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by **jovi_al01** » Fri Dec 03, 2021 10:59 pm

Code: Select all: +-----------------------------------+ | . . . 5 . 6 . . 7 | | | | . . 2 . . . . 6 . | | | | . 1 . . 9 . . . . | | | | 7 . 3 . . 4 . . 8 | | | | . . . . . . . . . | | | | 8 . . 3 . . 7 . 9 | | | | . . . . 7 . . 2 . | | | | . 4 . . . . 1 . . | | | | 9 . . 6 . 5 . . . | +-----------------------------------+ ...5.6..7..2....6..1..9....7.3..4..8.........8..3..7.9....7..2..4....1..9..6.5...

by **Cenoman** » Sat Dec 04, 2021 12:05 am

Code: Select all: +--------------------------+--------------------------+----------------------------+ | 34 389 489 | 5 ^*12348 6 | ^23489 *13489 7 | | 345 35789 2 | 1478 348-1 1378 | 34589 6 *1345 | | 3456 1 45678 | 2478 9 2378 | 3458-2 3458 ^2345 | +--------------------------+--------------------------+----------------------------+ | 7 2569 3 | 129 56-12 4 | 256 15 8 | |^*12456 569-2 4569-1 | 789-12 568-12 789-12 | 3456-2 345-1 ^*123456 | | 8 256 1456 | 3 56-12 12 | 7 145 9 | +--------------------------+--------------------------+----------------------------+ | *1356 3568 568-1 | 1489 7 1389 | 345689 2 3456 | | ^2356 4 5678 | 289 38-2 2389 | 1 35789 356 | | 9 ^2378 *178 | 6 ^*12348 5 | 348 3478 34 | +--------------------------+--------------------------+----------------------------+

The 1s and the 2s at r19c5, r5c19, b37 form two loops:
(1)r1c5 = r1c8 - r2c9 = r5c9 - r5c1 = r7c1 - r9c3 = r9c5 loop (*)
(2)r1c5 = r1c7 - r3c9 = r5c9 - r5c1 = r8c1 - r9c2 = r9c5 loop (^)
eliminating 1 r5c34568, 1 r2456c5, 1 r7c3, 2 r5c24567, 2r4568c5, 2r3c7; lclste

Edit:added the following note.
Note that these two chains can be appended to each other:
(1)r1c5 = r1c8 - r2c9 = r5c9 - r5c1 = r7c1 - r9c3 = (1-2)r9c5 = r9c2 - r8c1 = r5c1 - r5c9 = r3c9 - r1c7 = (2)r1c5 loop
=> the eliminations above, and in addition 348 r19c5, 3456 r5c19 (by symmetry, writing the loop with r5c1 and r5c9 as end and mid points); lclste

by **Leren** » Sat Dec 04, 2021 12:15 am

Code: Select all: *-------------------------------------------------------------------* |*34 389 489 | 5 12348 6 | 23489 13489 7 | |*345 35789 2 |*1478 348-1 *1378 | 34589 6 *1345 | |*3456 1 45678 |*2478 9 *2378 | 3458-2 3458 *2345 | |--------------------+----------------------+-----------------------| | 7 2569 3 | 129 1256 4 | 256 15 8 | | 12-456 2569 14569 | 1279-8 12568 1279-8 | 23456 1345 12-3456 | | 8 256 1456 | 3 1256 12 | 7 145 9 | |--------------------+----------------------+-----------------------| |*1356 3568 568-1 |*1489 7 *1389 | 345689 2 *3456 | |*2356 4 5678 |*289 38-2 *2389 | 1 35789 *356 | | 9 2378 178 | 6 12348 5 | 348 3478 *34 | *-------------------------------------------------------------------*

MSLS : 18 Truths ; r278 c1469 + r1c1 r3c1 r9c9 & r3c469 : 18 Links; 1r2 1r7 2r8 & 2r3 ; 3456c1 48c4 38c6 3456c9 ; 7b2 9b8 ; 13 Eliminations as marked ; btte

