## exocet pattern in hardest puzzles

Advanced methods and approaches for solving Sudoku puzzles
ronk wrote:
champagne wrote:Third group is a small list of other situations as example SK + BB . . .
dukdiamond1,coloin 3.2 SK *bb(2)r5c1289 r3c6 r7c4

I find the SK-loop and BB r46c5 r3c6 r7c4. What does r5c1289 have to do with it?

Good remark ronk. Let me try to answer with may-be to many details.

Preliminary statements :

1) Don't forget this is a kind of research.
2) For the time being, the solver scans all AC2 and all bi cells fo the form 123 123.

r5c1289 is (as r5c46) an AC2/AALS/AAHS and, as such, is scanned.
I think one reason why I included these patterns in the scan is that one fo the SLG constructions made by Allan for Golden Nugget had a similar definition.
3) The scan is done once. The idea is to focus on such patterns as a player could do,
4) When the SK loop is there, the scan is done after the SK loop has been cleaned. Forother puzzles, it is done the first time the solver reach the corresponding level of difficulty.

Back to our puzzle after SK loop was cleaned

Code: Select all
`1.......2.2.....6...34..5.....8.5.....8.3.9.....9.4.....5..34...7.....1.6.......7 dukdiamond1,coloin 3.2 SK *bb(2)r5c1289  r3c6 r7c41      45g89  46h79 |3e567 589   6789  |378   34j89  2      45G89  2      479   |13E57 589   1789  |1i378 6      34J89  7Â89   6H89   3     |4     12a67 12A67 |5     7ä89   1I89   -----------------------------------------------------------23479b 13469B 1267  |8     1267  5     |1267  2347   1346   2457   1456   8     |12q67 3     1267Ã |9     2457   1456   2357   1356   1267  |9     1267  4     |1267  23578c 13568C -----------------------------------------------------------2p89   1k89   5     |1267d 1267D 3     |4     2r89   6n89   3l489  7      249   |256   4f589 2689  |236N8 1      35m89  6      3L489  1K249 |125   4F589 1289  |238   35M89  7 `

Just some statistic to start. after the SK loop was found, with a scan including all AC2's, the solver found many flying fishes.

Eliminating redundancy and inactive ones, I found (about)

It seems to me that this is a common situation after a SK loop clearing. It is much less in other cases.

Let's concentrate now on partial Exocets.

First group found by the solver uses theses flying fishes

Code: Select all
`7r5c18  => r1c3  r7c4 => r1c6  r7c4 => r1c7  r7c4 => r2c3  r7c4 => r2c6  r7c4          => r2c7  r7c4 => r3c5  r7c4 => r3c6  r7c4 => r4c5  r7c4 => r6c5  r7c41r5c29  => r2c7  r7c4 => r3c6  r7c4 => r3c6  r9c36r5c29  => r1c3  r7c4 => r3c6  r7c4 => r3c6  r8c7`

and the solver finds
AC2:r5c29 one match
1r5c29 6r5c29 => r3c6 r7c4
AC2:r5c1289 three match (among them 2 with double target)
6r5c29 7r5c18 => r1c3 r7c4 => r3c6 r7c4
1r5c29 6r5c29 => r3c6 r7c4 (the same as above)
1r5c29 7r5c18 => r2c7 r7c4 => r3c6 r7c4

Second group is yours

Code: Select all
`1r46c5   => r2c7  r7c4 => r3c6  r5c2 => r3c6  r7c4 => r3c6  r9c3 => r5c9  r7c46r46c5   => r1c3  r7c4 => r3c6  r5c9 => r3c6  r7c4 => r3c6  r8c7 => r5c2  r7c4`

AC2:r46c5 one match
1r46c5 6r46c5 => r3c6 r7c4
AC2:r124689c5 one match (in fact it s the same)
1r46c5 6r46c5 => r3c6 r7c4

At the end, we have four "small" exocets (six if we split the "double matchs")

6r5c29 7r5c18 => r1c3 r7c4 => r3c6 r7c4
1r5c29 6r5c29 => r3c6 r7c4
1r5c29 7r5c18 => r2c7 r7c4 => r3c6 r7c4
1r46c5 6r46c5 => r3c6 r7c4

Only two of them are seen by the solver as being eliminated due to the double XWing pattern

6r5c29 7r5c18 => r1c3 r7c4
6r5c29 7r5c18 => r3c6 r7c4

Again, this is research. Does it bring enough simplification in the path after the SK loop has been found, this has to be analyzed. For the time being, I am focusng on a clean process of full Exocet pattern.

