The New Sudoku Players' Forum

Website · by **denis_berthier** » Mon Aug 01, 2022 6:39 am

.
After adding:
- to the generic part of CSP-Rules: OR3-Forcing-Whips
- to SudoRules, the detection of anti-tridagons with more than 2 guardians,
here is my new solution to this puzzle:

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 34789 2379 2479 ! 56789 479 5789 ! 59 5689 1 ! ! 1789 179 179 ! 156789 2 3 ! 59 4 689 ! ! 1489 5 6 ! 189 149 189 ! 2 3 7 ! +----------------------+----------------------+----------------------+ ! 134679 1379 1479 ! 179 8 2 ! 134579 15679 3469 ! ! 1479 1279 5 ! 3 179 6 ! 1479 12789 489 ! ! 13679 8 1279 ! 4 5 179 ! 1379 12679 369 ! +----------------------+----------------------+----------------------+ ! 179 4 3 ! 15789 179 15789 ! 6 179 2 ! ! 2 6 179 ! 179 3 4 ! 8 179 5 ! ! 5 179 8 ! 2 6 179 ! 13479 179 349 ! +----------------------+----------------------+----------------------+ 189 candidates

Code: Select all: naked-pairs-in-a-column: c7{r1 r2}{n5 n9} ==> r9c7≠9, r6c7≠9, r5c7≠9, r4c7≠9, r4c7≠5 hidden-single-in-a-block ==> r4c8=5 whip[1]: c7n9{r2 .} ==> r1c8≠9, r2c9≠9 hidden-pairs-in-a-row: r9{n3 n4}{c7 c9} ==> r9c9≠9, r9c7≠7, r9c7≠1 whip[1]: b9n1{r9c8 .} ==> r5c8≠1, r6c8≠1 whip[1]: b9n7{r9c8 .} ==> r5c8≠7, r6c8≠7 whip[1]: c9n9{r6 .} ==> r5c8≠9, r6c8≠9 hidden-pairs-in-a-row: r7{n5 n8}{c4 c6} ==> r7c6≠9, r7c6≠7, r7c6≠1, r7c4≠9, r7c4≠7, r7c4≠1 biv-chain[3]: r1c7{n9 n5} - r2n5{c7 c4} - b2n6{r2c4 r1c4} ==> r1c4≠9 biv-chain[4]: c3n4{r4 r1} - c3n2{r1 r6} - r6c8{n2 n6} - b4n6{r6c1 r4c1} ==> r4c1≠4 z-chain[5]: c2n2{r1 r5} - r5c8{n2 n8} - r1c8{n8 n6} - r2n6{c9 c4} - r2n7{c4 .} ==> r1c2≠7 biv-chain[6]: r1c7{n9 n5} - r2n5{c7 c4} - b2n6{r2c4 r1c4} - c8n6{r1 r6} - b6n2{r6c8 r5c8} - c2n2{r5 r1} ==> r1c2≠9 t-whip[5]: c1n6{r4 r6} - r6c8{n6 n2} - r5n2{c8 c2} - r1c2{n2 n3} - b4n3{r4c2 .} ==> r4c1≠1, r4c1≠7, r4c1≠9 z-chain[6]: r1n3{c1 c2} - c2n2{r1 r5} - r5c8{n2 n8} - r1c8{n8 n6} - r2n6{c9 c4} - r2n7{c4 .} ==> r1c1≠7 biv-chain[7]: r1c7{n9 n5} - r2n5{c7 c4} - b2n6{r2c4 r1c4} - c8n6{r1 r6} - b6n2{r6c8 r5c8} - c2n2{r5 r1} - b1n3{r1c2 r1c1} ==> r1c1≠9 +----------------------+----------------------+----------------------+ ! 348 23 2479 ! 5678 479 5789 ! 59 68 1 ! ! 1789 179 179 ! 156789 2 3 ! 59 4 68 ! ! 1489 5 6 ! 189 149 189 ! 2 3 7 ! +----------------------+----------------------+----------------------+ ! 36 1379 1479 ! 179 8 2 ! 1347 5 3469 ! ! 1479 1279 5 ! 3 179 6 ! 147 28 489 ! ! 13679 8 1279 ! 4 5 179 ! 137 26 369 ! +----------------------+----------------------+----------------------+ ! 179 4 3 ! 58 179 58 ! 6 179 2 ! ! 2 6 179 ! 179 3 4 ! 8 179 5 ! ! 5 179 8 ! 2 6 179 ! 34 179 34 ! +----------------------+----------------------+----------------------+ OR4-anti-tridagon[12] (type diag) for digits 1, 7 and 9 in blocks: b4, with cells: r4c3, r5c2, r6c1 b5, with cells: r4c4, r5c5, r6c6 b7, with cells: r8c3, r9c2, r7c1 b8, with cells: r8c4, r9c6, r7c5 with 4 guardians: n4r4c3 n2r5c2 n3r6c1 n6r6c1

