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Website · by **denis_berthier** » Fri Mar 17, 2023 6:44 am

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Slightly harder than previously proposed #14987, but the idea is the same: use the most frequent impossible patterns close to tridagon.

Code: Select all: +-------+-------+-------+ ! 1 2 . ! . 5 6 ! 7 . 9 ! ! . . . ! 7 . 9 ! 1 . 2 ! ! . . . ! 2 1 . ! . . . ! +-------+-------+-------+ ! . 6 . ! . . . ! . . . ! ! . . . ! . 9 . ! . 5 . ! ! . . . ! . 2 . ! 8 . 4 ! +-------+-------+-------+ ! . 9 1 ! . . 5 ! . 2 . ! ! 5 . 2 ! 1 . . ! . . . ! ! 6 7 . ! 9 . 2 ! . 1 . ! +-------+-------+-------+ 12..567.9...7.91.2...21.....6...........9..5.....2.8.4.91..5.2.5.21.....67.9.2.1.;4149;62311 SER = 11.1

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 1 2 348 ! 348 5 6 ! 7 348 9 ! ! 348 3458 34568 ! 7 348 9 ! 1 3468 2 ! ! 34789 348 346789 ! 2 1 348 ! 3456 3468 3568 ! +----------------------+----------------------+----------------------+ ! 234789 6 345789 ! 3458 3478 13478 ! 239 379 137 ! ! 23478 1348 3478 ! 3468 9 13478 ! 236 5 1367 ! ! 379 135 3579 ! 356 2 137 ! 8 3679 4 ! +----------------------+----------------------+----------------------+ ! 348 9 1 ! 348 34678 5 ! 346 2 3678 ! ! 5 348 2 ! 1 34678 3478 ! 3469 346789 3678 ! ! 6 7 348 ! 9 348 2 ! 345 1 358 ! +----------------------+----------------------+----------------------+ 196 candidates.

by **Cenoman** » Fri Mar 17, 2023 1:07 pm

Solved with TH + RT:

Code: Select all: +---------------------------+-------------------------+-------------------------+ | 1 2 348* | 348* 5 6 | 7 348 9 | | 348* 5 6 | 7 348* 9 | 1 348 2 | | 79 348* 79 | 2 1 348* | 3456 3468 3568 | +---------------------------+-------------------------+-------------------------+ | 234789 6 345789 | 3458 3478 13478 | 239 379 137 | | 23478 1348 3478 | 3468 9 13478 | 236 5 1367 | | 379 13 3579 | 356 2 137 | 8 3679 4 | +---------------------------+-------------------------+-------------------------+ | 348* 9 1 | 348* 34678 5 | 346 2 3678 | | 5 348* 2 | 1 34678 348+7* | 3469 346789 3678 | | 6 7 348* | 9 348* 2 | 345 1 358 | +---------------------------+-------------------------+-------------------------+

1. TH(348)b1278 having a single guardian => +7 r8c6; 11 placements

Code: Select all: +----------------------+----------------------+------------------------+ | 1 2 348 | 348 5 6 | 7 D348 9 | | 348 5 6 | 7 348 9 | 1 D348 2 | | 7 Ab348# 9 | 2 1 Aa348#^ | 356-4 D3468 356-8 | +----------------------+----------------------+------------------------+ | 2348 6 348 | 5 7 148-3 | 239 39 13 | | 2348 1-348 7 | 348^ 9 148-3 | 236 5 136 | | 9 c13 5 | 6 2 d13 | 8 7 4 | +----------------------+----------------------+------------------------+ | 348 9 1 | 348 3468 5 | 346 2 7 | | 5 Bb348# 2 | 1 3468 7 | 3469 C34689 368 | | 6 7 348 | 9 348 2 | 345 1 358 | +----------------------+----------------------+------------------------+

TH(348)b1278 => RT(348)r3c2, r3c6, r8c2 (#):
2. (3)r3c6 == r38c2 - r6c2 = (3)r6c6 => -3 r45c6
3. (4,8): r3c26 == r8c2 - r8c8 = r123c8 => -4 r3c7, -8 r3c9
4. ER(3,4,8)b5 => same digit at r3c6 and r5c4 (^) => RT(348)r5c4, r38c2 => -348 r5c2; ste

