The New Sudoku Players' Forum

by **mith** » Mon Feb 22, 2021 5:34 pm

Code: Select all: +-------+-------+-------+ | . 3 . | . . . | 1 4 . | | . . . | . 1 5 | . 9 . | | . . 2 | 6 . . | . . . | +-------+-------+-------+ | . . . | 5 . . | . 3 . | | . . 5 | . . . | 8 . . | | . 9 . | . . 7 | . . . | +-------+-------+-------+ | . . . | . . 9 | 3 . . | | . 2 . | 3 8 . | . . . | | . 4 6 | . . . | . 2 . | +-------+-------+-------+ .3....14.....15.9...26........5...3...5...8...9...7........93...2.38.....46....2.

(Not a hard puzzle, but I'm curious if anyone can find a nice one-step solution.)

by **pjb** » Mon Feb 22, 2021 10:09 pm

No single digit elimination produces stte result, therefore needs a multidigit approach which I can't see for now. In mean time, simple 2 AIC solution:
(2=8)r1c6 - (8=4)r2c4 - (4=2)r7c4 => -2 r1c4
(4=6)r5c6 - (6=4)r6c5 - (4)r6c7 = (4)r8c7 => -4 r8c6; stte

Phil

by **Cenoman** » Mon Feb 22, 2021 11:12 pm

mith wrote:I'm curious if anyone can find a nice one-step solution

Me too ! I'm even curious if anyone can find an ugly one-step solution...

In the meantime, let's have fun with two-step solutions:

Code: Select all: +------------------------+------------------------+------------------------+ | 5 3 89 | 289 7 28 | 1 4 6 | | 4678 678* 478 | 4-8 1 5 | 2 9 3 | | 49 1 2 | 6 349 34 | 57 8 57 | +------------------------+------------------------+------------------------+ | 124678 678* 1478 | 5 2469 2468 | 467 3 12479 | | 12467 67 5 | 1249 23469 2346 | 8 167 12479 | | 12468* 9 3 | 1248* 246 7 | 456 156 1245 | +------------------------+------------------------+------------------------+ | 178 5 178 | 24 246 9 | 3 167 147 | | 179 2 179 | 3 8 46 | 4567 1567 1457 | | 3 4 6 | 7 5 1 | 9 2 8 | +------------------------+------------------------+------------------------+

1. Kite (8)r6c4 = r6c1 - r5c2 = r2c2 => -8 r2c4; 26 placements and basics

Code: Select all: +-----------------+-----------------+---------------------+ | 5 3 9 | 8 7 2 | 1 4 6 | | 6 8 7 | 4 1 5 | 2 9 3 | | 4 1 2 | 6 9 3 | 57* 8 57* | +-----------------+-----------------+---------------------+ | 1 67* 4 | 5 2 8 | 67* 3 9 | | 2 67* 5 | 9 3 46 | 8 a167* 147 | | 8 9 3 | 1 46 7 | 456 56 2 | +-----------------+-----------------+---------------------+ | 7 5 8 | 2 46 9 | 3 6-1 c14 | | 9 2 1 | 3 8 46 | b4567* 567* b457* | | 3 4 6 | 7 5 1 | 9 2 8 | +-----------------+-----------------+---------------------+

2. MUG (567)r3c79, r45c2, b6p15, r8c789 using internals
(1)r5c8 == (4)r8c79 - (4=1)r7c9 => -1 r7c8; ste

by **mith** » Mon Feb 22, 2021 11:16 pm

Cenoman wrote:
mith wrote:I'm curious if anyone can find a nice one-step solution

Me too ! I'm even curious if anyone can find an ugly one-step solution...

Right? There are plenty of simple two step solutions, but the two steps are so far apart...

by **RSW** » Tue Feb 23, 2021 1:59 am

Cenoman wrote:
mith wrote:I'm curious if anyone can find a nice one-step solution

Me too ! I'm even curious if anyone can find an ugly one-step solution...

