The New Sudoku Players' Forum

by **Mauriès Robert** » Tue Oct 20, 2020 2:56 pm

Hi all,
I propose you this rather simple puzzle, to see the original resolutions that will be proposed.
Cordialy
Robert
......2..4725......9.1..8..8..2.9.6....4.1....1.8.6..7..6..4.5......5698..3......

puzzle: Show

by **Cenoman** » Tue Oct 20, 2020 9:37 pm

In two steps:

Code: Select all: +---------------------+--------------------+----------------------+ | 1 36 8 | 679 469 37 | 2 34 5 | | 4 7 2 | 5 68 b38 | c139 c13 d1369 | | 36 9 5 | 1 46 2 | 8 7 346 | +---------------------+--------------------+----------------------+ | 8 35 47 | 2 357 9 | 1345 6 134 | | 2356 2356 79 | 4 357 1 | 359 8 e239 | | 35-2 1 49 | 8 35 6 | 3459 e234 7 | +---------------------+--------------------+----------------------+ | a29 28 6 | a79 189 4 | 137 5 123 | | 7 4 1 | 3 2 5 | 6 9 8 | | 259 258 3 | 679 1689 b78 | 147 124 124 | +---------------------+--------------------+----------------------+

1. (2=97)r7c14 - (7=83)r29c6 - (3=19)r2c78 - r2c9 = (92)b6p68 => -2 r6c1; 11 placements & basics

Code: Select all: +-----------------+------------------+-------------------+ | 1 6 8 | 79 49 37 | 2 34 5 | | 4 7 2 | 5 68 38 | d9-1 13 c169 | | 3 9 5 | 1 46 2 | 8 7 46 | +-----------------+------------------+-------------------+ | 8 3 47* | 2 57* 9 | a145* 6 14 | | 6 2 79* | 4 57* 1 | 359* 8 b39 | | 5 1 49* | 8 3 6 | 49* 2 7 | +-----------------+------------------+-------------------+ | 29 8 6 | 79 19 4 | 137 5 123 | | 7 4 1 | 3 2 5 | 6 9 8 | | 29 5 3 | 6 189 78 | 147 14 124 | +-----------------+------------------+-------------------+

2. DP(4579)r456c357 (BUG-lite+2) using mixed internal-external
(1)r4c7 == (9)r5c9 - r2c9 = (9)r2c7 => -1 r2c7; ste

Or in one step (lclste finish only):

Code: Select all: +---------------------+--------------------+----------------------+ | 1 36 8 | 679 469 37 | 2 34 5 | | 4 7 2 | 5 68 Ee38 |Ff139 Ff13 136-9 | | 36 9 5 | 1 46 2 | 8 7 346 | +---------------------+--------------------+----------------------+ | 8 35 47 | 2 357 9 | 1345 6 134 | | 2356 2356 79 | 4 357 1 | 359 8 Aa239z | | c235 1 49 | 8 35 6 | 3459 b234 7 | +---------------------+--------------------+----------------------+ | d29 28 6 |Dd79 189 4 | C137 5 B123 | | 7 4 1 | 3 2 5 | 6 9 8 | | 259 258 3 | 679 1689 Ee78 | 147 124 124 | +---------------------+--------------------+----------------------+

Kraken cell (239)r5c9
(2)r5c9 - r6c8 = r6c1 - (2=97)r7c14 - (7=83)r29c6 - (3=19)r2c78
(3)r5c9 - r7c9 = (3-7)r7c7 = r7c4 - (7=83)r29c6 - (3=19)r2c78
(9)r5c9
=> -9 r2c9; lclste

by **Mauriès Robert** » Wed Oct 21, 2020 2:28 pm

Hi Cenoman,
Of your two resolutions, I prefer the second, which I interpret as a set of 3 tracks that have 9r2c7 in common.
Bravo for this Kraken.
Here is a resolution with short (antitracks) chains.

P'(8r9c6) : (-8r9c6)=>7r9c6->(7r7c7->3r7c9)->1r7c5 => -8r7c5 => r7c2=8

puzzle1: Show

P'(2r7c1) : (-2r7c1)=>2r7c9->2r6c8 => -2r6c1 => 2r6c8 + simprification by basics (6 placements).

puzzle2: Show

P'(1r2c7) : (-1r2c7)=>9r2c7->4r6c7->1r4c9 => -1r4c7, -1r2c9 => r4c9=1 => -4r9c7.

puzzle3: Show

P'(1r9c7) : (-1r9c7)=>7r9c7->8r9c6->3r2c6->1r2c8 => -1r2c7 => r2c7=9, stte.

puzzle4: Show

Website · by **denis_berthier** » Thu Oct 22, 2020 11:46 am

Mauriès Robert wrote:......2..4725......9.1..8..8..2.9.6....4.1....1.8.6..7..6..4.5......5698..3......