Sorry for such a long answer, I did not feel confortable with a shorter one

champagne
champagne
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champagne wrote:Sorry for such a long answer, I did not feel confortable with a shorter one

If you showed how any of that leads to an elimination, I don't see it. Using r5c1289, would you please clarify the eliminations(s) found?

[edit: BTW I found the BB r46c5 r3c6 r7c4 resulted in 10 eliminations: r123c5<>7, r3c6<>789, r7c4<>2, r789c5<>2 ]
ronk
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ronk wrote:
champagne wrote:Sorry for such a long answer, I did not feel confortable with a shorter one

If you showed how any of that leads to an elimination, I don't see it. Using r5c1289, would you please clarify the eliminations(s) found?

Each of these flying fishes provides additional weak links. Normally no direct elimination.

Partial BBs as
6r5c29 7r5c18 => r1c3 r7c4
6r5c29 7r5c18 => r3c6 r7c4

leading to double XWing eliminate super candidate.

We need a full BB to apply the Allan Barker findings.
We need a favourable combination of super candidates eliminations to do something equivalent to <7>r1c7 in Golden Nugget.

New weak links ease the procss, but the result is unpredictable.

I compared the two paths of the solver with existing processing of these patterns (scanning for BBs and without scan) .
The éliminations are shorter, undoubtly, but as more doors have been opened, the solver gives parallel and redundant paths in which one has to sort the best one.

I'll likely rework later that puzzle to check the process on several points.

ronk wrote:[edit: BTW I found the BB r46c5 r3c6 r7c4 resulted in 10 eliminations: r123c5<>7, r3c6<>789, r7c4<>2, r789c5<>2 ]

Nothing to object . I have indirect quick eliminations as well, but not these ones. May be you can explain how you came to that conclusion

champagne
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Im prepared to be shot down here......but arnt we going to have a different solution path from the outset - depending on which elimination is found and performed first.

Every "wrong" pencil mark can be shown to be wrong by foul means or fair.

As it happens the BB approach is deemed to be fair - so would I be right in saying that the initial elimination as found by champagne is perhaps deemed the easist ?.

And how are we comparing these eliminations in terms of complexity......because Im not sure.

Sudoku Explainer did it and we never understood that even now ! Indeed the SE rating in these puzzles is a fairly "mediocre" ~ 10.9.

Several eliminations will lead to a clue insertion - and this will pretty much crack the puzzle.

C
coloin

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coloin wrote:Im prepared to be shot down here......but arnt we going to have a different solution path from the outset - depending on which elimination is found and performed first.

Every "wrong" pencil mark can be shown to be wrong by foul means or fair.

C

If the topic is weekender, SK loop is the killer for that puzzle.

The standard processing including SK loop is 4.5 seconds and 77K print, same order of magnitude as Easter Monster.

For puzzles having SK loop, there is not that much to add, just to concentrates on the double belt is usually enough to crack it. As far as I can see, there are small chances to improve substantially the solution using BB’s, but I’ll check that on a debugged version of the program.

I did not try to reverse priorities scanning first BB’s before SK loop, but the work done by Allan Barker let me think that when the SK loop is there you have very small chances to find an EXOCET/ full”bb”. (it applies normally to AC2s/AAHS/AALS).

coloin wrote:Every "wrong" pencil mark can be shown to be wrong by foul means or fair.

As it happens the BB approach is deemed to be fair - so would I be right in saying that the initial elimination as found by champagne is perhaps deemed the easist ?.

C

This is still very fresh stuff. For sure, finding a BB pattern when it is located within a band/stack is something a player can do. Likely easier than many of the AIC’s nets crossing ALS/AC’s.

It seems to be the most common pattern and to have a very high frequency in the family of hardest puzzles.

Then, no doubt, focusing on that pattern is very destructive for the puzzle (and gives a path quite different of classical ones).

At the end, I rally completely your statement, If there is no SK loop, try first to locate Flying fishes.