Here's an ugly one step solution:

Code: Select all: +-----------------+--------------------+-----------------+ | 5 3 89 |T8-29 7 2-8 | 1 4 6 | | 4678 678 478 | 4-8 1 5 | 2 9 3 | | 49 1 2 | 6 39-4 3-4 | 57 8 57 | +-----------------+--------------------+-----------------+ | 124678 678 1478 | 5 269-4 T8-246 | 467 3 12479 | | 12467 67 5 | 129-4 2369-4 4-236 | 8 167 12479 | | 12468 9 3 | 12-48 26-4 7 | 456 156 1245 | +-----------------+--------------------+-----------------+ | 178 5 178 | 2-4 B246 9 | 3 167 147 | | 179 2 179 | 3 B8 6-4 | 4567 1567 1457 | | 3 4 6 | 7 5 1 | 9 2 8 | +-----------------+--------------------+-----------------+

Generic Exocet: (2468)r78c5, r2c4 r4c6 => -236r5c6 -246r4c6 -29r1c4 -4r7c4 -4r5c45 -4r46c5 -4r3c56 -4r8c6 -48r6c4 -8r2c4 -8r1c6; stte
Proviso: I'm not entirely convinced that the proof logic of my solver is correct. It's a work in progress.

Proof(?):: Show

Website · by **denis_berthier** » Tue Feb 23, 2021 5:05 am

mith wrote:
Code: Select all
+-------+-------+-------+ | . 3 . | . . . | 1 4 . | | . . . | . 1 5 | . 9 . | | . . 2 | 6 . . | . . . | +-------+-------+-------+ | . . . | 5 . . | . 3 . | | . . 5 | . . . | 8 . . | | . 9 . | . . 7 | . . . | +-------+-------+-------+ | . . . | . . 9 | 3 . . | | . 2 . | 3 8 . | . . . | | . 4 6 | . . . | . 2 . | +-------+-------+-------+ .3....14.....15.9...26........5...3...5...8...9...7........93...2.38.....46....2.

(Not a hard puzzle, but I'm curious if anyone can find a nice one-step solution.)

Mith, congrats for this noticeable puzzle.
It has no BRT-anti-backdoor, no W1-anti-backdoor and no S-anti-backdoor. As a result, there can't be any 1-elimination solution.
There could still be a 1-step solution, but it would have to eliminate at least two candidates.
I tried Forcing-T&E and Forcing{3}-T&E but they still need two steps.

SudoRules normal solution: Show

(solve ".3....14.....15.9...26........5...3...5...8...9...7........93...2.38.....46....2.")
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
*** Using CLIPS 6.32-r779
*** Download from: https://github.com/denis-berthier/CSP-Rules-V2.1
***********************************************************************************************
9 singles
Starting non trivial part of solution with the following RESOLUTION STATE:

Code: Select all: 56789 3 789 289 279 28 1 4 2567 4678 678 478 248 1 5 267 9 3 14579 157 2 6 3479 34 57 8 57 124678 1678 1478 5 2469 2468 2467 3 124679 12467 167 5 1249 23469 2346 8 167 124679 12468 9 3 1248 246 7 2456 156 12456 1578 1578 178 24 246 9 3 1567 14567 1579 2 179 3 8 46 4567 1567 14567 3 4 6 7 5 1 9 2 8 196 candidates, 1186 csp-links and 1186 links. Density = 6.21%

naked-pairs-in-a-row: r3{c7 c9}{n5 n7} ==> r3c5 ≠ 7, r3c2 ≠ 7, r3c2 ≠ 5, r3c1 ≠ 7, r3c1 ≠ 5
6 singles
finned-x-wing-in-columns: n8{c6 c2}{r4 r1} ==> r1c3 ≠ 8
26 singles
finned-x-wing-in-columns: n4{c7 c5}{r6 r8} ==> r8c6 ≠ 4
stte

