The New Sudoku Players' Forum

[eleven]

I should be in a position to deliver the stats for the full lot by the end of the next week.

One more comment: With 3.6+% exocets for ER 6.2+, i guess that Denis should have enough random puzzles to see, if there is a strong bias (which i personally don't believe).
However i don't know, if you can give him a binary or if Denis can give you the puzzles to check it ...

[denis_berthier]

As the minimum obvious precautions I had indicated in the "grey zone" thread (http://forum.enjoysudoku.com/the-sudoku-grey-zone-t31143-26.html) haven't been respected, the only conclusions that can be drawn from the above data are:
- JExocets present in the original puzzles are progressively destroyed when we modify a few givens;
- JExocets with 4 base digits are destroyed faster than JExocets with 3 base digits.
Not a real surprise.
We don't even get the slightest idea of the mean speed at which they are destroyed as the distance from the original puzzles grows.

Vicinity search has confirmed the intuition (originally eleven's, as far as I can remember) that hard puzzles (wrt SER) were somehow grouped like mountain peaks. However, this doesn't imply that easy puzzles cannot be in the close vicinity of the hardest ones. We haven't yet any idea how often this can happen; maybe from most of the summits, one can find very deep SER crevices after only a few steps that wouldn't be enough to destroy the JExocets.

With 3.6+% exocets for ER 6.2+, i guess that Denis should have enough random puzzles to see, if there is a strong bias (which i personally don't believe).
However i don't know, if you can give him a binary or if Denis can give you the puzzles to check it ...

I wouldn't be able to run a Windows binary. But anyone can generate millions of puzzles with SER between 6.2 to 7.5 in a few seconds; they will be biased wrt to the number of givens but much less wrt JExocet than if you start with the extreme ones.

[champagne]

the only conclusions that can be drawn from the above data are:
- JExocets present in the original puzzles are progressively destroyed when we modify a few givens;
- JExocets with 4 base digits are destroyed faster than JExocets with 3 base digits.

I have nothing against negative comments, but the vocabulary should stick to facts. Is really the word "destroy" appropriate

Original file 2400 Jexocets 3 digits 676 000 Jexocets 4 digits

new files equivalent more or less to 10% of these
grey area 708k Jexocets 3 digits 1.3 million Jexocets 4 digits
green area 226 K Jexocets 3 digits 220 K jexocets 4 digits

is really 2400 to 1 million a destruction??

Note, these are rough figures, I don't have a quick split for puzzles having a multi Jexocets pattern; I'll make a deeper analysis at the end.

But anyone can generate millions of puzzles with SER between 6.2 to 7.5 in a few seconds; they will be biased wrt to the number of givens but much less wrt JExocet than if you start with the extreme ones.

I can't. But I am interesting in having a description of such a process supposed to receive the label "acceptable to draw conclusion"

[denis_berthier]

the only conclusions that can be drawn from the above data are:
- JExocets present in the original puzzles are progressively destroyed when we modify a few givens;
- JExocets with 4 base digits are destroyed faster than JExocets with 3 base digits.

I have nothing against negative comments, but the vocabulary should stick to facts. Is really the word "destroy" appropriate

I didn't know that saying that a pattern can be destroyed was such an obscenity.

BTW, I commented the facts you had provided.You are now providing additional data, which suggest additional comments.

Original file 2400 Jexocets 3 digits 676 000 Jexocets 4 digits
new files equivalent more or less to 10% of these
grey area 708k Jexocets 3 digits 1.3 million Jexocets 4 digits
green area 226 K Jexocets 3 digits 220 K jexocets 4 digits
is really 2400 to 1 million a destruction?

Wait. Which "original file"? Which size? Which 10% (upper part, lower part, random?)
How many puzzles do you generate from one in the original file?
How many puzzles in the "new file"?
How many of these 708k J3's in the new file come from a J3 or from the partial destruction of a J4 or J5 in the original file?

How many of these JExocets are degenerated? How many eliminations do they allow (after at least SSTS has been applied)?

But anyone can generate millions of puzzles with SER between 6.2 to 7.5 in a few seconds; they will be biased wrt to the number of givens but much less wrt JExocet than if you start with the extreme ones.

I can't. But I am interesting in having a description of such a process supposed to receive the label "acceptable to draw conclusion"

Take suexg (or any other top-down generator) and filter the results for the desired SER interval. Within [6.2, 7.5], there should be no problem. It will be biased but less than starting from puzzles saturated with Exocets.

