c8} ==> r1c8 ≠ 7 biv-chain[2]: c8n7{r7 r4} - b4n7{r4c1 r6c2} ==> r7c2 ≠ 7 whip[1]: b7n7{r8c3 .} ==> r8c9 ≠ 7 biv-chain[3]: r5n6{c8 c3} - c3n2{r5 r4} - r4c5{n2 n6} ==> r4c8 ≠ 6 biv-chain[3]: b6n6{r6c7 r5c8} - r1c8{n6 n4} - r4c8{n4 n7} ==> r6c7 ≠ 7 biv-chain[3]: b6n7{r6c9 r4c8} - r7c8{n7 n5} - r8c9{n5 n1} ==> r6c9 ≠ 1 biv-chain[3]: r6c9{n5 n7} - c8n7{r4 r7} - b9n5{r7c8 r8c9} ==> r5c9 ≠ 5 naked-triplets-in-a-row: r5{c1 c2 c9}{n4 n8 n1} ==> r5c8 ≠ 4, r5c6 ≠ 1, r5c4 ≠ 1, r5c3 ≠ 4 hidden-single-in-a-block ==> r4c6 = 1 biv-chain-rc[3]: r9c6{n2 n7} - r3c6{n7 n8} - r2c5{n8 n2} ==> r1c6 ≠ 2 finned-x-wing-in-rows: n2{r7 r1}{c4 c7} ==> r2c7 ≠ 2 biv-chain[3]: c5n8{r2 r6} - r6n6{c5 c7} - r2n6{c7 c1} ==> r2c1 ≠ 8 naked-pairs-in-a-row: r2{c1 c7}{n6 n7} ==> r2c9 ≠ 7 biv-chain-rc[4]: r5c9{n1 n4} - r4c8{n4 n7} - r6c9{n7 n5} - r8c9{n5 n1} ==> r9c9 ≠ 1 hidden-single-in-a-row ==> r9c4 = 1 x-wing-in-rows: n1{r6 r7}{c2 c7} ==> r5c2 ≠ 1 stte

2 BACKDOORS: (589 451)
7 W1-BACKDOORS: (589 778 575 558 451 741 732)
7 S-BACKDOORS: (589 778 575 558 451 741 732)

by **Cenoman** » Tue Nov 03, 2020 9:59 pm

Two steps:

Code: Select all: +-------------------------+------------------------+----------------------+ | 5678 3 5679 | 2789 1 2789 | 267 467 2478 | | 678 4 1 | 5 28 3 | 267 9 278 | | 2 789 79 | 6 4 789 | 5 1 3 | +-------------------------+------------------------+----------------------+ | 1467 5 2467 | 3 26 12 | 8 467 9 | | 1468 168 246 | 12489 7 12589 | 3 456 145 | | 9 1678 3 | 148 568 158 | 167 2 1457 | +-------------------------+------------------------+----------------------+ | 3 179 8 | 127 259 4 | 1279 57 6 | | 157 2 579 | 178 589 6 | 4 3 157 | | 14567 1679 45679 | 127 3 1257 | 1279 8 1257 | +-------------------------+------------------------+----------------------+

1. Kraken cell (259)r7c5
(2)r7c5-(2=8)r2c5-r2c9=(8-4)r1c9=(4)r1c8
(5)r7c5 - (5=7)r7c8
(9)r7c5 - r8c5 = r8c3 - (9=7)r3c3 - r3c6 = (7)r1c46
----------
=>-7r1c8