by **yzfwsf** » Fri Mar 17, 2023 1:39 pm

Code: Select all: Locked Candidates 2 (Claiming): 5 in r2 => r3c2<>5,r3c3<>5 Locked Candidates 1 (Pointing): 6 in b5 => r7c4<>6 Naked Triple: in r1c3,r2c1,r3c2 => r2c2<>348,r2c3<>348,r3c1<>348,r3c3<>348, Naked Single: r2c2=5 Naked Single: r2c3=6 Triplet Oddagon Type 1: 348r38c26,r1c34,r2c15,r7c14,r9c35 => r8c6<>348 Naked Single: r8c6=7 Hidden Single: 7 in r7 => r7c9=7 Hidden Single: 7 in c5 => r4c5=7 Hidden Single: 7 in c8 => r6c8=7 Hidden Single: 6 in r6 => r6c4=6 Hidden Single: 5 in r6 => r6c3=5 Hidden Single: 5 in r4 => r4c4=5 Hidden Single: 9 in r6 => r6c1=9 Hidden Single: 9 in r3 => r3c3=9 Hidden Single: 7 in r3 => r3c1=7 Hidden Single: 7 in r5 => r5c3=7 Grouped X-Cycle with Triplet Oddagon: 3r3c6 = r38c2 - r6c2 = 3r6c6 => r5c26,r4c6<>3 Grouped X-Cycle with Triplet Oddagon: 4r5c4 = r45c6 - r3c6 = 4r38c2 => r5c2<>4 Grouped X-Cycle with Triplet Oddagon: 8r5c4 = r45c6 - r3c6 = 8r38c2 => r5c2<>8 Naked Single: r5c2=1 Hidden Single: 1 in r6 => r6c6=1 Full House: r6c2=3 Hidden Single: 1 in r4 => r4c9=1 Hidden Single: 3 in c6 => r3c6=3 Hidden Single: 3 in b5 => r5c4=3 Naked Single: r5c9=6 Naked Single: r5c7=2 Hidden Single: 2 in r4 => r4c1=2 Locked Candidates 1 (Pointing): 3 in b3 => r4c8<>3,r8c8<>3 Hidden Single: 3 in r4 => r4c7=3 Full House: r4c8=9 Hidden Single: 9 in r8 => r8c7=9 Dual Firework S-Wing: 48r3c8b3 is firework +48r8c2 => r3c8<>6 stte

by **Leren** » Fri Mar 17, 2023 8:29 pm

1. Same as Cenoman.

2.

Code: Select all: *------------------------------------------------------* | 1 2 348 | 348 5 6 | 7 b348 9 | | 348 5 6 | 7 348 9 | 1 b348 2 | | 7 A348 9 | 2 1 B348 |b3456 b3468 b3568 | |-----------------+----------------+-------------------| | 2348 6 348 | 5 7 b1348 | 239 39 13 | | 2348 a1-348 7 |b348 9 b1348 | 236 5 136 | | 9 13 5 | 6 2 13 | 8 7 4 | |-----------------+----------------+-------------------| | 348 9 1 | 348 3468 5 | 346 a2-348 7 | | 5 C348 2 | 1 3468 7 | 3469 69 368 | | 6 7 348 | 9 348 2 | 345 1 358 | *------------------------------------------------------*

RT r2c26, r8c2. RT contradiction chains via Box 3 => - 348 r7c8, RT contradiction chains via Box 5 => - 348 r5c2. Some basics.

3.

Code: Select all: *-------------------------------------------------* | 1 2 A348 |B48-3b 5 6 | 7 348 9 | | 348 5 6 | 7 348 9 | 1 348 2 | | 7 x48A 9 | 2 1 y3-48C | 356 3468 356 | |--------------+------------------+---------------| | 248 6 48a | 5 7 348 | 239 39 1 | | 248 1 7 | 348 9 348 | 236 5 36 | | 9 3 5 | 6 2 1 | 8 7 4 | |--------------+------------------+---------------| | 348 9 1 | 348 3468 5 | 346 2 7 | | 5 x48B 2 | 1 3468 7 | 3469 69 368 | | 6 7 C348 | 9 348 2 | 345 1 358 | *-------------------------------------------------*

RT r1c23, r9c3. Cell r4c3 can see 2 RT cells r19c3 and does not contain 3 => - 3 r1c4.
RT r3c26, r8c2. RT Naked Pair (48) r38c2. Remove NP digits from 3rd RT Cell r3c6 => - 48 r3c6; stte

Leren

Website · by **denis_berthier** » Sat Mar 18, 2023 5:38 am

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A solution that avoids RT but uses instead self-contained impossible patterns, indeed two of the most frequent ones:
EL13c290 (2 different such relations) and EL14c1