Note that this OR4 relation is detected, but not used, as I don't have OR4-Forcing-Whips currently. But we can do without it:

Code: Select all: +----------------------+----------------------+----------------------+ ! 348 23 2479 ! 5678 479 5789 ! 59 68 1 ! ! 1789 179 179 ! 156789 2 3 ! 59 4 68 ! ! 1489 5 6 ! 189 149 189 ! 2 3 7 ! +----------------------+----------------------+----------------------+ ! 36 1379 1479 ! 179 8 2 ! 1347 5 3469 ! ! 1479 1279 5 ! 3 179 6 ! 147 28 489 ! ! 13679 8 1279 ! 4 5 179 ! 137 26 369 ! +----------------------+----------------------+----------------------+ ! 179 4 3 ! 58 179 58 ! 6 179 2 ! ! 2 6 179 ! 179 3 4 ! 8 179 5 ! ! 5 179 8 ! 2 6 179 ! 34 179 34 ! +----------------------+----------------------+----------------------+ OR3-anti-tridagon[12] (type antidiag) for digits 1, 7 and 9 in blocks: b4, with cells: r4c2, r5c1, r6c3 b5, with cells: r4c4, r5c5, r6c6 b7, with cells: r9c2, r7c1, r8c3 b8, with cells: r9c6, r7c5, r8c4 with 3 guardians: n3r4c2 n4r5c1 n2r6c3 OR3-forcing-whip-elim[4] based on OR3-anti-tridagon[12] for n3r4c2, n4r5c1 and n2r6c3: ....partial-whip[1]: r1c2{n3 n2} - ....partial-whip[1]: c3n4{r4 r1} - ....partial-whip[1]: c2n2{r5 r1} - ==> r1c3≠2 singles ==> r1c2=2, r1c1=3, r4c1=6, r4c2=3, r6c3=2, r6c8=6, r1c8=8, r2c9=6, r5c8=2, r1c4=6, r5c9=8

A mere tridagon will allow to easily finish the puzzle:

Code: Select all: +-------------------+-------------------+-------------------+ ! 3 2 479 ! 6 479 579 ! 59 8 1 ! ! 1789 179 179 ! 15789 2 3 ! 59 4 6 ! ! 1489 5 6 ! 189 149 189 ! 2 3 7 ! +-------------------+-------------------+-------------------+ ! 6 3 1479 ! 179 8 2 ! 147 5 49 ! ! 1479 179 5 ! 3 179 6 ! 147 2 8 ! ! 179 8 2 ! 4 5 179 ! 137 6 39 ! +-------------------+-------------------+-------------------+ ! 179 4 3 ! 58 179 58 ! 6 179 2 ! ! 2 6 179 ! 179 3 4 ! 8 179 5 ! ! 5 179 8 ! 2 6 179 ! 34 179 34 ! +-------------------+-------------------+-------------------+ tridagon type diag for digits 1, 7 and 9 in blocks: b4, with cells: r4c3 (target cell), r5c2, r6c1 b5, with cells: r4c4, r5c5, r6c6 b7, with cells: r8c3, r9c2, r7c1 b8, with cells: r8c4, r9c6, r7c5 ==> r4c3≠1,7,9 singles ==> r4c3=4, r4c9=9, r6c9=3, r9c9=4, r9c7=3, r5c7=4, r3c1=4, r2c1=8, r1c5=4 whip[1]: r3n1{c6 .} ==> r2c4≠1 whip[1]: r3n9{c6 .} ==> r1c6≠9, r2c4≠9 finned-x-wing-in-columns: n7{c5 c1}{r7 r5} ==> r5c2≠7 whip[1]: b4n7{r6c1 .} ==> r7c1≠7 biv-chain[2]: c2n7{r9 r2} - b2n7{r2c4 r1c6} ==> r9c6≠7 biv-chain[3]: b2n8{r3c6 r3c4} - c4n9{r3 r8} - r9c6{n9 n1} ==> r3c6≠1 biv-chain[3]: c6n1{r9 r6} - r4c4{n1 n7} - b8n7{r8c4 r7c5} ==> r7c5≠1 biv-chain[3]: r5n7{c1 c5} - r7c5{n7 n9} - r7c1{n9 n1} ==> r5c1≠1 finned-x-wing-in-columns: n1{c6 c1}{r6 r9} ==> r9c2≠1 t-whip[4]: r1c3{n9 n7} - r2n7{c3 c4} - r4c4{n7 n1} - r8c4{n1 .} ==> r8c3≠9 whip[1]: c3n9{r2 .} ==> r2c2≠9 biv-chain[2]: b7n9{r9c2 r7c1} - r6n9{c1 c6} ==> r9c6≠9 naked-single ==> r9c6=1 biv-chain[3]: r2c2{n7 n1} - r5n1{c2 c5} - r4c4{n1 n7} ==> r2c4≠7 singles ==> r2c4=5, r1c6=7, r1c3=9, r1c7=5, r6c6=9, r3c6=8, r7c6=5, r2c7=9, r7c4=8 biv-chain[3]: c1n9{r7 r5} - r5n7{c1 c5} - r7c5{n7 n9} ==> r7c8≠9 biv-chain[3]: b9n1{r7c8 r8c8} - c8n9{r8 r9} - b7n9{r9c2 r7c1} ==> r7c1≠1 stte

