- Code: Select all
`. 1 .|. 2 .|9 . .`

. 3 .|. . 4|. . 6

7 . .|1 . .|4 . .

-----+-----+-----

. . .|. . .|. 8 4

. 6 8|4 . 5|2 1 .

4 5 .|. . .|. . .

-----+-----+-----

. . 5|. . 3|. . 1

6 . .|7 . .|. 4 .

. . 1|. 6 .|. 2 .

200e200w

15 posts
• Page **1** of **1**

- Code: Select all
`. 1 .|. 2 .|9 . .`

. 3 .|. . 4|. . 6

7 . .|1 . .|4 . .

-----+-----+-----

. . .|. . .|. 8 4

. 6 8|4 . 5|2 1 .

4 5 .|. . .|. . .

-----+-----+-----

. . 5|. . 3|. . 1

6 . .|7 . .|. 4 .

. . 1|. 6 .|. 2 .

200e200w

- 200e200w
**Posts:**208**Joined:**20 January 2018

- Code: Select all
`+----------------+------------------+---------------+`

| 5 1 4 | 36 2 67 | 9 37 8 |

| 289 3 29 | 589 5789 4 | 1 57 6 |

| 7 89* 6 | 1 35 89* | 4 35 2 |

+----------------+------------------+---------------+

| 1 29 2379 | 2369 379 267 | 5 8 4 |

| 39 6 8 | 4 379 5 | 2 1 379 |

| 4 5 2379 | 2389 13789 127 | 367 69 379 |

+----------------+------------------+---------------+

| 289 7 5 | 289# 4 3 | 68 69 1 |

| 6 289* 239 | 7 1589* 12 | 38# 4 359 |

| 389 4 1 | 589# 6 9*-8 | 378 2 3579 |

+----------------+------------------+---------------+

- Code: Select all
`8r79c4 - 8r9c6;`

8r8c7 - ??? - 8r9c6; stte.

Now, as I understand Oddagon theory, a chain should exist for 8r8c7, but it's not at all obvious to me. I also believe that Cenoman's amazing network code could find one, so that code is eliminated (temporarily) from the competition.

Any other takers?

SteveC

- Sudtyro2
**Posts:**539**Joined:**15 April 2013

Okay, this is not a normal submission. I was just experimenting with nr/nc spaces and used this puzzle as a test bed. I have no idea if anything below is even close to correct, as I was just playing around and seeing if normal solving can even be done in one of those spaces without maintaining a normal rc-grid as well. Seems like it can be done, as I didn't even begin to solve the puzzle normally at all. I just mapped it into nr-space (not rn, which seems useless to me) and solved directly there. To be honest I don't really know what I did because I haven't tried to convert anything back into rc-space. Everything's done manually (except for checking the backdoor) so there can be mistakes of all kinds. Anyway, here goes nothing.

So, this is in nr-space, meaning that rows represent numbers (n), columns represent rows (r), and candidates represent columns (c).

Kraken "cell": n3r5 (3s in row 5 in rc) => -c2 n8r3 (i.e. -8 r3c2):

So, this is in nr-space, meaning that rows represent numbers (n), columns represent rows (r), and candidates represent columns (c).

- Code: Select all
`r1 r2 r3 r4 r5 r6 r7 r8 r9`

.-------------------.----------------------.-------------------.

n1 | 2 7 4 | 1 8 56 | 9 56 3 |

n2 | 5 13 9 | 2346 7 346 | 14 236 8 |

n3 | 48 2 58 | 345 *159 34579 | 6 379 179 |

| | | |

n4 | 3 6 7 | 9 4 1 | 5 8 2 |

n5 | 1 458 58 | 7 6 2 | 3 59 49 |

n6 | 46 9 3 | 46 2 78 | 78 1 5 |

| | | |

n7 | 68 58 1 | 356 59 35679 | 2 4 79 |

n8 | 9 145 x6-2 | 8 3 45 | 147 257 1467 |

n9 | 7 1345 26 | 2345 159 34589 | 148 2359 1469 |

'-------------------'----------------------'-------------------'