For so easy puzzles, there are lots of possibilities. Here's one with only Subsets and xy-chains (bivalue-chains in rc space):

Code: Select all: *********************************************************************************************** *** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = TyBC+SFin *** Using CLIPS 6.32-r773 *********************************************************************************************** singles ==> r3c3 = 5, r5c8 = 8, r1c9 = 5, r1c3 = 8, r1c1 = 1, r8c3 = 1, r8c2 = 4 160 candidates, 807 csp-links and 807 links. Density = 6.34% whip[1]: c7n7{r9 .} ==> r9c8 ≠ 7 whip[1]: r8n3{c5 .} ==> r7c5 ≠ 3, r7c4 ≠ 3 whip[1]: c3n9{r6 .} ==> r6c1 ≠ 9, r5c1 ≠ 9 whip[1]: c3n7{r5 .} ==> r5c1 ≠ 7 whip[1]: c6n3{r3 .} ==> r3c5 ≠ 3, r1c4 ≠ 3, r1c5 ≠ 3, r2c5 ≠ 3 hidden-single-in-a-column ==> r8c4 = 3 whip[1]: r1n9{c5 .} ==> r2c5 ≠ 9 whip[1]: b5n7{r5c5 .} ==> r9c5 ≠ 7, r1c5 ≠ 7, r3c5 ≠ 7, r7c5 ≠ 7, r8c5 ≠ 7 singles ==> r8c5 = 2, r8c1 = 7, r3c6 = 2, r3c8 = 7 finned-swordfish-in-columns: n3{c6 c8 c2}{r1 r2 r6} ==> r6c1 ≠ 3 hidden-pairs-in-a-column: c1{n3 n6}{r3 r5} ==> r5c1 ≠ 5, r5c1 ≠ 2 finned-x-wing-in-columns: n2{c8 c1}{r6 r9} ==> r9c2 ≠ 2 biv-chain-rc[4]: r1c6{n3 n7} - r9c6{n7 n8} - r9c2{n8 n5} - r4c2{n5 n3} ==> r1c2 ≠ 3 singles ==> r1c2 = 6, r3c1 = 3, r5c1 = 6, r9c4 = 6 biv-chain-rc[4]: r7c2{n8 n2} - r7c1{n2 n9} - r7c4{n9 n7} - r9c6{n7 n8} ==> r9c2 ≠ 8, r7c5 ≠ 8 singles ==> r9c2 = 5, r4c2 = 3, r5c2 = 2, r6c1 = 5, r6c5 = 3, r7c2 = 8, r6c8 = 2 whip[1]: c8n3{r2 .} ==> r2c7 ≠ 3, r2c9 ≠ 3 biv-chain-rc[3]: r2c7{n1 n9} - r6c7{n9 n4} - r4c9{n4 n1} ==> r2c9 ≠ 1, r4c7 ≠ 1 hidden-single-in-a-block ==> r4c9 = 1 whip[1]: b6n4{r6c7 .} ==> r9c7 ≠ 4 biv-chain-rc[4]: r1c6{n7 n3} - r1c8{n3 n4} - r9c8{n4 n1} - r9c7{n1 n7} ==> r9c6 ≠ 7 stte init-time = 0.21s, solve-time = 0.17s, total-time = 0.38s

by **RSW** » Fri Oct 23, 2020 8:12 am

Code: Select all: +--------------+-------------+---------------+ | 1 36 8 | 679 469 37 | 2 34 5 | | 4 7 2 | 5 68 38 | 139 13 1369 | | 36 9 5 | 1 46 2 | 8 7 346 | +--------------+-------------+---------------+ | 8 35 47 | 2 357 9 | 1345 6 134 | | 2356 2356 79 | 4 357 1 | 359 8 239 | | 235 1 49 | 8 35 6 | 3459 234 7 | +--------------+-------------+---------------+ | 29 28 6 | 79 189 4 | 137 5 123 | | 7 4 1 | 3 2 5 | 6 9 8 | | 259 258 3 | 679 1689 78 | 147 124 124 | +--------------+-------------+---------------+

One step with a Nishio Net:

Hidden Text: Show

Code: Select all: You'll need a wide screen for this: +-----------------------+ / \ / \ --> 2r7c1 --+--> 8r7c2 -- \ / \ \ \ / \ \ \ / +---------->\ \ / \ \ 7?r9c6 -+--> 9r7c4 --+--> -9r9c45 --> 9r9c1 --------->+-->+ --> 1r7c5 --+--> 3r7c9 --> -3r5c9 ------------ \ \ \ \ \ \ \ \ +--> -9r5c9 --> -9r6c7 \ \ \ / \ \ \ / | \ +--> 5r9c2 --+--> -2r5c2 --> -2r5c9 ------ | \ \ | \ \ | \ +--> -2r9c8 -- | \ \ | \ +------> 1r9c8 --> 4r9c7 --> -4r6c7 --+--> ?r6c7 => -7r9c6 stte \ / | +--> 3r1c6 --+--------------> -4r9c8 ------------------------------------- | \ | \ /| +-> 6r1c2 --> 3r3c1 --> 5r6c1 --+--> 3r6c5 -------------------------------------------> -3r6c7 / | \ | \ / ---------------------------------------------------> -5r6c7 /

=> -7r9c6, stte

(Probably not was anyone was expecting

)

by **SpAce** » Fri Oct 23, 2020 12:43 pm

RSW wrote:One step with a Nishio Net:
Hidden Text: Show
Code: Select all
You'll need a wide screen for this: +-----------------------+ / \ / \ --> 2r7c1 --+--> 8r7c2 -- \ / \ \ \ / \ \ \ / +---------->\ \ / \ \ 7?r9c6 -+--> 9r7c4 --+--> -9r9c45 --> 9r9c1 --------->+-->+ --> 1r7c5 --+--> 3r7c9 --> -3r5c9 ------------ \ \ \ \ \ \ \ \ +--> -9r5c9 --> -9r6c7 \ \ \ / \ \ \ / | \ +--> 5r9c2 --+--> -2r5c2 --> -2r5c9 ------ | \ \ | \ \ | \ +--> -2r9c8 -- | \ \ | \ +------> 1r9c8 --> 4r9c7 --> -4r6c7 --+--> ?r6c7 => -7r9c6 stte \ / | +--> 3r1c6 --+--------------> -4r9c8 ------------------------------------- | \ | \ /| +-> 6r1c2 --> 3r3c1 --> 5r6c1 --+--> 3r6c5 -------------------------------------------> -3r6c7 / | \ | \ / ---------------------------------------------------> -5r6c7 /

=> -7r9c6, stte

The logic is correct, but the notation has several mistakes (besides being unreadable). The easiest to fix is to check which nodes should and shouldn't have a '-' sign. Many are wrong, which alone makes the logic very hard to follow.

Secondly, some of the implications don't make sense as written even if all unmarked memories from preceding nodes are counted. For example, how do you get from 5r9c2 to -2r9c8? I think you need 2r9c9 for that, but it's missing. (Of course the path from 5r9c2 to -2r5c2 is totally unclear as well, but at least it's findable by noting the 8r7c2 node elsewhere). In a correctly written net all join points should be clearly shown. See some of Robert's examples for how to do it with the implication notation, if you must use that (bad choice anyway).

So, if you want to use such monster nets and expect anyone to actually read them, you should probably learn to notate them more completely, readably, and hopefully more compactly as well. Preferably they should also be marked in the grid to make them possible to follow, though in this case that might not help much.

The full logic as a matrix:

19x19 TM: Show

Cenoman would probably write that as a multi-kraken and Denis as a braid. One of those options is perfectly readable and shows the full logic like the matrix.

by **Mauriès Robert** » Fri Oct 23, 2020 2:47 pm

Hi all,
Indeed, this Nishio from RSW is very complicated for such a simple puzzle.
It is possible to solve the puzzle with only one chain (anti-track), but of greater length (9 candidates) like this :
P'(6r2c9) : (-6r2c9)=>6r2c5->8r2c6->7r9c6->[(7r7c7->3r7c9*)->9r7c4->2r7c1->2r5c2*]->9r5c9 => -9r2c9 => r2c7=9 and finish with the basic techniques.

puzzle: Show

So we should be able to solve the puzzle with a single whip [9] or a single AIC??
Robert

by **SpAce** » Fri Oct 23, 2020 3:29 pm

Hi Robert,

Mauriès Robert wrote:It is possible to solve the puzzle with only one chain (anti-track), but of greater length (9 candidates) like this :
P'(6r2c9) : (-6r2c9)=>6r2c5->8r2c6->7r9c6->[(7r7c7->3r7c9*)->9r7c4->2r7c1->2r5c2*]->9r5c9 => -9r2c9 => r2c7=9 and finish with the basic techniques.
So we should be able to solve the puzzle with a single whip [9] or a single AIC??