Leren

by **shye** » Sat Dec 04, 2021 4:13 am

same as cenoman!

by **P.O.** » Sat Dec 04, 2021 6:54 am

Code: Select all: four chains in the first state of the grid, just a small difference from Cenoman’s eliminations: 34 389 489 5 12348 6 23489 13489 7 345 35789 2 1478 ×1348 1378 34589 6 1345 3456 1 45678 2478 9 2378 23458 3458 2345 7 2569 3 1×29 ×1×256 4 256 15 8 12456 2569 ×14569 ×1×2789 ×1×2568 ×1×2789 23456 ×1345 123456 8 ×256 1456 3 ×1×256 12 7 145 9 1356 3568 1568 1489 7 1389 345689 2 3456 2356 4 5678 289 ×238 2389 1 35789 356 9 2378 178 6 12348 5 348 3478 34 c1n1{r5 r7} - r9n1{c3 c5} - r1n1{c5 c8} - c9n1{r2 r5} => r5c3 r5c4 r5c5 r5c6 r5c8 <> 1 r9n1{c5 c3} - c1n1{r7 r5} - c9n1{r5 r2} - r1n1{c8 c5} => r2c5 r4c5 r5c5 r6c5 <> 1 r6c6{n2 n1} - r4n1{c4c5 c8} - c9n1{r5 r2} - c4n1{r2 r7} - b8n4{r7c4 r9c5} - r9n2{c5 c2} - r6n2{c2 c5} => r4c4 r4c5 r5c4 r5c5 r5c6 r6c2 <> 2 r1n2{c5 c7} - c9n2{r3 r5} - c1n2{r5 r8} - r9n2{c2 c5} => r4c5 r5c5 r6c5 r8c5 <> 2 ste.

Website · by **denis_berthier** » Sat Dec 04, 2021 7:12 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 34 389 489 ! 5 12348 6 ! 23489 13489 7 ! ! 345 35789 2 ! 1478 1348 1378 ! 34589 6 1345 ! ! 3456 1 45678 ! 2478 9 2378 ! 23458 3458 2345 ! +----------------------+----------------------+----------------------+ ! 7 2569 3 ! 129 1256 4 ! 256 15 8 ! ! 12456 2569 14569 ! 12789 12568 12789 ! 23456 1345 123456 ! ! 8 256 1456 ! 3 1256 12 ! 7 145 9 ! +----------------------+----------------------+----------------------+ ! 1356 3568 1568 ! 1489 7 1389 ! 345689 2 3456 ! ! 2356 4 5678 ! 289 238 2389 ! 1 35789 356 ! ! 9 2378 178 ! 6 12348 5 ! 348 3478 34 ! +----------------------+----------------------+----------------------+

Normal solution is in Z3.

whip[8]: b8n4{r9c5 r7c4} - b8n1{r7c4 r7c6} - c1n1{r7 r5} - c9n1{r5 r2} - c4n1{r2 r4} - r4n9{c4 c2} - r2n9{c2 c7} - r7n9{c7 .} ==> r9c5≠2
stte

by **DEFISE** » Sat Dec 04, 2021 2:32 pm

No initial basics.
whip[4]: r9n2{c2 c5}- b8n4{r9c5 r7c4}- b8n1{r7c4 r7c6}- r6c6{n1 .} => -2r6c2
Box/Line: 2r6b5 => -2r4c4 -2r4c5 -2r5c4 -2r5c5 -2r5c6
Swordfish in rows: 2r149c257 => -2r3c7 -2r5c2 -2r5c7 -2r6c5 -2r8c5
Single: 2r6c6
Swordfish in rows: 1r169c358 => -1r2c5 -1r4c5 -1r4c8 -1r5c3 -1r5c5 -1r5c8 -1r7c3
STTE

by **jovi_al01** » Sun Dec 05, 2021 2:15 am

Cenoman found my solution! Thank you all for solving

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