Kraken "cell": n3r5 (3s in row 5 in rc) => -c2 n8r3 (i.e. -8 r3c2):

- Code: Select all
`(1)n3r5-(1=79)n37c9-(9=4)n5r9-(4=85)n57r2-(5)n8r2`

|| ||

|| (1)n8r2-(2)n8r3 x

|| ||

|| (4)n8r2-(4=5)n8r6-(5=6)n1r6-n1r8=n2r8-(4=1)n2r7

|| | |

|| (1)n8r2===========================(1)n8r7

|| ||

|| (1-6)n8r9=(6-2)n8r3 x

||

(5)n3r5-n3r3=(5-8)n5r3=n5r2-(8=5)n7r2-(5)n8r2 ... (see above)

||

(9)n3r5-(1)n3r5=n3r9-----------------------(1)n8r9

| | ||

| (3)n3r8 ||

| || ||

(9)n3r8======(7)n3r8-(7)n8r8 ||

|| ||

(7)n8r7-(1)n8r7=(1)n8r2-(2)n8r3 x

||

(7-6)n8r9=(6-2)n8r3 x

Last edited by SpAce on Fri Feb 23, 2018 2:57 am, edited 1 time in total.

- SpAce
**Posts:**224**Joined:**22 May 2017

Here's the same converted into normal rc:

Kraken row (3)r5 => -8 r3c2, stte.

- Code: Select all
`.----------------.------------------.---------------.`

| 5 1 4 | 36 2 67 | 9 37 8 |

| 289 3 29 | 589 5789 4 | 1 57 6 |

| 7 x9-8 6 | 1 35 89 | 4 35 2 |

:----------------+------------------+---------------:

| 1 29 2379 | 2369 379 267 | 5 8 4 |

|*39 6 8 | 4 *379 5 | 2 1 *379 |

| 4 5 2379 | 2389 13789 127 | 367 69 379 |

:----------------+------------------+---------------:

| 289 7 5 | 289 4 3 | 68 69 1 |

| 6 289 239 | 7 1589 12 | 38 4 359 |

| 389 4 1 | 589 6 89 | 378 2 3579 |

'----------------'------------------'---------------'

Kraken row (3)r5 => -8 r3c2, stte.

- Code: Select all
`(3)r5c1-r9c9=HP:(37-5)r9c79=r9c4=HP:(57-8)r2c58`

|| ||

|| (8)r2c1-(8)r3c2 x

|| ||

|| (8)r2c4-r6c4=(8-1)r6c5=r6c6-

|| | (1=2)r8c6-(2)r7c4=(2-8)r7c1

|| | ||

|| (8)r2c1==================(8)r9c1-r9c6=r3c6-(8)r3c2 x

||

(3)r5c5-r3c5=(3-5)r3c8=(5-7)r2c8=(7-8)r2c5 ... (see above)

||

(3)r5c9-r5c1=r9c1-(8)r9c1==============

| | ||

| (3)r8c3 ||

| || ||

(3)r8c9=======(3-8)r8c7 ||

|| ||

(8)r7c7-r7c1=(8)r2c1-(8)r3c2 x

||

(8)r9c7-r9c6=r3c6-(8)r3c2 x

- SpAce
**Posts:**224**Joined:**22 May 2017

Strange puzzle. S.E. rating is 7.3, not that hard. But I have found no simpler path than the following sequence of AIC's. (@SteveC: the net rationale for the 8s oddagon, as well as the one for a one-step solution are ugly ! )

1. (39=8)r59c1 - r9c6 = r3c6 - r3c2 = (8)r2c1 => -9 r2c1

2. (5)r8c5 = r9c4 - r2c4 = (57-8)r2c58 = (81)r68c5 => -9 r8c5

3. (5)r8c9 = (57-3)r9c79 = r9c1 - (3=9)r5c1 - r79c1 = (9)r8c23 => -9 r8c9; 4 placements