Do you have a means of detecting only what I'll call basic J3-(or J4-) Exocets, i.e. with this definition (http://forum.enjoysudoku.com/jexocet-pattern-defintion-t31133-12.html) but with each base digit restricted to two ROWS in the S cells (in case the S lines are COLUMNS) and not decided in these rows - or with rows and columns playing inverse roles? (I mean no blocks are taken into account, no column is allowed to cover an S column.)

[David P Bird]

Here's an interesting case (one of two) arising from a puzzle posted by Champagne on page 3

The base cells hold 3 digits (124) but in the S cells only one instance of digit (2) is possible - in column 1.
Consequently (2) can be eliminated immediately from the base digits, as either, it would have to occupy both target cells, or one target cell and another cell in sight of the base cells.

4..........57..6...1..5..2..8.6.9.....3.7.9.....3...4..2..8..1...7..35..........2; ;1;0;r4c5 r6c5 r2c6 r8c4 124

Code: Select all

 *-------------------------*-------------------------*-------------------------*
 | <4>     3679    2689    | 289-1   2369-1  1268    | 1378    35789   35789-1 |
 | 2389    39      <5>     | <7>     239-14  #14-28  | <6>     389     1'34'89 | S
 | 36789   <1>     689     | 89-4    <5>     468     | 3478    <2>     3789-4  |
 *-------------------------*-------------------------*-------------------------*
 | 257-1   <8>     124     | <6>     #14-2   <9>     | 1237    357     357-1   |
 | 1'256   4'56    <3>     | 258-14  <7>     258-14  | <9>     568     1'568   | S
 | 25679-1 5679    1269    | <3>     #1-2    258-1   | 1278    <4>     5678-1  |
 *-------------------------*-------------------------*-------------------------*
 | 3569    <2>     469     | 459     <8>     567-4   | 347     <1>     3679-4  |
 | 1'689   4'69    <7>     | #14-29  269-14  <3>     | <5>     689     4'689   | S
 | 35689-1 3569-4  14689   | 1459    69-14   567-14  | 3478    36789   <2>     |
 *-------------------------*-------------------------*-------------------------*
     1       4                                                          14

JExocet:(124)r46c5,r2c6,r8c4
Eliminations:
r46c5 <> 2 (the partial fish cells can hold only one instance in column 1)
r2c6 <> 28, r8c4 <> 29 (non-base digits in the target cells)
r1c5 <> 1, r289c5 <> 14, r5c46 <> 14, r6c6 <> 1, (seen by the base cells)
r1c4 <> 1, r3c4 <> 4, r7c6 <> 4, r9c6 <> 14 (seen by both target cells)
r469c1,r146c9 <> 1, r9c2,r37c9 <> 4 (fin cells)

A couple of thoughts I've had while I've been looking for illustrative examples*:

1. I like Denis's idea of adding the number of base digits to the description because it gives 3 character abbreviations, JE3 & JE4, that can be searched for in the forum.

2. A characteristic of JEs is that the base digits typically occur as two givens all of which are absent from one band of boxes. Therefore I agree that using the number of givens in a puzzle, there must be particular ranges that would favour JE3s & JE4s.

*Champagne have you got a set of moderate puzzles containing different types of Exocets? Without a solver program I'm not making much progress finding suitable puzzles.

[Edit fin eliminations corrected - thanks to Leren]

[champagne]

*Champagne have you got a set of moderate puzzles containing different types of Exocets? Without a solver program I'm not making much progress finding suitable puzzles.

Hi David,

As I wrote above, I have 3.6% * 12 millions (about 450k) of such puzzles.

I have now pending the next load of puzzles generated out of the file of potential hardest.

If you can wait one week, till the end of that phase, I promise a deep analysis of the results. Generating, filtering, rating ... 300 millions ED puzzles is a huge task.

I can tell you that from the stats, if the frequency is lower, we have a lot of new combinations of Jexocets in the same puzzle, but the huge majority remains the classical Jexocet 3 or 4 digits

[David P Bird]

Hi Champagne,

Thanks. I've no problems waiting for a while – having a reasonable sized sample to browse would save me a lot of work.

David

[eleven]

But anyone can generate millions of puzzles with SER between 6.2 to 7.5 in a few seconds; they will be biased wrt to the number of givens but much less wrt JExocet than if you start with the extreme ones.