by **yzfwsf** » Mon Aug 01, 2022 10:25 am

The output of my solver：

Code: Select all: Locked Pair: in r1c7,r2c7 => r1c8<>59,r2c9<>9,r4c7<>59,r5c7<>9,r6c7<>9,r9c7<>9, Hidden Single: 5 in r4 => r4c8=5 Locked Triple: in r7c8,r8c8,r9c8 => r5c8<>179,r6c8<>179,r9c7<>17,r9c9<>9, Hidden Pair: 58 in r7c4,r7c6 => r7c4<>179,r7c6<>179 Triplet Oddagon Forcing Chain: Each true guardian of Triplet Oddagon will all lead To: r4c179,r1c2,r6c1<>3,r4c2<>7,r4c2<>9 3r4c2 4r5c1 - (4=17893)b1p14567 - 3r1c2 = 3r4c2 2r6c3 - (2=1793)r2459c2 Hidden Single: 3 in r1 => r1c1=3 Hidden Single: 3 in r4 => r4c2=3 Triplet Oddagon Forcing Chain: Each true guardian of Triplet Oddagon will all lead To: r2c4,r3c1<>1,r2c49,r3c1<>8,r23c1<>9 4r4c3 - (4=12798)b1p23456 2r5c2 - (2=1798)b1p2456 6r6c1 - (6=2)r6c8 - 2r6c3 = 2r1c3 - (2=1798)b1p2456 Hidden Single: 8 in r2 => r2c1=8 Hidden Single: 8 in c9 => r5c9=8 Hidden Single: 8 in c8 => r1c8=8 Hidden Single: 6 in r1 => r1c4=6 Hidden Single: 6 in r2 => r2c9=6 Hidden Single: 6 in r4 => r4c1=6 Hidden Single: 6 in r6 => r6c8=6 Hidden Single: 2 in r6 => r6c3=2 Hidden Single: 2 in r1 => r1c2=2 Hidden Single: 2 in r5 => r5c8=2 Naked Single: r3c1=4 Hidden Single: 4 in r1 => r1c5=4 Hidden Single: 4 in r5 => r5c7=4 Hidden Single: 4 in r4 => r4c3=4 Hidden Single: 4 in r9 => r9c9=4 Hidden Single: 3 in r9 => r9c7=3 Hidden Single: 3 in r6 => r6c9=3 Full House: r4c9=9 Locked Candidates 2 (Claiming): 9 in r3 => r1c6<>9,r2c4<>9 Finned X-Wing:7c15\r57 fr6c1 => r5c2<>7 Locked Candidates 1 (Pointing): 7 in b4 => r7c1<>7 Sashimi Swordfish:7r178\c368 fb8p24 => r9c6<>7 AIC Type 2: (9=7)r1c3 - r1c6 = (7-9)r6c6 = r6c1 - (9=1)r7c1 - r8c3 = 1r2c3 => r2c3<>9 Discontinuous Nice Loop: 9r1c3 = r1c7 - (9=5)r2c7 - r2c4 = (5-8)r7c4 = (8-9)r3c4 = r8c4 - r8c3 = 9r1c3 => r1c3=9 Hidden Single: 7 in r1 => r1c6=7 Full House: r1c7=5 Full House: r2c7=9 Hidden Single: 5 in r2 => r2c4=5 Hidden Single: 5 in r7 => r7c6=5 Hidden Single: 8 in r7 => r7c4=8 Hidden Single: 8 in r3 => r3c6=8 Sashimi X-Wing:9c26\r59 fr6c6 => r5c5<>9 Hidden Single: 9 in b5 => r6c6=9 Full House: r9c6=1 Dual Firework S-Wing: 79r5c1b4 is firework => r5c1<>1 XY-Chain: (7=1)r2c3 - (1=7)r8c3 - (7=9)r8c4 - (9=7)r7c5 - (7=1)r5c5 - (1=9)r5c2 - (9=7)r9c2 => r2c2,r8c3<>7 stte