4. (9=8)r9c6 - r3c6 = r3c2 - (8=2)r2c1 - r7c1 = (2)r7c4 => -9 r7c4; 4 placements

5. BUG+2

(5-7)r2c5 = (7)r5c5

(8)r8c5 - r9c6 = (8-7)r9c7 = r9c9

=> -7 r5c9; stte

- Code: Select all
`+---------------------+-----------------------+--------------------+`

| 5 1 4 | 36 2 67 | 9 37 8 |

| e28-9 3 29 | C589 D5789 4 | 1 D57 6 |

| 7 d89 6 | 1 35 c89 | 4 35 2 |

+---------------------+-----------------------+--------------------+

| 1 29 2379 | 2369 379 267 | 5 8 4 |

| a39x 6 8 | 4 379 5 | 2 1 379 |

| 4 5 2379 | 2389 E13789 127 | 367 69 379 |

+---------------------+-----------------------+--------------------+

| 289y 7 5 | 289 4 3 | 68 69 1 |

| 6 289z 239z | 7 AE158-9 12 | 38 4 u359 |

| a389wy 4 1 | B589 6 b89 | 378v 2 3579v |

+---------------------+-----------------------+--------------------+

1. (39=8)r59c1 - r9c6 = r3c6 - r3c2 = (8)r2c1 => -9 r2c1

2. (5)r8c5 = r9c4 - r2c4 = (57-8)r2c58 = (81)r68c5 => -9 r8c5

3. (5)r8c9 = (57-3)r9c79 = r9c1 - (3=9)r5c1 - r79c1 = (9)r8c23 => -9 r8c9; 4 placements

- Code: Select all
`+-----------------+-------------------+-------------------+`

| 5 1 4 | 36 2 67 | 9 37 8 |

| d28 3 29 | 589 578 4 | 1 57 6 |

| 7 c89 6 | 1 35 b89 | 4 35 2 |

+-----------------+-------------------+-------------------+

| 1 2 37 | 36 9 67 | 5 8 4 |

| 9 6 8 | 4 37 5 | 2 1 37 |

| 4 5 37 | 28 18 12 | 367 69 379 |

+-----------------+-------------------+-------------------+

| e28 7 5 | 28-9 4 3 | 68 69 1 |

| 6 89 29 | 7 158 12 | 38 4 35 |

| 3 4 1 | 589 6 a89 | 78 2 579 |

+-----------------+-------------------+-------------------+

4. (9=8)r9c6 - r3c6 = r3c2 - (8=2)r2c1 - r7c1 = (2)r7c4 => -9 r7c4; 4 placements

- Code: Select all
`+-----------------+------------------+-----------------+`

| 5 1 4 | 36 2 67 | 9 37 8 |

| 28 3 29 | 59 a78+5 4 | 1 57 6 |

| 7 89 6 | 1 35 89 | 4 35 2 |

+-----------------+------------------+-----------------+

| 1 2 37 | 36 9 67 | 5 8 4 |

| 9 6 8 | 4 b37 5 | 2 1 3-7 |

| 4 5 37 | 28 18 12 | 37 6 9 |

+-----------------+------------------+-----------------+

| 28 7 5 | 28 4 3 | 6 9 1 |

| 6 89 29 | 7 A15+8 12 | 38 4 35 |

| 3 4 1 | 59 6 B89 | C78 2 D57 |

+-----------------+------------------+-----------------+

5. BUG+2

(5-7)r2c5 = (7)r5c5

(8)r8c5 - r9c6 = (8-7)r9c7 = r9c9

=> -7 r5c9; stte

Cenoman

- Cenoman
**Posts:**650**Joined:**21 November 2016**Location:**Paris, France

Special thanks and kudos to SpAce and Cenoman for their determined efforts to solve this challenging puzzle. I had initially started [what I thought, incorrectly, was] a manual 3D Medusa on the grid but gave up at six levels deep. After seeing SpAce's network, continued coloring later revealed the Kraken 3s at level ten. I strongly suspect that if someone worked up a puzzle rating system for single-step stte eliminations it might very well be the Medusa depth level.

SteveC

SteveC

Last edited by Sudtyro2 on Sun Mar 04, 2018 4:35 pm, edited 1 time in total.

- Sudtyro2
**Posts:**539**Joined:**15 April 2013

Sudtyro2,

This is the (8) map for the grid.