I can't. But I am interesting in having a description of such a process supposed to receive the label "acceptable to draw conclusion"

Take suexg (or any other top-down generator) and filter the results for the desired SER interval. Within [6.2, 7.5], there should be no problem. It will be biased but less than starting from puzzles saturated with Exocets.

I made a quick test.
It would take me almost 3 hours (on one core) to generate a mio pseudo random puzzles and rate them with sfkr. There should be about 500 9.x puzzles, 30000 8.x, 190000 7.x and 55000 6.2-6.9 in them.
I should have a free CPU over the weekend, so i hope, that i can generate a bigger set of 6.2+ puzzles then.

[champagne]

I made a quick test.
It would take me almost 3 hours (on one core) to generate a mio pseudo random puzzles and rate them with sfkr. There should be about 500 9.x puzzles, 30000 8.x, 190000 7.x and 55000 6.2-6.9 in them.
I should have a free CPU over the weekend, so i hope, that i can generate a bigger set of 6.2+ puzzles then.

I was expecting worst results. It's not so bad, at least for the "green area". I guess these are ED minimal puzzles. Just for information, my cut off green/grey is "aligned triplet". So the command "-r<7.6" could speed up the filtration.

I do it (with skmpp but it's just faster) in 2 steps

equivalent to skfr "-r<6.2" to clean the lower fraction
equivalent to skfr "-r<7.5" to have the split green/grey area

[champagne]

A first indication on what happens on Jexocets for lower ratings

I have analysed a lot of 31 millions puzzle in the area SER 7.6 -> not "potential hardest" (A)
and a lot of 12 millions puzzles in the area SER 6.2 to 7.5 (B)

I got the following results

Jexocets/total number of puzzles
(0) 76% (last status of the "potential hardest" file)
(A) 13%
(B) 3.6%

Jexocets 3 digits / Jexocets 4 digits

(0) 0.35%
(A) 60%
(B)105%

this corresponds more or less to puzzles generated by the first 10% of the file of "potential hardest"

I have now covered a little less than 2/3 of the way.

I have
114 millions ED puzzles in the grey area
34 millions ED puzzles in the green area.
(888k in the data base or potential hardest)

the frequency is slightly growing and the ratio J3/J4 slightly decreasing, but no true change in the tendency.

One key question is now how to define the target to serve david's expectations.
Just to give an idea, the number of "strange puzzles" (more than 2 Jexocets in the same puzzle or a mix of J3 and J4) in the green area is 40 000. This is my smallest number in the statistics.

[David P Bird]

Hi Champagne

One key question is now how to define the target to serve david's expectations.
Just to give an idea, the number of "strange puzzles" (more than 2 Jexocets in the same puzzle or a mix of J3 and J4) in the green area is 40 000. This is my smallest number in the statistics.

I'm looking for JExocets that illustrate how the various inferences in the primary band can be utilised when the conditions are suitable. Undoubtedly the possible interactions between two JEs in different bands will make for some interesting later research but will distract from the main points that need to be made. So the puzzles with just one JE are best for this purpose.

In particular I'd like to find cases where there are givens in the same mini-rows as well as the same mini-columns as the target, and also where there are almost locked sets in the JE band. I'm not expecting you to find these though!

My wish list is to split out:
Single JE3s
Single JE4s
Double JE4s
JE+s or twin JEs as you originally called them, where the two object cells contain a Almost Hidden Pair with single locked digit and any combination of base and non-base digits.
(According to blue the frequency, of JE++s where the Almost Hidden Set is larger is too small to make them worth searching for)

I don’t like using ABI loops on principle because I class them as assumptive net-based methods rather than patterns (nothing to do with assuming uniqueness). However as a method I appreciate that they are quite acceptable to many others. I'd therefore like to know if they allow the base pairs to be fully or partially resolved as you did before.

From my limited studies of them I think there are certain tell-tale signs that will indicate when two base digits can or cannot occur together:
a) are there UR threats for the digit pair?
b) do the two digits occur in the same boxes in the cross lines? (you've mentioned this yourself)
c) where are any givens provided for the two digits situated?
These could possibly be worked up into a set of qualifying conditions, but I can't say how complicated they would need to be and there are a lot of cases to explore.

It would also help if you could label any puzzles that also contain SK loops (I don't agree with ronk's distinctions)

So there you have what I'd like to do, and anything you can to help me would be appreciated.