by **P.O.** » Mon Aug 01, 2022 1:25 pm

i have checked some of the puzzles solved with the tridagon rule with the POM procedure, they all exhibit the same repartion of templates at the start: three values have a relatively higher number of templates than the six others (whose number of templates is rather low), the three values in the tridagon. That repartition make them easy to solve with POM has it lower the number of combinations.

puzzle / #templates at the start / combinations tested

Code: Select all: ..............1..2....34.56.14.78...73.94....8.91.37...98......17.......4.3.19.8. #VT: (8 64 20 14 99 79 6 13 14) (2 2 3 2 2 3 2 3 2 3 2 3 4 2 2 3) ........1.....2.3.....4.56......7.....481.2..19..248...89..1..742..78..97.1.9.... #VT: (4 6 96 13 119 99 8 8 9) (2 2 3 2 3 2 3 2 3 4 2 2 3 2 2 3 2 3 2 2 2 3 4) ........1.....2.3.....4.56....7.8.....491.2..17..249...97..1..842..89...8.1.7.... #VT: (4 6 91 13 140 96 10 8 8) (2 2 3 2 3 2 3 4) ........1.....2.3.....4.56....7.8.....491.2..18..249...98..1..742..79...7.1.8.... #VT: (4 6 91 13 140 96 6 14 8) (2 2 3 2 3 2 3 4) ..............1..2....34.56.17......34..18.9.9.8.......9314.7..47.8.3...8.1.79... #VT: (8 68 20 20 106 88 6 11 13) (2 2 3 2 2 3 2 3 2 3 2 3 2 3 4) ...........1.23.45..214.3.6......45..5...46.1.6..51.32.4.......7....2...8.9.36... #VT: (8 6 13 4 11 7 91 123 146) (2 2 3 2 2 3 2 3 2 3 4 2 2) ........1.....234..35.1.......4..65....6.12.36....5.1...7.4.....89.5....21.....3. #VT: (4 16 12 10 4 18 387 387 387) (2 2 3 2 2 3 2 2 3 2 2 3 2 3 2 2 3 2 2 3 2 3 2 3 2 3 4 2 2 3 2 2 3 2 3 2 3 2 3 4) .......12.....34.5..514.6......6.3...2.35..6..6.4.1.5..1.23....7.8......932....4. #VT: (12 2 4 10 7 12 184 197 196) (2 2 3 2 3 2 3 4 2 3 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 2 3 4 5 2 2 3 2 2 3 2 3 4 2 2 3 2 3 4 2 2 3 2 2 3 2 3 2 3 2 2 3) Tanngrisnir and Tanngnjóstr (SER 11.7, te3 ID 19252) #VT: (100 2 6 8 4 4 117 7 396) (2 2 3 2 2 3 2 3 4 2 3 2 3 4 2 3 2 2 3 2 2 3)