The cells marked 8# are members of an impossible fish r2389c1256, impossible because it produces a contradiction when the cells are coloured.

Therefore this fish cannot be true and at least one fin cell (and one Potential Elimination cell) must be true.

As there are only two fin cells there is a derived strong link (8)r6c5 = (8)r7c1 from which various elimination AICs can be found.

The impossible fish contains multiple oddagons of which r2c5-r8c5-r8c2-r9c1-r2c1 has the two fin cells as guardians. However I like the impossible fish approach. It is easy to spot if you look for three boxes with candidates in one diagonal direction and the fourth box with the candidates in the other diagonal direction.

As this is a 200e200w Nightmare puzzle, I think the aim is to find any solution, not a single-stepper.

.

This is the (8) map for the grid.

- Code: Select all
`*-------------------*-------------------*-------------------*`

| . . . | . . . | . . 8 |

| 8# . . | 8 PE 8# . | . . . |

| . 8# . | . . 8# | . . . |

*-------------------*-------------------*-------------------*

| . . . | . . . | . 8 . |

| . . 8 | . . . | . . . |

| . . . | 8 8 Fin . | . . . |

*-------------------*-------------------*-------------------*

| 8 Fin . . | 8 . . | 8 . . |

| . 8# . | . 8# . | 8 PE . . |

| 8# . . | 8 PE . 8# | 8 PE . . |

*-------------------*-------------------*-------------------*

The cells marked 8# are members of an impossible fish r2389c1256, impossible because it produces a contradiction when the cells are coloured.

Therefore this fish cannot be true and at least one fin cell (and one Potential Elimination cell) must be true.

As there are only two fin cells there is a derived strong link (8)r6c5 = (8)r7c1 from which various elimination AICs can be found.

The impossible fish contains multiple oddagons of which r2c5-r8c5-r8c2-r9c1-r2c1 has the two fin cells as guardians. However I like the impossible fish approach. It is easy to spot if you look for three boxes with candidates in one diagonal direction and the fourth box with the candidates in the other diagonal direction.

As this is a 200e200w Nightmare puzzle, I think the aim is to find any solution, not a single-stepper.

.

Last edited by David P Bird on Sat Feb 24, 2018 9:11 am, edited 1 time in total.

- David P Bird
- 2010 Supporter
**Posts:**1008**Joined:**16 September 2008**Location:**Middle England

David P Bird wrote:As this is a 200e200w Nightmare puzzle, I think the aim is to find any solution, not a single-stepper.

Yes. My Nightmare puzzles are not designed to be solved using a one non-basic step (unless it is a Kraken, a net or more advanced technique). SE rates them from 7.1 to 8.1, sometimes slightly higher. All Nightmares so far were generated using SudoCue software, but this will change with Nightmare #62 (which I believe it will be in March/April).

200e200w

- 200e200w
**Posts:**208**Joined:**20 January 2018

My "normal" solution would be:

1. Skyscraper: (8)r8c2 = r3c2 - r3c6 = (8)r9c6 => -8 r9c1, r8c5

2. AIC-2: (6)r7c7 = (6-9)r7c8 = r7c4 - r9c6 = (9-8)r3c6 = r3c2 - r8c2 = (8)r8c7 => -8 r7c7

3. AIC-Loop: (2=8)r7c4 - r6c4 = (8-1)r6c5 = r6c6 - (1=2)r8c6 - loop => -8 r29c4, -379 r6c5

4. BUG+1: -78 r2c5

1. Skyscraper: (8)r8c2 = r3c2 - r3c6 = (8)r9c6 => -8 r9c1, r8c5

2. AIC-2: (6)r7c7 = (6-9)r7c8 = r7c4 - r9c6 = (9-8)r3c6 = r3c2 - r8c2 = (8)r8c7 => -8 r7c7

3. AIC-Loop: (2=8)r7c4 - r6c4 = (8-1)r6c5 = r6c6 - (1=2)r8c6 - loop => -8 r29c4, -379 r6c5

4. BUG+1: -78 r2c5

- SpAce
**Posts:**224**Joined:**22 May 2017

Sudtyro2 wrote:I had initially started a manual 3D Medusa on the grid but gave up at six levels deep. After seeing SpAce's network, continued coloring later revealed the Kraken 3s at level ten. I strongly suspect that if someone worked up a puzzle rating system for single-step stte eliminations it might very well be the Medusa depth level.