Another important point is that the pattern is there at the very beginning at a moment where there are not so many flying fishes and not so many possible starts (you are usually in a band/stack where none of the ¾ digits are given and the most common base pattern has 2 cells belonging to a row/column.)

coloin wrote:And how are we comparing these eliminations in terms of complexity......because Im not sure.

Sudoku Explainer did it and we never understood that even now ! Indeed the SE rating in these puzzles is a fairly "mediocre" ~ 10.9.

Several eliminations will lead to a clue insertion - and this will pretty much crack the puzzle.

C

Some long discussions took place in that forum, with a lot of statistics and correlation calculations to compare ranking tools.

I have to say that I did not find something very convincing. SK loop and now the EXOCET in the simplest form are easy to find compared to many of the moves classified as very complex by these ranking programs.

No surprise, using these tools, you get comparative results that don’t correlate to other programs. It was already the case with basic stuff. The length of a chain is not a concern if you use full tagging. It is as far as I can see in all other ranking methods.

Finally, if you take care to be consistent in the way you are handling all situations, the processing time is not that bad as a rough ranking indicator. (not very stable overtime unless you stop development)

Another advantage is that it can be closer to up to date ways to fight against puzzles.

champagne
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champagne wrote:
ronk wrote:[edit: BTW I found the BB r46c5 r3c6 r7c4 resulted in 10 eliminations: r123c5<>7, r3c6<>789, r7c4<>2, r789c5<>2 ]
Nothing to object . I have indirect quick eliminations as well, but not these ones. May be you can explain how you came to that conclusion

ronk, nice find!
Based on SK loop => r12c5<>7, r36<>89, r89c5<>2 .
For example, using BB r46c5 r3c6 r7c4 and bilocations 2’s r3c56 & 7’s r7c45:

r3c5<>7:
1- If r46c5=7 => r3c5<>7
2- If r46c5<>7 => r3c6 & r7c4<>7 => r7c5=7 => r3c5<>7

r3c6<>7
1- If r46c5<>7 => r3c6<>7
2- If r46c5=7 => r7c5<>7 => r7c4=7 => r3c6<>7

The same way for r7c45<>2

ttt
ttt

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Hi ttt and ronk,

I was reluctant to comment on that start because I had found a unexplained weak link coming out of the scan for flying fishes.
The problem is now fixed, so I can add small things.

The solver finds the same things, in a slightly different way, but surely with flyng fishes..

He also comes to r7c5 <2> , something found in the reference solution thru an AIC net in an easier way.
Here, elimination comes analyzing AC2r5c46 remaining super candidates

The most interesting (and most questionable) finding in that start is the following nice loop

Code: Select all
`1     4589  46j79 |3567 589  6789 |378   3489  2      4589  2     479   |1357 589  1789 |1J378 6     3489  789   6J89  3     |4    12a6 126  |5     789   1j89   -----------------------------------------------------------23479 13469 1267  |8    1267 5    |1267  2347  1346   2457  1456  8     |1267 3    1267 |9     2457  1456   2357  1356  1267  |9    1267 4    |1267  23578 13568 -----------------------------------------------------------289   1a89  5     |167f 167F 3    |4     289   6A89   3489  7     249   |256  4589 2689 |236a8 1     3589  6     3489  1A249 |125  4589 1289 |238   3589  7  `

Analyzing r3c89 and r7c89, the solver scanned the map for flyng fishes linked to 1r3c9 and 6r7c9.

He found 15 fishes in each case, among them
1r3c9 => r5c2 r7c5 giving the weak link 1r3c9 - 1r7c2
6r7c9 => r3c5 r5c2 giving the weak link 6r7c9 - 6r3c2

using the ALS/AHS/AC r7c45 we have the Nice Loop

[]1r3c9.j - 1r7c2.a = 1r7c45.A - 6r7c45.a = 6r7c9.A - 6r3c2.J

Combine with the SK double belt, this leads to immediate elimination of many super candidates.

I said this is questionnable just because I have no clue to detect the appropriate fishes in that situation and there are a lot of them..

The next problem for the solver (should not be a problem for a player) is that it opens so many parallel paths that the print is bigger than the reference one.

champagne
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Hi, all.