Hidden Text: Show

Code: Select all: Tanngrisnir and Tanngnjóstr (SER 11.7, te3 ID 19252) #VT: (100 2 6 8 4 4 117 7 396) Cells: nil nil nil nil nil nil nil nil nil Candidates:nil nil nil nil nil nil nil nil nil 2 #VT: (94 2 6 8 4 4 112 7 343) Cells: nil nil nil nil nil nil nil nil nil Candidates:nil nil nil nil nil nil nil nil nil 2 3 #VT: (39 2 6 7 3 3 43 7 67) Cells: nil nil nil nil (35) nil nil nil nil SetVC: ( n5r4c8 ) #VT: (91 2 6 8 3 3 106 7 367) Cells: nil nil nil nil nil nil nil nil nil Candidates:nil nil nil nil nil nil nil nil nil 2 #VT: (86 2 6 8 3 3 98 7 309) Cells: nil nil nil nil nil nil nil nil nil Candidates:nil nil nil nil nil nil nil nil nil 2 3 #VT: (39 2 6 7 3 3 41 7 64) Cells: nil nil nil nil nil nil nil nil nil Candidates:(44 53 58 60 79) nil nil nil nil nil (2 44 53 58 60 79) nil (4 8 18 34 43 44 52 53 58 60 79 81) 2 3 4 #VT: (33 2 6 6 3 3 32 7 19) Cells: nil nil nil nil nil nil nil nil nil Candidates:nil nil nil (28) nil nil (1) nil (2 13 28) 2 3 #VT: (27 2 6 6 3 3 31 7 19) Cells: nil nil nil nil nil nil nil nil nil Candidates:nil nil nil nil nil nil nil nil nil 2 3 4 #VT: (19 2 6 6 3 3 21 7 16) Cells: nil nil nil nil nil nil nil nil nil Candidates:(48) nil nil nil nil nil (48) nil nil 2 3 #VT: (19 2 6 6 3 3 21 7 13) Cells: nil nil nil nil nil nil nil nil nil Candidates:nil nil nil nil nil nil nil nil (1 48) EraseCC: ( n2r6c3 n6r6c8 n8r1c8 n6r2c9 n2r5c8 n2r1c2 n3r4c2 n3r1c1 n6r4c1 n6r1c4 n8r5c9 ) #VT: (40 1 2 3 2 1 30 3 46) Cells: nil nil nil nil nil nil nil nil nil Candidates:nil nil nil nil nil nil nil nil nil 2 #VT: (32 1 2 3 2 1 23 3 35) Cells: nil nil nil nil nil nil nil nil nil Candidates:nil nil nil nil nil nil nil nil nil 2 3 #VT: (5 1 2 3 2 1 9 3 6) Cells: nil nil nil nil nil nil nil nil nil Candidates:(10 13 19 43 59) nil nil nil nil nil nil nil (11 22 46 59 71) EraseCC: ( n7r7c5 ) #VT: (29 1 2 3 2 1 6 3 36) Cells: nil nil nil nil nil nil nil nil nil Candidates:nil nil nil nil nil nil (30) nil nil 2 #VT: (15 1 2 3 2 1 6 3 17) Cells: nil nil nil nil nil nil nil nil nil Candidates:nil nil nil nil nil nil nil nil (6) 2 3 #VT: (3 1 2 3 2 1 2 2 1) Cells: nil nil nil nil nil nil (37 71 74) (10) (3 16 23 36 38 51 55 67 80) SetVC: ( n9r1c3 n4r1c5 n5r1c7 n8r2c1 n9r2c7 n4r3c1 n9r3c5 n9r4c9 n7r5c1 n9r5c2 n1r5c5 n4r5c7 n1r6c1 n9r6c6 n3r6c9 n9r7c1 n1r7c8 n9r8c4 n7r8c8 n7r9c2 n1r9c6 n3r9c7 n9r9c8 n4r9c9 n7r1c6 n1r2c2 n7r2c3 n5r2c4 n8r3c6 n4r4c3 n7r4c4 n1r4c7 n7r6c7 n8r7c4 n5r7c6 n1r8c3 n1r3c4 ) 3 2 9 6 4 7 5 8 1 8 1 7 5 2 3 9 4 6 4 5 6 1 9 8 2 3 7 6 3 4 7 8 2 1 5 9 7 9 5 3 1 6 4 2 8 1 8 2 4 5 9 7 6 3 9 4 3 8 7 5 6 1 2 2 6 1 9 3 4 8 7 5 5 7 8 2 6 1 3 9 4 (2 2 3 2 2 3 2 3 4 2 3 2 3 4 2 3 2 2 3 2 2 3)

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Tanngrisnir and Tanngnjóstr (SER 11.7, te3 ID 19252)

Re: Tanngrisnir and Tanngnjóstr (SER 11.7, te3 ID 19252)

Re: Tanngrisnir and Tanngnjóstr (SER 11.7, te3 ID 19252)

Re: Tanngrisnir and Tanngnjóstr (SER 11.7, te3 ID 19252)