Can you explain what this means and how you did it? I understand 3D Medusa but what do you mean by its depth levels? Is it something like multi-coloring using several Medusa clusters?

I arrived at my horrible net solution by cheating, i.e. knowing the backdoors and thus what candidates should produce a contradiction. Then I drew a half-GEM analysis by assuming one of those candidates (I ignored the other parity because I knew it wasn't important), which ended up emptying the nr-cell (rc-row). In other words it was just t & (guaranteed) e. Then I worked it out in reverse to turn the contradiction into a verity, but it was just cosmetics (looks a bit more legit, doesn't it? ).

The interesting question is how one could find the backdoor(s) manually without cheating. In this case I think it's quite likely to find a backdoor with a powerful enough coloring approach, as you demonstrated with your Medusa approach. Full GEM (using both parities) should also do the trick here relatively easily, as I already did half of it -- you just have to hit the right seeds, but it's not that unlikely here.

- SpAce
**Posts:**224**Joined:**22 May 2017

SpAce wrote: Can you explain what this means and how you did it? I understand 3D Medusa but what do you mean by its depth levels? Is it something like multi-coloring using several Medusa clusters?

In response to SpAce's questions, I have worked up a tutorial of sorts from my scattered notes describing what I assumed (incorrectly) was a Medusa-like approach for solving some of the tougher problems. All comments are welcomed regarding the hidden text below...

SteveC

Last edited by Sudtyro2 on Sun Mar 04, 2018 9:04 pm, edited 3 times in total.

- Sudtyro2
**Posts:**539**Joined:**15 April 2013

SteveC, thanks for that example! If I understand it correctly, I think it's actually very similar to what I did with the "half-GEM" approach. I just got confused when you called it 3D Medusa. I think it's a misnomer, because the real 3D Medusa uses two parities and only colors strongly-linked clusters, and neither of them is true here. Full GEM also uses two parities, but it follows weak links too (like your system), which is why I call it "3D Medusa on steroids". When you have foreknowledge of the elimination digit, only one parity is interesting because you're looking for contradictions resulting from that particular assumption, instead of eliminations resulting from the combo of both parities. That's why I only used half-GEM here, which seems to be pretty much what you did as well (I just use a different mark-up).

Have you looked at GEM? It's a very powerful coloring technique which makes it trivial to find most linear and network-based eliminations (caused by both parities) and/or contradictions (within just one parity), or in this case to find a network proof (through a contradiction) for a known ED. It's also very easy and quick to use for a pencil-and-paper solver -- if you have an intuitive graphical mark-up for it (not included in the original, but not that hard to create). Personally I think David's original spreadsheet-based approach makes GEM look much more complicated than it really is (not to even mention his unfortunate choice of non-keyboard characters for parity markers).

http://sudopedia.enjoysudoku.com/Graded_Equivalence_Marks.html

http://forum.enjoysudoku.com/post249854.html

Have you looked at GEM? It's a very powerful coloring technique which makes it trivial to find most linear and network-based eliminations (caused by both parities) and/or contradictions (within just one parity), or in this case to find a network proof (through a contradiction) for a known ED. It's also very easy and quick to use for a pencil-and-paper solver -- if you have an intuitive graphical mark-up for it (not included in the original, but not that hard to create). Personally I think David's original spreadsheet-based approach makes GEM look much more complicated than it really is (not to even mention his unfortunate choice of non-keyboard characters for parity markers).

http://sudopedia.enjoysudoku.com/Graded_Equivalence_Marks.html

http://forum.enjoysudoku.com/post249854.html

- SpAce
**Posts:**224**Joined:**22 May 2017

Thanks are due again for additional constructive comments by SpAce and also by DPB (since withdrawn) regarding both terminology and advanced methods available for this puzzle. I was only vaguely aware of GEM, and not much better with 3D Medusa. Accordingly, I will correct some of the nomenclature in my previous writeup. I can fault DPB for only one thing...his old post here was my introduction to the Oddagon, and that, afterall, is what initiated the lead post.