Yes, I think so. Your anti-track could be written as an AIC:

(6)r2c9 = (6-8)r2c5 = r2c6 - (8=7)r9c6 - r7c4 = (927)r7c417 - 2r56c1|3r7c7 = (2,3)r5c2,r7c9 - (2|3=9)r5c9 => -9 r2c9; btte

(Btw, the group node 2r56c1 could be avoided by using 2r6c8 instead of 2r5c2, as in Cenoman's kraken.) A direct matrix translation would look like this:

9x9 TM: Show

I think that would be a braid[9] because of the discontinuity at 3r7c9. However, rearranging some of the rows and columns gives us:

9x9 TM: Show

That's a whip[9], I think:

r2n6{c9 c5} - r2n8{c5 c6} - r9c6{n8 n7} - r7n7{c4 c7} - r7n3{c7 c9} - r5c9{n3 n2} - b4n2{r5c2 r6c1} - r7c1{n2 n9} - r7c4{n9 .} ==> r2c9 ≠ 9; btte

by **Mauriès Robert** » Fri Oct 23, 2020 7:53 pm

Hi RSW,

RSW wrote:One step with a Nishio Net:

Your Nishio aims to eliminate 7r9c6. To do this elimination, here is how I would proceed.

Code: Select all: ->3r7c9->-------------------------------------------- / \ \ \ P'(7r9c7) : (-7r9c7)=>7r7c7->9r7c4->2r7c1->2r6c8->9r5c9->7r5c3->4r4c3->1r4c9->1r2c8->3r1c8->7r1c6 \ / / ->9r2c7----------------- => -7r9c6 => r9c6=8, stte.

puzzle: Show

Much simpler than your diagram

Cordialy
Robert

by **SpAce** » Fri Oct 23, 2020 8:56 pm

Mauriès Robert wrote:Your Nishio aims to eliminate 7r9c6. To do this elimination, here is how I would proceed.

Hidden Text: Show
Code: Select all
->3r7c9->-------------------------------------------- / \ \ \ P'(7r9c7) : (-7r9c7)=>7r7c7->9r7c4->2r7c1->2r6c8->9r5c9->7r5c3->4r4c3->1r4c9->1r2c8->3r1c8->7r1c6 \ / / ->9r2c7----------------- => -7r9c6 => r9c6=8, stte.

Much simpler than your diagram

Indeed. Even more importantly it's correct and contains enough information to follow it. Of course it's not as much as I'd like, but it's very simple to rewrite as a matrix that has it all:

13x13 TM: Show

Btw, technically this would be slightly simpler (except as a drawing):

Code: Select all: ->3r7c9->------------------------------ / \ \ P'(7r9c7) : (-7r9c7)=>7r7c7->9r7c4->2r7c1->2r6c8->9r5c9->7r5c3->4r4c3->1r4c9->1r2c8->3r1c8->7r1c6 \ \ / / \ ->9r2c7---------- / ------------------------------- => -7r9c6 => r9c6=8, stte.

The matrix size is the same, but instead of using the 5-SIS of 3s in box 3 it uses the 3-SIS in column 8 to imply 3r1c8.

13x13 TM: Show

Either one would be a braid[13], I think. At least I doubt any rearrangement could turn that mess into a whip.

--
Edit. Fixed a mistake in both matrices, thanks to Robert.

by **Mauriès Robert** » Sat Oct 24, 2020 10:41 am

Hi Space,
Why, in your TMs, do you write 7r1c8 on the last line when it is eliminated in the puzzle?
Shouldn't we write :

Code: Select all: 7r9c7 7r7c7 . . . 7r7c4 9r7c4 . . . . . . 9r7c1 2r7c1 . . . . . . . . . 2r6c1 2r6c8 . . . 3r7c7 . . . . . . . . . 3r7c9 . . . . . . . . . . . . 2r5c9 3r5c9 . 9r5c9 . . . . . . . . . . . . . . . . . . . 9r5c3 7r5c3 . . . . . . . . . . . . . . . . . . . . . . 7r4c3 4r4c3 . . . . . . . . . . . . . . . 3r4c9 . . . . . . . 4r4c9 1r4c9 . . . . . . . . . . . . . . . . . . . 9r2c9 . . . . . . . . . 9r2c7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1r2c9 1r2c7 1r2c8 . . . . . . . . . . . . . . . 3r23c9 . . . . . . . . . . . . 3r2c7 3r2c8 3r1c8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3r1c6 7r1c6 ===================================================================================== -7r9c6

Robert

by **SpAce** » Sat Oct 24, 2020 11:52 am

Mauriès Robert wrote:Why, in your TMs, do you write 7r1c8 on the last line when it is eliminated in the puzzle?