David

[champagne]

In particular I'd like to find cases where there are givens in the same mini-rows as well as the same mini-columns as the target, and also where there are almost locked sets in the JE band. I'm not expecting you to find these though!

right, in the search for JEs, I have no chance to find that.

My wish list is to split out:
Single JE3s
Single JE4s
Double JE4s
JE+s or twin JEs as you originally called them, where the two object cells contain a Almost Hidden Pair with single locked digit and any combination of base and non-base digits.
(According to blue the frequency, of JE++s where the Almost Hidden Set is larger is too small to make them worth searching for)

I have no chance with my code to find AHS not in a cross line.
I see no reason not to have double JE3s, but I have to look for them
The only problem here is that these are the most common patterns. The corresponding files will have tens millions of puzzle
You should try to find extraction criteria. The other possibility is to produce a sample file (one every ....)

I don’t like using ABI loops on principle because I class them as assumptive net-based methods rather than patterns (nothing to do with assuming uniqueness). However as a method I appreciate that they are quite acceptable to many others. I'd therefore like to know if they allow the base pairs to be fully or partially resolved as you did before.

On my side, the "abi loop" is clearly a pattern and searched as such, may be because I made the analysis you mention later

It would also help if you could label any puzzles that also contain SK loops

This can be easily done. No idea so far about the volume, but the SK loop frequency seems to stay in the 1% to 2% area (in the grey and in the green zone)

The only problem is to have a process to match such big files. my previous process through ACCESS fails with files over 1GB

[David P Bird]

Hi Champagne

Thanks for your very encouraging response.

The only problem here is that these are the most common patterns. The corresponding files will have tens millions of puzzle
You should try to find extraction criteria. The other possibility is to produce a sample file (one every ....)

Because I'll be looking for those fruitful sub-patterns I mentioned, I think a sampling regime that produces files of about 1000 of each type would be best for me. But others with batch solvers may find them useful too so I wouldn't mind if you made them bigger than that – say 5000.

On my side, the "abi loop" is clearly a pattern and searched as such, may be because I made the analysis you mention later

Don't give up hope, there's still a chance that you may convert me!

BTW I'd like to congratulate you on how much your English has improved since you've been contributing here.

David

[denis_berthier]

J-Exocets in SudoRules

I have coded basic Jk-Exocets (k = 2, 3, 4, 5) in SudoRules.
By basic, I mean that, for each base digit, the instances of this digit in the S lines are covered by 2 orthogonal lines (no blocks are considered).

My rules are not yet fully tested, but I've tried them on the first puzzles in the "04a double exocet.txt" file in Champagne 2012-10-20. I chose the highest level ones because the results should be insensitive to the presence of other rules (here SSTS).
I find the same base digits and cells and the same target cells as in this list. As the eliminations are not listed, I can't check them.
So, here is what I get for the first 10 puzzles.

Hidden Text: Show

Code: Select all

(solve "1......8...71....6.9.....5...56....7..17.4..5......34.57.2.............2..2.61...")
*****  SudoRules 16.2 based on CSP-Rules 1.2, config: SSTS+Exocets   *****
1......8...71....6.9.....5...56....7..17.4..5......34.57.2.............2..2.61...
23 givens, 250 candidates, 1887 csp-links and 1887 links. Initial density = 1.51566265060241
singles ==> r8c2 = 1, r6c1 = 7
whip[1]: r9n7{c8 .} ==> r8c7 <> 7
whip[1]: r9n7{c8 .} ==> r8c8 <> 7
hidden-single-in-a-column ==> r9c8 = 7
whip[1]: r6n6{c3 .} ==> r5c1 <> 6, r5c2 <> 6
J4-Exocet-in-columns:
     base digits = n4, n9, n3, n8
     base cells = r7c5, r7c6
     S columns = c4, c3, c9
     target cells = r8c3, r9c9
      ==> r8c3 <> 6
J4-Exocet-in-columns:
     base digits = n8, n9, n3, n4
     base cells = r9c1, r9c2
     S columns = c3, c4, c9
     target cells = r8c4, r7c9
      ==> r8c4 <> 5, r7c9 <> 1