I have posted a collection of base/cover set logic loops for tarx0134, coly013, coly510, and ducdiamond1.
As Champagne has shown, ducdiamond has both BB logic and SK loops. The set logic solution, which was proposed by RonK, shows how the two are integrated together. RonK also suggested the Coly510 solution. Other examples show massive exoset damage .

I have put them all here in the More Monster .... thread.
Allan Barker

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champagne wrote:Analyzing r3c89 and r7c89, the solver scanned the map for flyng fishes linked to 1r3c9 and 6r7c9.

He found 15 fishes in each case, among them
1r3c9 => r5c2 r7c5 giving the weak link 1r3c9 - 1r7c2
6r7c9 => r3c5 r5c2 giving the weak link 6r7c9 - 6r3c2

using the ALS/AHS/AC r7c45 we have the Nice Loop

[]1r3c9.j - 1r7c2.a = 1r7c45.A - 6r7c45.a = 6r7c9.A - 6r3c2.J

Since tag 'j' excludes tag 'J' there isn't a contradiction, so what are the eliminations?
ronk
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ronk wrote:. . . .
Since tag 'j' excludes tag 'J' there isn't a contradiction, so what are the eliminations?

First of all, the only process I know providing immediate eliminations whatever is the context is Allan model.
The drawback is the size of the SLG, but with the new features he is implementing, the procss is more and more human.

In other processes, you quickly need indirect paths, unless you are prepared to build crazy AIC's nets.

This is a Nice loop without any elimination, which is very common as soon as you pass level 2 in the tagging process.

These loop point usually on some vicinity properties.

Here for example, you learn that 1r3c9.j - r7c2.a is in fact a strong link.
Same for 6r7c9.A - 6r3c2.J.

In the map of candidates, you can replace all 'j' by 'A' and all 'J' by 'a'.

Code: Select all
`1     4589  46j79 |3567 589  6789 |378   3489  2      4589  2     479   |1357 589  1789 |1J378 6     3489  789   6J89  3     |4    12a6 126  |5     789   1j89   ---------------------------------------------------23479 13469 1267  |8    1267 5    |1267  2347  1346   2457  1456  8     |1267 3    1267 |9     2457  1456   2357  1356  1267  |9    1267 4    |1267  23578 13568 ---------------------------------------------------289   1a89  5     |167f 167F 3    |4     289   6A89   3489  7     249   |256  4589 2689 |236a8 1     3589  6     3489  1A249 |125  4589 1289 |238   3589  7  `

becomes

Code: Select all
`1     4589  46A79 |3567 589  6789 |378   3489  2      4589  2     479   |1357 589  1789 |1a378 6     3489  789   6a89  3     |4    12a6 126  |5     789   1A89   ---------------------------------------------------23479 13469 1267  |8    1267 5    |1267  2347  1346   2457  1456  8     |1267 3    1267 |9     2457  1456   2357  1356  1267  |9    1267 4    |1267  23578 13568 ---------------------------------------------------289   1a89  5     |167f 167F 3    |4     289   6A89   3489  7     249   |256  4589 2689 |236a8 1     3589  6     3489  1A249 |125  4589 1289 |238   3589  7  `

If you now look at the double belt of the SK loop, you have immediate eliminations of super candidates:
The SK loop chained

Code: Select all
`r3c12 r3c89 r12c7  r89c7 r7c89 r7c12 r89c3 r12c36789  8917  1738   3826  2689  8912  1249  4967  loop                r46c7                   r46c3               17 26                   12 67`

An example of immediate clearing of super candidate

Code: Select all
`(8&9)r7c12 => (1&2)r89c3 =>(4&9)r12c3 => (6&7)r3c12 not 'a'                                  => 'a'                                 `

so (6&7)r3c12 . . . . is not valid.

This comes as well without that nice loop. It's just longer.
Showing that the double belt is in an exclusive or condition is nearly common to all SK loops.
The way to establish it is slightly different from one puzzle to another one.

Here you have in the same way
#(8&9)r3c12 . . .
(6&9)r37c2 . . . #(1&8)r37c9 . . .

and others. As I said before, multiple parallel paths are opened.