SteveC

SteveC

- Sudtyro2
**Posts:**539**Joined:**15 April 2013

Btw, no matter which of these two ways we use to find the contradiction network, isn't it simply an application of Nishio? Turning it into its Kraken counterpart doesn't really change that or make the process less t&e, even if the end result looks somewhat nicer. The question is: why do we bother making that transformation? Why don't we just use the original Nishio and leave it at that? It's an equally logical proof for the same elimination. Is it somehow more palatable if presented as a Kraken? (I guess I thought so, which is why I did it, but in the end it's just a different wrapping for the same ugly beast.)

What would interest me is figuring out a manually applicable way to find Kraken eliminations directly. GEM or other coloring techniques I know don't really help there, as they can only track two strongly-linked starting assumptions at the same time. Tracking three or more on the same grid manually seems pretty hard, but that's exactly what one would need to use a SIS > 2 as the starting point.

What would interest me is figuring out a manually applicable way to find Kraken eliminations directly. GEM or other coloring techniques I know don't really help there, as they can only track two strongly-linked starting assumptions at the same time. Tracking three or more on the same grid manually seems pretty hard, but that's exactly what one would need to use a SIS > 2 as the starting point.

- SpAce
**Posts:**224**Joined:**22 May 2017

Sudtyro2,

After critically reviewing my second post I pulled it because keeping it succinct had caused it to be somewhat distorted, the example was poor, and regarding what you seemed to be aiming to achieve it didn't help much. A major factor was that, unlike you, I won't use branched networks until I've exhausted all other options.

The same factor also bears on the use of oddagons and fish. The more complex fish require too much case by case analysis to be acceptable for me or most manual solvers – but where the dividing line should be placed is a moot point. In comparison, checking for oddagons can be done quite easily and is worth trying first. However, as you found, for one to be of use, a minimum set of guardians must provide suitable ongoing links to produce a useable deduction.

The impossible fish pattern I identified is a bit of an odd ball exception to the above as it provides a series of overlapping oddagons to use. It's relatively easy to spot and it allows the two potential guardian sets for all of them to be identified simultaneously: the external candidates in either the same rows (set A) or the same columns (set B) as the fish. As each of these sets must contain at least one truth, the linking opportunities are easier to identify (but they may not kill the puzzle which was what you were aiming for).

From a quick review of the grid in the post you referenced (well remembered!), it didn't have a simple impossible fish. The situation seemed far more complicated to analyse and included potential rival fish, whereas there was a simple oddagon available that produced the same elimination.

DPB

.

After critically reviewing my second post I pulled it because keeping it succinct had caused it to be somewhat distorted, the example was poor, and regarding what you seemed to be aiming to achieve it didn't help much. A major factor was that, unlike you, I won't use branched networks until I've exhausted all other options.

The same factor also bears on the use of oddagons and fish. The more complex fish require too much case by case analysis to be acceptable for me or most manual solvers – but where the dividing line should be placed is a moot point. In comparison, checking for oddagons can be done quite easily and is worth trying first. However, as you found, for one to be of use, a minimum set of guardians must provide suitable ongoing links to produce a useable deduction.

The impossible fish pattern I identified is a bit of an odd ball exception to the above as it provides a series of overlapping oddagons to use. It's relatively easy to spot and it allows the two potential guardian sets for all of them to be identified simultaneously: the external candidates in either the same rows (set A) or the same columns (set B) as the fish. As each of these sets must contain at least one truth, the linking opportunities are easier to identify (but they may not kill the puzzle which was what you were aiming for).

From a quick review of the grid in the post you referenced (well remembered!), it didn't have a simple impossible fish. The situation seemed far more complicated to analyse and included potential rival fish, whereas there was a simple oddagon available that produced the same elimination.

DPB

.

- David P Bird
- 2010 Supporter
**Posts:**1008**Joined:**16 September 2008**Location:**Middle England

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