(solve ".23.....94.....1...9..3..4.2..81...4.....78..9...4...23...9...1.6..........5.....")
*****  SudoRules 16.2 based on CSP-Rules 1.2, config: config: SSTS+Exocets   *****
J4-Exocet-in-columns:
     base digits = n6, n7, n5, n8
     base cells = r1c7, r1c8
     S columns = c9, c1, c5
     target cells = r3c1, r2c5
      ==> r3c1 <> 1, r2c5 <> 2
J4-Exocet-in-columns:
     base digits = n7, n8, n5, n6
     base cells = r2c2, r2c3
     S columns = c1, c5, c9
     target cells = r1c5, r3c9
      ==> NO ELIMINATION


(solve "..3..6...45.7.....7...3..4.2................8..46...7......19....75...3...53...61")
*****  SudoRules 16.2 based on CSP-Rules 1.2, config: SSTS+Exocets   *****
J4-Exocet-in-columns:
     base digits = n1, n9, n2, n8
     base cells = r2c5, r2c6
     S columns = c4, c3, c8
     target cells = r3c3, r1c8
      ==> r3c3 <> 6, r1c8 <> 5
J4-Exocet-in-columns:
     base digits = n8, n9, n1, n2
     base cells = r1c1, r1c2
     S columns = c3, c4, c8
     target cells = r3c4, r2c8
      ==> NO ELIMINATION



(solve "...4..7......89.3..8..3...4.7.3...4.6....5....359...7.........1.4.8...9...2......")
*****  SudoRules 16.2 based on CSP-Rules 1.2, config: SSTS+Exocets   *****
J4-Exocet-in-columns:
     base digits = n1, n6, n2, n5
     base cells = r2c7, r2c9
     S columns = c8, c2, c4
     target cells = r1c2, r3c4
      ==> r3c4 <> 7, r1c2 <> 9
J4-Exocet-in-columns:
     base digits = n5, n6, n1, n2
     base cells = r1c5, r1c6
     S columns = c4, c2, c8
     target cells = r2c2, r3c8
      ==> NO ELIMINATION



(solve "....8..5..1.....3...23..7....45...7.9.....2.......64...9..1.....8..6......54....7")
*****  SudoRules 16.2 based on CSP-Rules 1.2, config: SSTS+Exocets   *****
whip[1]: c8n2{r9 .} ==> r7c9 <> 2, r8c9 <> 2
whip[1]: c7n5{r7 .} ==> r8c9 <> 5
whip[1]: c7n5{r8 .} ==> r7c9 <> 5
whip[1]: c5n5{r2 .} ==> r3c6 <> 5
whip[1]: c5n5{r3 .} ==> r2c6 <> 5
whip[1]: c2n4{r3 .} ==> r1c1 <> 4, r2c1 <> 4, r3c1 <> 4
J4-Exocet-in-rows:
     base digits = n6, n8, n1, n9
     base cells = r5c8, r6c8
     S rows = r4, r3, r9
     target cells = r3c9, r9c7
      ==> r9c7 <> 3, r3c9 <> 4
J4-Exocet-in-rows:
     base digits = n1, n9, n6, n8
     base cells = r1c7, r2c7
     S rows = r3, r4, r9
     target cells = r4c9, r9c8
      ==> r9c8 <> 2, r4c9 <> 3



(solve "1.....7....71.9...68..7......1.9.6.....3...2..4......3..8.6.1..5......4......2..5")
*****  SudoRules 16.2 based on CSP-Rules 1.2, config: SSTS+Exocets   *****
whip[1]: r2n6{c9 .} ==> r1c8 <> 6, r1c9 <> 6
J4-Exocet-in-columns:
     base digits = n2, n5, n3, n4
     base cells = r3c4, r3c6
     S columns = c5, c3, c7
     target cells = r1c3, r2c7
      ==> r2c7 <> 8, r1c3 <> 9
J4-Exocet-in-columns:
     base digits = n3, n4, n2, n5
     base cells = r2c1, r2c2
     S columns = c3, c5, c7
     target cells = r1c5, r3c7
      ==> r3c7 <> 9, r1c5 <> 8



(solve "1...5......7..9....8.3...4.....7.3...3.2....4..5..362...8..1..2.6.8..4..9.......8")
*****  SudoRules 16.2 based on CSP-Rules 1.2, config: SSTS+Exocets   *****
whip[1]: c9n6{r3 .} ==> r1c8 <> 6, r2c8 <> 6
J4-Exocet-in-rows:
     base digits = n7, n9, n1, n5
     base cells = r7c7, r9c7
     S rows = r8, r3, r5
     target cells = r3c9, r5c8
      ==> r5c8 <> 8, r3c9 <> 6
J4-Exocet-in-rows:
     base digits = n5, n9, n1, n7
     base cells = r4c9, r6c9
     S rows = r5, r3, r8
     target cells = r3c7, r8c8
      ==> r8c8 <> 3, r3c7 <> 2