2. Multi Krakens row (2,7)r7c24578, row (6)r6c257, cell (259)r7c5
As a net:

Code: Select all: (6 - 7)r6c2 = (7)r6c79 * || || - - - - - - - - - - - - - - - - - - - - - - - - - - - (2)r7c5 || / || (6 - 2)r6c5 = (2)r4c5 - (2=8)r2c5 - r3c6 = (8-9)r3c2 = r79c2 - r8c3 = r8c5 - (9)r7c5 || || || (5)r7c5 - (5=7)r7c8 * || (6=278)b3p146 - - - - - - (8=2)r2c5 - - - - - - (2)r7c5 || / || (6)r6c7 - (6=27)r12c7 - - - - - - - - - - - - - - - - - (27)r7c47 \ || (6)r12c7 = (6-7)r1c8 = [r7c8=r4c8-r6c79=r6c2] - (7)r7c2 || (7)r7c8 * ------------------------- => -7 r4c8; lclste

Matrix 13x13 BTM

Hidden Text: Show

A one-step solution is even available, with a similar, but more complex net than the above:

Hidden Text: Show

Code: Select all: - - - (7=268)b3p146 - - - (8=2)r2c5 - - - - (2)r7c5 / || (7)r1c8 - (7)r1c46 = r3c6 - (7=9)r3c3 - r8c3 = r8c5 - (9)r7c5 || || (6 - 7)r6c2 = (7)r6c79 - (7)r4c8 (5)r7c5 * || || || (7)r7c8 * || || - - - - - - - - - - - - - - - - - - - - - - - - - - - (2)r7c5 || / || (6 - 2)r6c5 = (2)r4c5 - (2=8)r2c5 - r3c6 = (8-9)r3c2 = r79c2 - r8c3 = r8c5 - (9)r7c5 || || || (5)r7c5 * || - (6=278)b3p146 - - - - - - (8=2)r2c5 - - - - - - (2)r7c5 || / || (6)r6c7 - -(6=27)r12c7 - - - - - - - - - - - - - - - - - - (27)r7c47 \ || - (6)r12c7 = (6-7)r1c8 = [r7c8=r4c8-r6c79=r6c2] - (7)r7c2 || (7)r7c8 * ------------------------- => -5 r7c8; lclste

Matrix 17x17 Embedded double BTM

Code: Select all: Kept in a condensed form: derived chain 2r2c5 == 9r8c5 {(2=8)r2c5 - r3c6 = (8-9)r3c2 = r79c2 - r8c3 = r8c5 } and chain 7r1c46 == 9r8c5 {(7)r1c46 = r3c6 - (7=9)r3c3 - r8c3 = r8c5 } 7r7c8 7r4c8 . . . . . . . . . . . . . . . . . . . . . . . . . . | 7r1c8 . . 7r6c79 7r6c2 | | . . . . 6r6c2 6r6c5 . . . . . |6r6c7 | . . . . . . 2r6c5 2r4c5 | | . . . . . . . . 2r2c5 == 9r8c5| | 5r7c5 . . . . . . 2r7c5 . 9r7c5| | -------------------------------------------------------------------------------------------| . . . . . . . . . . . . . |6r12c7 278b3p146 | . . . . . . . . . . . . . | . . 8r2c5 . 2r2c5 | . . . . . . . . . . . . . |6r12c7 . . . . . 27r12c7 | 7r7c8 . . . . . . . . . . . | . . . . . 2r7c5 27r7c47 7r7c2 | . . . . . . . . . . . . . |6r12c7 . . . . . . . . . . 6r1c8 | . . . . . . . . . . . . . | . . . . . . . . . . 7r7c8 7r1c8 7r4c8 | . . . . . . . . . . . . . | . . . . . . . . . . 7r6c2 . . 7r6c79| -------------------------------------------------------------------------------------------------------------------------- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | 7r1c46 . == 9r8c5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |726b3p146 . . . 8r2c9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | . . . . . . 8r2c5 2r2c5 5r7c5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . | . . . . 9r7c5 . . 2r7c5 ------- -5r7c8; lclste

Horizontal and vertical lines show the sub-TMs of this double BTM

The New Sudoku Players' Forum

More Pi 5 (SER 9.0)

More Pi 5 (SER 9.0)

Re: More Pi 5 (SER 9.0)

Re: More Pi 5 (SER 9.0)