My mistake, thanks. Weird. I guess I didn't look at the grid when I wrote that part. That's a risk when reading implication chains/nets that don't include all of the information

They put the burden on the reader to figure out the actual route, which is tiresome. Still, my mistake. (Glad you actually read the matrices and noticed it!)

Shouldn't we write :

Hidden Text: Show
Code: Select all
7r9c7 7r7c7 . . . 7r7c4 9r7c4 . . . . . . 9r7c1 2r7c1 . . . . . . . . . 2r6c1 2r6c8 . . . 3r7c7 . . . . . . . . . 3r7c9 . . . . . . . . . . . . 2r5c9 3r5c9 . 9r5c9 . . . . . . . . . . . . . . . . . . . 9r5c3 7r5c3 . . . . . . . . . . . . . . . . . . . . . . 7r4c3 4r4c3 . . . . . . . . . . . . . . . 3r4c9 . . . . . . . 4r4c9 1r4c9 . . . . . . . . . . . . . . . . . . . 9r2c9 . . . . . . . . . 9r2c7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1r2c9 1r2c7 1r2c8 . . . . . . . . . . . . . . . 3r23c9 . . . . . . . . . . . . 3r2c7 3r2c8 3r1c8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3r1c6 7r1c6 ===================================================================================== -7r9c6

Yes, but the 7r1c6 should be in the first column (which is the result column). All candidates linked to the elimination(s) should be there, i.e. AIC and kraken end-points (which map to the first LLC and z-candidates in Denis' system).

The whole point of a matrix is to prove that the candidates in the first column form a strong inference set (SIS), which means that at least one of them must be true. Since all of them are weakly-linked to the target(s), the latter can't be true.

That's the verity-style interpretation which I prefer, but a matrix can be read as a contradiction pattern just as well. If you assume the target to be true, it eliminates all candidates in the first column, which empties the last row of the matrix if you read it from top to bottom. That's how you'd read it as a Nishio, or a whip, or a braid.

The same matrix works whether you write or think the logic as an AIC, Kraken, anti-track, Nishio, whip, braid, whatever, because it's language-agnostic and supports all points of view. That's one reason why I really like them.

Website · by **denis_berthier** » Sat Oct 24, 2020 4:07 pm

I haven't followed all the discussion in detail, but on seeing some proposed solution, I added a new function to SudoRules.

I can now focus the search of whips or braids to a predefined list of candidates. For obvious reasons, the focus applies only to whips or braids of length >1.

In the present case, I chose a single candidate: n9r2c9.

The command is:

Code: Select all: (try-to-eliminate-candidates "......2..4725......9.1..8..8..2.9.6....4.1....1.8.6..7..6..4.5......5698..3......" (create$ (nrc-to-label 9 2 9))

And SudoRules finds a (different) whip[9] for the elimination mentioned in a post above:

Code: Select all: *********************************************************************************************** *** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W *** Using CLIPS 6.32-r774 *********************************************************************************************** singles ==> r3c3 = 5, r5c8 = 8, r1c9 = 5, r1c3 = 8, r1c1 = 1, r8c3 = 1, r8c2 = 4 160 candidates, 807 csp-links and 807 links. Density = 6.34% whip[1]: c7n7{r9 .} ==> r9c8 ≠ 7 whip[1]: r8n3{c5 .} ==> r7c5 ≠ 3, r7c4 ≠ 3 whip[1]: c3n9{r6 .} ==> r6c1 ≠ 9, r5c1 ≠ 9 whip[1]: c3n7{r5 .} ==> r5c1 ≠ 7 whip[1]: c6n3{r3 .} ==> r3c5 ≠ 3, r1c4 ≠ 3, r1c5 ≠ 3, r2c5 ≠ 3 hidden-single-in-a-column ==> r8c4 = 3 whip[1]: r1n9{c5 .} ==> r2c5 ≠ 9 whip[1]: b5n7{r5c5 .} ==> r9c5 ≠ 7, r1c5 ≠ 7, r3c5 ≠ 7, r7c5 ≠ 7, r8c5 ≠ 7 singles ==> r8c5 = 2, r8c1 = 7, r3c6 = 2, r3c8 = 7 whip[9]: r2n6{c9 c5} - r2n8{c5 c6} - r9c6{n8 n7} - r7c4{n7 n9} - r7c1{n9 n2} - c2n2{r9 r5} - r5c9{n2 n3} - r7n3{c9 c7} - r7n7{c7 .} ==> r2c9 ≠ 9 stte+Whip[1]