(solve "......7....71.9...68..7......1.9.6.....3...2..4......3..8.6.1..5......4..1...2..5")
*****  SudoRules 16.2 based on CSP-Rules 1.2, config: SSTS+Exocets   *****
whip[1]: r2n6{c9 .} ==> r1c8 <> 6
whip[1]: r2n6{c9 .} ==> r1c9 <> 6
J4-Exocet-in-columns:
     base digits = n2, n5, n3, n4
     base cells = r3c4, r3c6
     S columns = c5, c3, c7
     target cells = r1c3, r2c7
      ==> r2c7 <> 8, r1c3 <> 9
J4-Exocet-in-columns:
     base digits = n3, n4, n2, n5
     base cells = r2c1, r2c2
     S columns = c3, c5, c7
     target cells = r1c5, r3c7
      ==> r3c7 <> 9, r1c5 <> 8



(solve "12...67....7....63....7.........8.9..4.5.......1.2.3..5....4......9....8..2.6.1..")
*****  SudoRules 16.2 based on CSP-Rules 1.2, config: SSTS+Exocets   *****
whip[1]: r2n1{c4 .} ==> r3c6 <> 1, r3c4 <> 1
J4-Exocet-in-columns:
     base digits = n5, n8, n4, n9
     base cells = r1c8, r1c9
     S columns = c7, c3, c5
     target cells = r3c3, r2c5
      ==> r3c3 <> 6, r3c3 <> 3, r2c5 <> 1
J4-Exocet-in-columns:
     base digits = n4, n9, n5, n8
     base cells = r2c1, r2c2
     S columns = c3, c5, c7
     target cells = r1c5, r3c7
      ==> r3c7 <> 2, r1c5 <> 3



(solve "98.7.......7.65.........7..7...4..3..2......1..95..6..1......2...59..8.......3..4")
*****  SudoRules 16.2 based on CSP-Rules 1.2, config: SSTS+Exocets   *****
whip[1]: r2n9{c7 .} ==> r3c9 <> 9, r3c8 <> 9
whip[1]: r1n5{c7 .} ==> r3c9 <> 5, r3c8 <> 5
J4-Exocet-in-columns:
     base digits = n2, n3, n1, n4
     base cells = r1c5, r1c6
     S columns = c4, c3, c7
     target cells = r3c3, r2c7
      ==> r3c3 <> 6, r2c7 <> 9
J4-Exocet-in-columns:
     base digits = n2, n4, n1, n3
     base cells = r2c1, r2c2
     S columns = c3, c4, c7
     target cells = r3c4, r1c7
      ==> r3c4 <> 8, r1c7 <> 5


It appears that 3 out of the 10 secondary JExocets allow no elimination.
Counting JExocets without checking whether they are useful is therefore not a good idea.

[champagne]

[b]

It appears that 3 out of the 10 secondary JExocets allow no elimination.
Counting JExocets without checking whether they are useful is therefore not a good idea.

Hi Denis,

Even if you don't use the abi loop, it would be good to code completely the exocet rules.

In the case of double exocets, forgetting to apply the "double" rule leads to a completely wrong picture.

For the first one, the situation seen by my solver is the following

the double exocet appears in that position

Code: Select all

1     23456 346   |3459  234579 235679 |2479  8    349   
2348  23458 7     |1     234589 23589  |249   239  6     
23468 9     3468  |348   23478  23678  |1247  5    134   
--------------------------------------------------------
23489 2348  5     |6     12389  2389   |1289  129  7     
2389  238   1     |7     2389   4      |2689  269  5     
7     268   689   |589   12589  2589   |3     4    189   
--------------------------------------------------------
5     7     34689 |2     3489   389    |14689 1369 13489
34689 1     34689 |34589 345789 35789  |45689 369  2     
3489  348   2     |34589 6      1      |4589  7    3489 


r7c5r7c6 r8c3 r9c9
r9c1r9c2 r8c4 r7c9

giving immediately (no uniqueness assumption in that)

r7c3=6
r9c4=5
r8c8=6

the puzzle is nearly solved