Code: Select all: hidden-pairs-in-a-row: r3{n7 n9}{c1 c3} ==> r3c3≠8, r3c3≠6, r3c3≠4, r3c3≠3, r3c1≠8, r3c1≠4, r3c1≠3 singles ==> r2c3=6, r2c2=5 +----------------------+----------------------+----------------------+ ! 1 2 348# ! 348# 5 6 ! 7 348 9 ! ! 348# 5 6 ! 7 348# 9 ! 1 348 2 ! ! 79 348# 79 ! 2 1 348# ! 3456 3468 3568 ! +----------------------+----------------------+----------------------+ ! 234789 6 345789 ! 3458 3478 13478 ! 239 379 137 ! ! 23478 1348 3478 ! 3468 9 13478 ! 236 5 1367 ! ! 379 13 3579 ! 356 2 137 ! 8 3679 4 ! +----------------------+----------------------+----------------------+ ! 348# 9 1 ! 348# 34678 5 ! 346 2 3678 ! ! 5 348# 2 ! 1 34678 3478#@ ! 3469 346789 3678 ! ! 6 7 348# ! 9 348# 2 ! 345 1 358 ! +----------------------+----------------------+----------------------+ tridagon for digits 3, 4 and 8 in blocks: b8, with cells (marked #): r8c6 (target cell, marked @), r9c5, r7c4 b7, with cells (marked #): r8c2, r9c3, r7c1 b2, with cells (marked #): r3c6, r2c5, r1c4 b1, with cells (marked #): r3c2, r2c1, r1c3 ==> r8c6≠3,4,8

singles ==> r8c6=7, r4c5=7, r6c8=7, r7c9=7, r6c4=6, r4c4=5, r6c3=5, r6c1=9, r3c1=7, r3c3=9, r5c3=7

Code: Select all: EL13c290s-OR2-relation for digits: 3, 4 and 8 in cells (marked #): (r4c3 r4c1 r4c6 r7c1 r7c4 r9c3 r9c5 r2c1 r2c5 r1c3 r1c4 r3c2 r3c6) with 2 guardians (in cells marked @) : n2r4c1 n1r4c6 +----------------------+----------------------+----------------------+ ! 1 2 348# ! 348# 5 6 ! 7 348 9 ! ! 348# 5 6 ! 7 348# 9 ! 1 348 2 ! ! 7 348# 9 ! 2 1 348# ! 3456 3468 3568 ! +----------------------+----------------------+----------------------+ ! 2348#@ 6 348# ! 5 7 1348#@ ! 239 39 13 ! ! 2348 1348 7 ! 348 9 1348 ! 236 5 136 ! ! 9 13 5 ! 6 2 13 ! 8 7 4 ! +----------------------+----------------------+----------------------+ ! 348# 9 1 ! 348# 3468 5 ! 346 2 7 ! ! 5 348 2 ! 1 3468 7 ! 3469 34689 368 ! ! 6 7 348# ! 9 348# 2 ! 345 1 358 ! +----------------------+----------------------+----------------------+

EL13c290s-OR2-whip[2]: OR2{{n2r4c1 | n1r4c6}} - r4c9{n1 .} ==> r4c1≠3

Code: Select all: EL13c290-OR2-relation for digits: 3, 4 and 8 in cells (marked #): (r3c2 r2c8 r2c5 r2c1 r1c8 r1c4 r1c3 r9c5 r9c3 r7c4 r7c1 r8c8 r8c2) with 2 guardians (in cells marked @) : n6r8c8 n9r8c8 +-------------------------+-------------------------+-------------------------+ ! 1 2 348# ! 348# 5 6 ! 7 348# 9 ! ! 348# 5 6 ! 7 348# 9 ! 1 348# 2 ! ! 7 348# 9 ! 2 1 348 ! 3456 3468 3568 ! +-------------------------+-------------------------+-------------------------+ ! 248 6 348 ! 5 7 1348 ! 239 39 13 ! ! 2348 1348 7 ! 348 9 1348 ! 236 5 136 ! ! 9 13 5 ! 6 2 13 ! 8 7 4 ! +-------------------------+-------------------------+-------------------------+ ! 348# 9 1 ! 348# 3468 5 ! 346 2 7 ! ! 5 348# 2 ! 1 3468 7 ! 3469 34689#@ 368 ! ! 6 7 348# ! 9 348# 2 ! 345 1 358 ! +-------------------------+-------------------------+-------------------------+

EL13c290-OR2-whip[1]: OR2{{n9r8c8 n6r8c8 | .}} ==> r8c8≠8
whip[1]: b9n8{r9c9 .} ==> r3c9≠8
EL13c290-OR2-whip[1]: OR2{{n9r8c8 n6r8c8 | .}} ==> r8c8≠4
whip[1]: b9n4{r9c7 .} ==> r3c7≠4
EL13c290-OR2-whip[1]: OR2{{n9r8c8 n6r8c8 | .}} ==> r8c8≠3

