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by **jovi_al01** » Sun Jan 16, 2022 9:27 pm

Code: Select all: ..5.8.7.....1....43....2...2..6..8...5..7..9...6..8..3...3....21....4.....7.6.9..

looking forward to your solutions

Website · by **denis_berthier** » Mon Jan 17, 2022 7:35 am

.

Code: Select all: +-------+-------+-------+ ! . . 5 ! . 8 . ! 7 . . ! ! . . . ! 1 . . ! . . 4 ! ! 3 . . ! . . 2 ! . . . ! +-------+-------+-------+ ! 2 . . ! 6 . . ! 8 . . ! ! . 5 . ! . 7 . ! . 9 . ! ! . . 6 ! . . 8 ! . . 3 ! +-------+-------+-------+ ! . . . ! 3 . . ! . . 2 ! ! 1 . . ! . . 4 ! . . . ! ! . . 7 ! . 6 . ! 9 . . ! +-------+-------+-------+ SER = 8.3

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 469 12469 5 ! 49 8 369 ! 7 1236 169 ! ! 6789 26789 289 ! 1 359 35679 ! 2356 23568 4 ! ! 3 146789 1489 ! 4579 459 2 ! 156 1568 15689 ! +----------------------+----------------------+----------------------+ ! 2 13479 1349 ! 6 13459 1359 ! 8 1457 157 ! ! 48 5 1348 ! 24 7 13 ! 1246 9 16 ! ! 479 1479 6 ! 2459 12459 8 ! 1245 12457 3 ! +----------------------+----------------------+----------------------+ ! 45689 4689 489 ! 3 159 1579 ! 1456 145678 2 ! ! 1 23689 2389 ! 25789 259 4 ! 356 35678 5678 ! ! 458 2348 7 ! 258 6 15 ! 9 13458 158 ! +----------------------+----------------------+----------------------+ 222 candidates.

Interesting puzzle!

First thing to notice is the very high number of candidates (222) after Singles and whips[1] have been applied. This is often a sign that the resolution paths will be longer.
Jovi_al01, did you select this puzzle for this reason?

The puzzle has a solution in W5

Simplest-first solution in W5: Show

As expected, it has many non-W1 steps (53). (This number can probably be reduced, even in W5.)

For people who prefer using only reversible chains, there is also a solution in Z6 (it requires slightly longer chains than when using whips)

simplest-first solution in Z6: Show

This makes 55 non-W1 steps. (This number can probably be reduced, even in Z6.)

There are no W1-anti-backdoors and no W1-anti-backdoor-pairs. Therefore, there can't be any 1-step or 2-step solution based on whips, braids, g-whips or g-braids of any length.

Here is now a 1-step solution using the nukes:

Code: Select all: FORCING[3]-T&E(BRT) applied to trivalue candidates n4r1c1, n4r1c2 and n4r1c4 : ===> 7 values decided in the three cases: n8r5c1 n5r6c4 n7r3c4 n6r5c9 n9r4c6 n7r7c6 n6r8c2 ===> 101 candidates eliminated in the three cases: n9r1c1 n6r1c2 n9r1c2 n9r1c6 n1r1c8 n6r1c8 n6r1c9 n6r2c1 n8r2c1 n9r2c1 n6r2c2 n9r2c2 n8r2c3 n3r2c6 n7r2c6 n9r2c6 n2r2c7 n5r2c7 n3r2c8 n6r2c8 n4r3c2 n6r3c2 n7r3c2 n9r3c3 n4r3c4 n5r3c4 n9r3c4 n9r3c5 n1r3c8 n8r3c8 n1r3c9 n5r3c9 n6r3c9 n3r4c2 n7r4c2 n9r4c2 n9r4c3 n4r4c5 n5r4c5 n9r4c5 n1r4c6 n3r4c6 n5r4c6 n1r4c8 n4r4c8 n1r4c9 n4r5c1 n4r5c3 n8r5c3 n1r5c7 n6r5c7 n1r5c9 n4r6c1 n1r6c2 n4r6c2 n2r6c4 n4r6c4 n9r6c4 n1r6c5 n5r6c5 n9r6c5 n5r6c7 n2r6c8 n5r6c8 n7r6c8 n4r7c1 n6r7c1 n8r7c1 n4r7c2 n6r7c2 n9r7c5 n1r7c6 n5r7c6 n9r7c6 n5r7c7 n1r7c8 n4r7c8 n5r7c8 n7r7c8 n2r8c2 n3r8c2 n8r8c2 n9r8c2 n3r8c3 n9r8c3 n2r8c4 n5r8c4 n7r8c4 n5r8c5 n6r8c7 n6r8c8 n8r8c8 n6r8c9 n8r8c9 n8r9c1 n4r9c2 n8r9c2 n5r9c4 n5r9c8 n8r9c8 n5r9c9 stte

Remember that FORCING[3]-T&E is the lazy version of what some call skyscrapers.

by **yzfwsf** » Mon Jan 17, 2022 8:41 am

two steps

Code: Select all: Dynamic Contradiction Chain: If r9c2<>3 Then r5c7=4 And r5c7<>4 simultaneously,so r9c2=3