No real breakthrough, just a much easier path.

champagne
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An attempt on dukdiamond1

Code: Select all
`1.......2.2.....6...34..5.....8.5.....8.3.9.....9.4.....5..34...7.....1.6.......7 dukdiamond1After SK loop and ronk’s deductions *--------------------------------------------------------------------* | 1      4589   4679   | 3567   589    6789   | 378    3489   2      | | 4589   2      479    | 1357   589    1789   | 1378   6      3489   | | 789    689    3      | 4      126    126    | 5      789    189    | |----------------------+----------------------+----------------------| | 23479  13469  1267   | 8      1267   5      | 1267   2347   1346   | | 2457   1456   8      | 1267   3      1267   | 9      2457   1456   | | 2357   1356   1267   | 9      1267   4      | 1267   23578  13568  | |----------------------+----------------------+----------------------| | 289    189    5      | 167    167    3      | 4      289    689    | | 3489   7      249    | 256    4589   2689   | 2368   1      3589   | | 6      3489   1249   | 125    4589   1289   | 238    3589   7      | *--------------------------------------------------------------------*`

Present as diagram: => r9c3<>4

Code: Select all
`AALS(24679)r128c3 ||(479)r128c3* ||(2)r8c3--(2)r8c4 ||    |  || ||    | (6)r8c4-(6=hp17)r7c45-(1)r7c2=(1)r9c3*  ||    |  || ||    |  ||                   ||    |  ||                   ||    | (5)r8c4-(5)r8c9=(5)r9c8--(9)r9c8   ||    |                           ||        ||     ----------(2)r7c2=(2)r7c8-(9)r7c8  ||                                || ||                               (9)r78c9-(9)r3c9 ||                                         || ||                                        (8)r3c9-(8)r3c12=(hp58-4)r2c1/r1c2=(4)r12c3* ||                                         || ||                                        (1)r3c9 ||                                         | ||                                         | ||                                --------- ||                               |(6)r1c3-(6=ht789)r3c128-(89=1)r3c9------(1)r3c5                                  |      ||                                  |     (1)r7c5-(1)r7c2=(1)r9c3*                                  |      ||                                  |     (1)r46c5-(1)r5c46                                  |               ||                                   --------------(1)r5c9                                                  ||                                                 (1)r5c2-(1)r7c2=(1)r9c3*`

ttt
ttt

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ttt wrote:An attempt on dukdiamond1 ttt

Hi ttt,

A late indirect comment to your post, if the form of "how the solver defines the new path for that puzzle".

As I said before, I had to sort in the paralll paths (and to fix some bugs) to show what can be done.

The following image relfects how I think on should fight against the SK loop.

Use of Flying fishes eases the process, but that puzzle is solved as well without.

The full solution will be soon on the web site.

champagne
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Hi,

I have finished the reshaping of the solver version for Duke Diamond.
It can be found here

http://pagesperso-orange.fr/gpenet/UX/Sample8FM/FM_fichiers/DD00.htm

It can be accessed as well thru the "examples" index

This is far fo the solver path beyond what is published above, but it reflects my view of how one can fight againt a SK loop.

champagne
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Hi Champagne,

I think the following Duke Diamond elimination must be similar to your tagging solution above as it eliminates the same 8 candidates. The set logic shows a partially connected SK loop + 2 small asymmetric layers (digits 1,6). This is the most symmetrical mixed type example I have seen so far.

Code: Select all
`DUCE 68 Nodes, Raw Rank = 12 (linksets - sets)     20 Sets = {16R5 16C5 37N1 37N2 1289N3 1289N7 37N8 37N9}     32 Links = {1679r3 12689r7 1c29 3c7 4c3 6c29 8c7 9c389 1b357 2b9 6b159 7b13 8b39 9b17}     8 Eliminations, 0 Assignments -->   r28c1<>9, r19c2<>9, r19c8<>8, r28c9<>8`
Allan Barker

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Allan Barker wrote:Hi Champagne,

I think the following Duke Diamond elimination must be similar to your tagging solution above as it eliminates the same 8 candidates. The set logic shows a partially connected SK loop + 2 small asymmetric layers (digits 1,6). This is the most symmetrical mixed type example I have seen so far.

Hi Allan,

This is not a surprise for me. All that logic based on Flying fishes and Exocets is much closer to your model (don't forget I am using your permutation logic) than other paths.

Moreover, concentrating on the SK loop is what can be expected as next steps in your solution.

Still a lot of work to come, but all that is very interesting.

champagne
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