Code: Select all: EL14c1s-OR2-relation for digits: 3, 4 and 8 in cells (marked #): (r5c4 r5c1 r5c2 r8c2 r7c4 r7c1 r9c5 r9c3 r1c4 r1c3 r2c5 r2c1 r3c6 r3c2) with 2 guardians (in cells marked @) : n2r5c1 n1r5c2 +----------------------+----------------------+----------------------+ ! 1 2 348# ! 348# 5 6 ! 7 348 9 ! ! 348# 5 6 ! 7 348# 9 ! 1 348 2 ! ! 7 348# 9 ! 2 1 348# ! 356 3468 356 ! +----------------------+----------------------+----------------------+ ! 248 6 348 ! 5 7 1348 ! 239 39 13 ! ! 2348#@ 1348#@ 7 ! 348# 9 1348 ! 236 5 136 ! ! 9 13 5 ! 6 2 13 ! 8 7 4 ! +----------------------+----------------------+----------------------+ ! 348# 9 1 ! 348# 3468 5 ! 346 2 7 ! ! 5 348# 2 ! 1 3468 7 ! 3469 69 368 ! ! 6 7 348# ! 9 348# 2 ! 345 1 358 ! +----------------------+----------------------+----------------------+

EL14c1s-OR2-whip[2]: OR2{{n2r5c1 | n1r5c2}} - r6c2{n1 .} ==> r5c1≠3
finned-x-wing-in-columns: n3{c1 c5}{r2 r7} ==> r7c4≠3
whip[1]: b8n3{r9c5 .} ==> r2c5≠3
EL13c290s-OR2-whip[3]: OR2{{n1r4c6 | n2r4c1}} - r4n4{c1 c3} - r4n8{c3 .} ==> r4c6≠3
EL13c290s-OR2-whip[3]: r4c9{n3 n1} - OR2{{n1r4c6 | n2r4c1}} - c7n2{r4 .} ==> r5c7≠3
biv-chain[4]: b6n6{r5c9 r5c7} - b6n2{r5c7 r4c7} - b6n9{r4c7 r4c8} - r8c8{n9 n6} ==> r8c9≠6
whip[4]: c5n6{r8 r7} - r7n8{c5 c1} - r7n3{c1 c7} - r8c9{n3 .} ==> r8c5≠8
EL13c290s-OR2-whip[4]: r4c9{n3 n1} - OR2{{n1r4c6 | n2r4c1}} - r4n4{c1 c6} - r4n8{c6 .} ==> r4c3≠3
whip[1]: r4n3{c9 .} ==> r5c9≠3
whip[1]: b4n3{r6c2 .} ==> r3c2≠3, r8c2≠3
naked-pairs-in-a-column: c2{r3 r8}{n4 n8} ==> r5c2≠8, r5c2≠4
EL14c1s-OR2-whip[3]: OR2{{n1r5c2 | n2r5c1}} - r5c7{n2 n6} - r5c9{n6 .} ==> r5c6≠1

The end is easy:

Code: Select all: t-whip[5]: r7n6{c5 c7} - r8c8{n6 n9} - r4c8{n9 n3} - r2n3{c8 c1} - r7n3{c1 .} ==> r7c5≠8, r7c5≠4 biv-chain[2]: r7n8{c1 c4} - c5n8{r9 r2} ==> r2c1≠8 finned-swordfish-in-columns: n8{c9 c2 c5}{r9 r8 r3} ==> r3c6≠8 whip[1]: c6n8{r5 .} ==> r5c4≠8 biv-chain[3]: c3n3{r9 r1} - r2c1{n3 n4} - c2n4{r3 r8} ==> r9c3≠4 biv-chain[4]: r9n4{c5 c7} - b9n5{r9c7 r9c9} - c9n8{r9 r8} - r8c2{n8 n4} ==> r8c5≠4 naked-pairs-in-a-block: b8{r7c5 r8c5}{n3 n6} ==> r9c5≠3 biv-chain[4]: c2n8{r3 r8} - r8c9{n8 n3} - r8c5{n3 n6} - c8n6{r8 r3} ==> r3c8≠8 singles ==> r3c2=8, r8c2=4, r8c9=8 finned-swordfish-in-rows: n3{r7 r8 r2}{c1 c5 c7} ==> r3c7≠3 biv-chain[3]: c3n3{r1 r9} - r9n8{c3 c5} - b2n8{r2c5 r1c4} ==> r1c4≠3 stte

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Re: #17508 in 158,276 mith's T&E(3) min-expands

Re: #17508 in 158,276 mith's T&E(3) min-expands

Re: #17508 in 158,276 mith's T&E(3) min-expands