Hidden Text: Show

Single and Locked Candidates

Code: Select all: AIC Type 1: (1=3)r5c6 - r1c6 = (3-2)r1c8 = (2-8)r2c8 = r3c8 - (8=1)r3c3 => r5c3<>1 stte

by **DEFISE** » Mon Jan 17, 2022 11:51 am

Symmetry / central cell
with the following matches: 1-4 , 2-3 , 5-9 , 6-8 , 7-7

No initial basics.
if 1r9c6 is true, then: 3r5c6 and 3r1c8 too.
But 3r1c8 => 2r9c2 by symmetry.
So number 2 is impossible in row 1.
=> -1r9c6
Singles : 5r9c6, 5r7c1
=> by symmetry: singles: 9r1c4, 9r3c9

Box/Line: 4r1b1 => -4r3c2 -4r3c3
Box/Line: 1r9b9 => -1r7c7 -1r7c8
Box/Line: 6c1b1 => -6r1c2 -6r2c2 -6r3c2
Box/Line: 6r3b3 => -6r1c8 -6r1c9 -6r2c7 -6r2c8
STTE

by **eleven** » Mon Jan 17, 2022 2:09 pm

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 469 a12469 5 | 49 8 369 | 7 b1236 169 | | 6789 26789 289 | 1 359 35679 | 2356 23568 4 | | 3 146789 1489 | 4579 459 2 | 156 1568 15689 | +-------------------------+-------------------------+-------------------------+ | 2 13479 1349 | 6 13459 1359 | 8 1457 157 | | 48 5 1348 | 24 7 13 | 1246 9 16 | | 479 1479 6 | 2459 12459 8 | 1245 12457 3 | +-------------------------+-------------------------+-------------------------+ | 45689 4689 489 | 3 159 1579 | 1456 145678 2 | | 1 23689 2389 | 25789 259 4 | 356 35678 5678 | | 458 b2348 7 | 258 6 15 | 9 13458 158 | +-------------------------+-------------------------+-------------------------+

2r1c2 = 2r1c8 & 3r9c2 (symmetry) => -2r9c2, -3r1c8, stte

by **yzfwsf** » Mon Jan 17, 2022 5:19 pm

This technique is now implemented in my solver,thanks for the puzzle.

Code: Select all: Gurth's symmetry placement: => Axisymmetric Conjugate Pair: r2c7,r9c2<>2,r1c8,r8c3<>3 Candidate's mapping in Central: 1<=>4 2<=>3 5<=>9 6<=>8 7<=>7

by **P.O.** » Tue Jan 18, 2022 11:02 am

Code: Select all: four chains in two grid states: 469 12469 5 49 8 369 7 1236 169 6789 26789 289 1 359 35679 23×56 23568 4 3 146789 1489 4579 459 2 156 1568 15689 2 13479 1349 6 13459 1359 8 1457 157 48 5 1348 24 7 13 1246 9 16 479 1479 6 2459 12459 8 1245 12457 3 45689 4689 489 3 159 1579 1456 145678 2 1 23689 238×9 25789 259 4 356 35678 5678 458 2348 7 258 6 15 9 13458 158 first state: c7n3{r2 r8} - r9n3{c8 c2} - r9n2{c2 c4} - c4{r1r5}{n4n9} - c4{r3r6}{n5n7} - b2{r1c6r2c5r2c6}{n3n5n6} => r2c7 <> 5 c3n2{r8 r2} - r1n2{c2 c8} - r1n3{c8 c6} - c6{r5r9}{n1n5} - c6{r4r7}{n7n9} - b8{r8c4r8c5r9c4}{n2n8n9} => r8c3 <> 9 469 12469 5 49 8 369 7 1236 169 6789 26789 289 1 359 35679 236 23568 4 3 146789 1489 4579 459 2 156 1568 15689 2 1×3479 1×349 6 13459 1359 8 1457 157 48 5 1348 ×24 7 1×3 1246 9 16 479 1479 6 2459 12459 8 1245 12457 3 45689 4689 489 3 159 1579 1456 145678 2 1 23689 238 25789 259 4 356 35678 5678 458 2348 7 258 6 15 9 13458 158 second state: r9n2{c4 c2} - r9n3{c2 c8} - r1n3{c8 c6} - r5n3{c6 c3} - r8c3{n2n3 n8} - r7n8{c1c2c3 c8} - c8n4{r7 r4r6} - r5{c6c7c9}{n1n2n6} => r5c4 <> 2 b5n3{r4c5 r4c6r5c6} - r1n3{c6 c8} - r1n2{c8 c2} - r9n2{c2 c4} - r5n2{c4 c7} - r2c7{n2n3 n6} - r3n6{c7c8c9 c2} - c2n1{r3 r4r6} - r5{c1c3c4}{n3n4n8} => r4c2 r4c3 r5c6 <> 3 ste.

by **champagne** » Tue Jan 18, 2022 12:18 pm

eleven wrote:2r1c2 = 2r1c8 & 3r9c2 (symmetry) => -2r9c2, -3r1c8, stte

Hi eleven,

This pushes me back years ago. But thanks to the one posting such an example.
Difficult to beat and nice solution.
My very first solver (full tagging) was perfectly designed to extract a similar chain. Not 100% sure that this is true to-day, but i did not work for long on the solver side.

BTW the symmetry seems to be studied again.

EDIT: I wrote this post relying on the expertise of eleven. I must confess that more details on the reasoning would be welcome on my side.
Edit2: showing 4r1c4;1r9c6 wrong seems easier to me

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