Of course, this is absurd for this puzzle in my approach, as there's a much simper solution. But it could be used in other circumstances in conjunction with known backdoors.

by **SpAce** » Sat Oct 24, 2020 4:27 pm

denis_berthier wrote:I haven't followed all the discussion in detail, but on seeing some proposed solution, I added a new function to SudoRules.
I can now focus the search of whips or braids to a predefined list of candidates.

That's long overdue, but better late than never. I'm glad you did that because I'd like to see your one-stepper (or short) solutions. They'd be much more interesting and comparable than the ones with many trivial steps.

What does your new function suggest for 7r9c6? Can it find anything simpler than a braid[13] (which I think Robert's proposal is)?

Added.

And SudoRules finds a (different) whip[9] for the elimination mentioned in a post above

I presume you noticed it's practically the same as the whip I wrote. It does the same exact things, only partly in a reversed order and with one trivial routing difference. Yours as a matrix:

9x9 TM: Denis-whip: Show

Note that rows 4-9 can be flipped around at will because they form a (discontinuous) loop. If we do that:

9x9 TM: Denis-whip partly reversed: Show

...it's almost identical to the whip I wrote for Robert's solution:

9x9 TM: SpAce-whip: Show

The only difference is the 2r79c2 instead of 2r56c1. That routing was unspecified in Robert's solution, so it could just as well be the same. (And as I said earlier, the simplest routing would be to 2r6c8 instead of 2r5c2.) My whole point is that sometimes things look much more different than they really are.

Btw, here's Cenoman's kraken as a matrix:

10x10 BTM: Cenoman-kraken: Show

That should look familiar. Besides the better routing with 2r6c8, the only difference is the beginning with the almost-naked-pair. I guess that would make it an S-whip[10 ?], but I don't know how to write that right-linking subset node. There's a whole section of that in PBCS but no relevant examples that I could easily find, which is interesting. Based on how you write normal subsets (plenty of those examples around), I guess it's something like this:

r2{c7n9 {c7 c8}{n1 n3}} - r2c6{n3 n8} - ...

--

For Robert. Related to the mentioned loop in the matrix, here's another way to write your solution as an AIC:

(6)r2c9 = (6-8)r2c5 = r2c6 - (8=7)r9c6 - [(7)r7c4 = (7-3)r7c7 = r7c9 - (3=2)r5c9 - r6c8 = r6c1 - (2=9)r7c1 - (9=7)r7c4] = (9)r5c9 => -9 r2c9

Instead of using split-nodes as the previous one, this uses a nested chain (blue). It's the part in the matrix that can be flipped, so it could be written either way in the AIC as well.

Website · by **denis_berthier** » Sun Oct 25, 2020 5:49 am

Trying to eliminate n7r9c6, here is a still more absurd solution (max chain length 13, when 4 is enough)

Code: Select all: (try-to-eliminate-candidates "......2..4725......9.1..8..8..2.9.6....4.1....1.8.6..7..6..4.5......5698..3......" (create$ (nrc-to-label 7 9 6)) ) *********************************************************************************************** *** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W *** Using CLIPS 6.32-r774 *********************************************************************************************** same start as in my previous post, until before the whip[9] whip[13]: r7c4{n7 n9} - r7c1{n9 n2} - c2n2{r9 r5} - r7c2{n2 n8} - r9n8{c2 c5} - r7c5{n8 n1} - r7c9{n1 n3} - r5c9{n3 n9} - r6n9{c7 c3} - c3n4{r6 r4} - r4c9{n4 n1} - r2c9{n1 n6} - r2c5{n6 .} ==> r9c6 ≠ 7 stte

The New Sudoku Players' Forum

Robert's puzzles 2020-10-20

Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20

Re: Robert's puzzles 2020-10-20