I computed all the anti-backdoor pairs (there are 105), in case anyone wanted to try some of them. The format is: n1r1c1, n2r2c2:

BRT-anti-backdoor-pairs: Show

Code: Select all: 589, 983 589, 864 589, 931 589, 816 589, 914 487, 983 487, 864 487, 931 487, 816 487, 914 486, 983 486, 864 486, 931 486, 816 486, 914 479, 983 479, 864 479, 931 479, 816 479, 914 178, 983 178, 864 178, 931 178, 816 178, 914 675, 983 675, 864 675, 931 675, 816 675, 914 275, 739 275, 537 474, 739 474, 537 465, 983 465, 864 465, 931 465, 816 465, 914 459, 983 459, 864 459, 931 459, 816 459, 914 159, 983 159, 864 159, 931 159, 816 159, 914 658, 758 656, 983 656, 864 656, 931 656, 816 656, 914 154, 589 154, 487 154, 486 154, 479 154, 178 154, 675 154, 465 154, 459 154, 159 154, 656 154, 752 154, 747 154, 642 154, 739 154, 537 752, 983 752, 864 752, 931 752, 816 752, 914 747, 983 747, 864 747, 931 747, 816 747, 914 642, 983 642, 864 642, 931 642, 816 642, 914 739, 983 739, 871 739, 864 739, 842 739, 931 739, 824 739, 816 739, 914 739, 813 537, 983 537, 871 537, 864 537, 842 537, 931 537, 824 537, 816 537, 914 537, 813 214, 739 214, 537

Website · by **denis_berthier** » Sun Feb 28, 2021 10:43 am

.
I finally decided to try some of the anti-backdoor pairs I found in my previous post.
To be clear about what I did:
1) the resolution path starts from the givens, with:

Code: Select all: singles ==> r9c6 = 1, r9c4 = 7, r9c5 = 5, r9c7 = 9, r9c9 = 8, r9c1 = 3, r6c3 = 3, r3c8 = 8, r2c9 = 3 Starting non trivial part of solution with the following RESOLUTION STATE: 56789 3 789 289 279 28 1 4 2567 4678 678 478 248 1 5 267 9 3 14579 157 2 6 3479 34 57 8 57 124678 1678 1478 5 2469 2468 2467 3 124679 12467 167 5 1249 23469 2346 8 167 124679 12468 9 3 1248 246 7 2456 156 12456 1578 1578 178 24 246 9 3 1567 14567 1579 2 179 3 8 46 4567 1567 14567 3 4 6 7 5 1 9 2 8

and these trivial Singles are not considered as steps.

2) Non counted steps between two eliminations can consist of Singles
3) Final steps (after the second whip[≥1] elimination is found) can only be Singles.
4) What I find is not only 2-step but also 2-elimination before stte.

Code: Select all: whip[7]: c4n1{r6 r5} - c4n9{r5 r1} - b2n8{r1c4 r1c6} - r1c3{n8 n7} - r2n7{c3 c7} - r3c9{n7 n5} - r3c7{n5 .} ==> r6c4 ≠ 8 singles ==> r4c6 = 8, r1c6 = 2, r2c7 = 2, r1c9 = 6, r1c1 = 5, r7c2 = 5, r2c2 = 8, r2c4 = 4, r2c3 = 7, r1c3 = 9, r1c4 = 8, r1c5 = 7, r8c3 = 1, r4c3 = 4, r7c3 = 8, r7c1 = 7, r8c1 = 9, r2c1 = 6, r3c2 = 1, r3c1 = 4, r3c6 = 3, r3c5 = 9, r7c4 = 2, r6c4 = 1, r5c4 = 9, r4c9 = 9, r4c1 = 1, r5c1 = 2, r6c1 = 8, r6c9 = 2, r4c5 = 2, r5c5 = 3 whip[2]: r7n4{c9 c5} - r6n4{c5 .} ==> r8c7 ≠ 4 stte

There are other possibilities, but all involve at least a whip[7].

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