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by **P.O.** » Thu Feb 24, 2022 9:06 am

Code: Select all: . 7 . 1 . . . . . . . . . 3 . . . 8 5 . . . . 9 6 . . . 5 . . . . 9 . . . . 2 . 1 . . . 3 6 . . . . 7 . 5 . . . . 8 . . . 4 . . . 9 . . . . . 5 3 . . . . 6 7 . . .7.1.........3...85....96...5....9....2.1...36....7.5....8...4...9.....53....67..

by **pjb** » Thu Feb 24, 2022 9:45 pm

(6=5)r5c12678 - (5=7)r12c6, r3c45 - (7=6)r13679c9 => -6 r4c9, -6 r8c8;
(basics)
(5=7)r7c1267 - (7=5)r5c1267 - loop => -5 r12c6, -7 r4c1, -49 r5c4, -8 r5c8, -9 r6c2, -1 r7c3
(basics)
(1=4)r2c3 - (4)r4c3 = (4-2)r4c4 = (2-8)r6c5 = (8)r6c3 - (8=1)r4c1 => -1 r4c3; stte

Phil

by **DEFISE** » Fri Feb 25, 2022 10:25 am

No initial basics.

g-whip[5]: r2n7{c8 c4}- b2n6{r2c4 r1c5}- c5n5{r1 r79}- c4n5{r9 r5}- r5n6{c4 .} => -7r5c8
Single(s): 7r5c1, 7r7c3, 5r9c3
Box/Line: 9c1b1 => -9r2c2
Box/Line: 6c3b1 => -6r2c2

whip[4]: r4n7{c9 c8}- r2n7{c8 c4}- c4n5{r2 r5}- r5n6{c4 .} => -6r4c9
Singles and Box/Line =>

Code: Select all: |-----------------------------------------| | 28 7 6 | 1 5 248 | 24 3 9 | | 9 124 14 | 6 3 24 | 5 7 8 | | 5 234 348 | 7 48 9 | 6 1 24 | |-----------------------------------------| | 18 5 148 | 24 6 3 | 9 28 7 | | 7 9 2 | 5 1 48 | 48 6 3 | | 6 34 348 | 9 248 7 | 1 5 24 | |-----------------------------------------| | 12 12 7 | 8 9 5 | 3 4 6 | | 4 6 9 | 3 7 1 | 28 28 5 | | 3 8 5 | 24 24 6 | 7 9 1 | |-----------------------------------------|

whip[3]: r3c5{n8 n4}- r3c9{n4 n2}- r6n2{c9 .} => -8r6c5
STTE

by **P.O.** » Fri Feb 25, 2022 12:22 pm

Code: Select all: I found a chain that combines the two key eliminations: 2489 7 3468 1 b245+68 2458 2345 239 249 1249 12469 146 d24+567 3 245 1245 e12+79 8 5 12348 1348 247 2478 9 6 1237 f124-7 1478 5 13478 2346 b24-68 2348 9 12678 f124×6+7 4789 489 2 a45+69 1 458 48 a±6×78 3 6 13489 1348 2349 2489 7 1248 5 124 127 126 1567 8 c2*579 1235 123 4 1269 12478 12468 9 2347 247 1234 1238 12368 5 3 1248 1458 d24-59 c24*59 6 7 1289 129 r5n6{c8 c4} - c5n6{r4 r1} - c5n5{r1 r7r9} - c4n5{r9 r2} - r2n7{c4 c8} - c9n7{r3 r4} => r5c8 <> 7, r4c9 <> 6 singles: ( r3c8b3 n1 r6c7b6 n1 r9c9b9 n1 r2c1b1 n9 r1c9b3 n9 r9c8b9 n9 r9c2b7 n8 r4c9b6 n7 r2c7b3 n5 r8c1b7 n4 r1c8b3 n3 r6c4b5 n9 r5c2b4 n9 r2c8b3 n7 r3c4b2 n7 r8c5b8 n7 r1c3b1 n6 r2c4b2 n6 r5c8b6 n6 r4c5b5 n6 r5c4b5 n5 r1c5b2 n5 r4c6b5 n3 r7c7b9 n3 r8c4b8 n3 r8c6b8 n1 r9c3b7 n5 r7c6b8 n5 r7c3b7 n7 r8c2b7 n6 r7c5b8 n9 r5c1b4 n7 r7c9b9 n6 ) intersection: c6n2{r1r2} => r3c5 <> 2 r4n2{c4 c8} - b6n8{r4c8 r5c7} - r5c6{n8 n4} => r4c4 <> 4 ste.

Website · by **denis_berthier** » Fri Feb 25, 2022 12:57 pm

.

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 2489 7 3468 ! 1 24568 2458 ! 2345 239 249 ! ! 1249 12469 146 ! 24567 3 245 ! 1245 1279 8 ! ! 5 12348 1348 ! 247 2478 9 ! 6 1237 1247 ! +-------------------+-------------------+-------------------+ ! 1478 5 13478 ! 2346 2468 2348 ! 9 12678 12467 ! ! 4789 489 2 ! 4569 1 458 ! 48 678 3 ! ! 6 13489 1348 ! 2349 2489 7 ! 1248 5 124 ! +-------------------+-------------------+-------------------+ ! 127 126 1567 ! 8 2579 1235 ! 123 4 1269 ! ! 12478 12468 9 ! 2347 247 1234 ! 1238 12368 5 ! ! 3 1248 1458 ! 2459 2459 6 ! 7 1289 129 ! +-------------------+-------------------+-------------------+ 231 candidates.

The puzzle is in Z6 and in gW5.

simplest-first solution in Z6: Show

simplest-first solution in gW5: Show

There doesn't seem to be a solution in 2 or 3 steps in Z6 or even in W6. However, there's one in 3 steps in gW5 (same eliminations as François's solution, obtained after a single try of the fewer steps algorithm):
g-whip[5]: r2n7{c8 c4} - b2n6{r2c4 r1c5} - c5n5{r1 r789} - c4n5{r9 r5} - r5n6{c4 .} ==> r5c8≠7
singles ==> r5c1=7, r7c3=7, r9c3=5
whip[1]: b7n6{r8c2 .} ==> r2c2≠6
whip[1]: b4n9{r6c2 .} ==> r2c2≠9
biv-chain[4]: r4n7{c9 c8} - r2n7{c8 c4} - c4n5{r2 r5} - r5n6{c4 c8} ==> r4c9≠6
singles ==> r7c9=6, r8c2=6, r7c5=9, r7c6=5, r5c4=5, r1c5=5, r2c4=6, r1c3=6, r2c8=7, r2c1=9, r4c9=7, r4c5=6, r5c8=6, r2c7=5, r6c4=9, r5c2=9, r8c6=1, r8c4=3, r4c6=3, r8c5=7, r3c4=7, r8c1=4, r9c2=8, r7c7=3, r1c8=3, r1c9=9, r9c8=9, r9c9=1, r3c8=1, r6c7=1
whip[1]: c6n2{r2 .} ==> r3c5≠2
biv-chain[3]: r6c9{n4 n2} - b5n2{r6c5 r4c4} - r4n4{c4 c3} ==> r6c3≠4, r6c2≠4
stte

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