The New Sudoku Players' Forum

[champagne]

Together these points suggest
1) basic eliminations should be made before the search.
2) For each band determine which digits don't appear as givens and use that set to test for the base and target cells.
3) For green area puzzles only score hits with eliminations in the target cells.
4) For grey area puzzles score all hits.

As you can only do the screening in 3) above, I suggest you process the green area puzzles first.
In the longer term, I think using 2) above could speed up your code tremendously.

Eventually we could then evaluate where the green/grey boundary should be by seeing where the extra inferences help solve puzzles.

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.

I thought you were working towards that, but from your file headings you have mixed them up. However if you add the details of the pattern found as you've done on the ones you posted in the project files, it won’t matter so much as that file can be searched.

hi David,

Just for information, the run time in the JE search is not at all an issue. Rating puzzles is much more expensive.

I am thinking on how to filter "trivial cases" using your clues. IMO, some ideas as "no direct elimination" can be dangerous and I have to translate that in another filter.

I'll test an easy filter "don't start the search if the puzzles has more than xx (say 30) given after simples moves";

I did not extract puzzles with AHS, but you have them in the list either by the number of cells or by one code. I guess the number of cells is a better clue.

elimination of puzzles where a given of the base is in the band is easy,

I should have results this week

[eleven]

First of all, I found only 75 puzzles having the exocet pattern in the rand 8.6 file.

So even in hard (ER between 8.6 and 9) random puzzles exocets are very rare, less than 3 in 10000 puzzles (the ratio in unbiased random puzzles should be a bit worse, because they have more clues on average).

Then the many exocet puzzles with lower ratings you could find are a nice exotic collection.

[champagne]

First of all, I found only 75 puzzles having the exocet pattern in the rand 8.6 file.

So even in hard (ER between 8.6 and 9) random puzzles exocets are very rare, less than 3 in 10000 puzzles (the ratio in unbiased random puzzles should be a bit worse, because they have more clues on average).

Then the many exocet puzzles with lower ratings you could find are a nice exotic collection.

I basically agree, the only point is that we have to conclude (the price to pay for a better sample would be too high) with only one point representing 1/1000 of the sample file.

But I think that more points have a good chance to bring some comfort to the ratio you got.

Seen the size of the first run, a second run (say another +-3) can not be considered. May be one could try a +-1 outside the pattern to see what happens (still in the vicinity of the potential hardest file).

I have also been greatly struck by the similarity of the distribution of puzzles between your run and the sample file (after implicit adjustment of the fact that the 26 clues area has not yet been searched for potential hardest)

[David P Bird]

Champagne, thanks.

I also think we should standardise what we call "clues" or "givens". These are the occupied cells in the original puzzle. Where a cell has been reduced to a single it should be classed as "solved". At any stage in a solution "known" cells are those that were givens originally or have been solved.

My spreadsheet screens out cells containing band-givens but not band-solved because that shows when a pattern could possibly have been found earlier, but that’s an academic point. I think what you will be doing will be screening out band-knowns, which is better. It's only now that I realise I should have used knowns rather than givens in my previous posts.

Anyway I'm pleased you can screen them out and even though you say speed isn't an issue, I bet it will run faster!

To clarify "immediate eliminations", using bit encoding of the digits, to test for an elimination in the target cells all you have to do is
((Target1 OR Target2) AND NOT (Base1 OR Base2)) > 0

That's all I was suggesting, nothing more.

I look forward to getting your output.

David

[denis_berthier]

First of all, I found only 75 puzzles having the exocet pattern in the rand 8.6 file.

So even in hard (ER between 8.6 and 9) random puzzles exocets are very rare, less than 3 in 10000 puzzles (the ratio in unbiased random puzzles should be a bit worse, because they have more clues on average).

Yes, quite a bit worse. We could easily have a much closer estimate if we had the distribution of clues for these 75 puzzles.

[champagne]

sorry if this is off topic


corundum is quite a common mineral.

Sapphire and ruby are special forms of corundum

I have some difficulties to imagine what is the frequency of sapphire and ruby in the nature.

However, they are intensively searched.

Potential hardest have been searched for long. The frequency of such puzzles is much lower than some of our exotic patterns, nevertheless, many players in the field of sudoku spent a lot of time to find them.

I have doubt that the sapphire and ruby have in terms of tons a ratio jewels/corundum better than potential hardest or exotic patterns against all sudokus

For sure, all those who looked for hardest puzzles are crazy.

Humanity is always looking for something special. That's life

[David P Bird]

I think found one of your Double J3s in your lists today which is interesting as one target cell is common both Exocets.
98.7..6..5...4......3..9...4......5..6.2..7....9..3....1.....67...9...8.....281.. base set (345) tier 3.
However I can see other possibilities too which need to be sorted out!

And in a jiffy Leren finds this one
98.7.......7.65.........7..4...3..2..1......9..95..8..1......4...59..6.......2..3
After basic eliminations:

Code: Select all

 *----------------------------*----------------------------*----------------------------*
 | <9>      <8>      12346    | <7>      b124     b134     | T234-15  1356     12456    |
 | B23      B234     <7>      | 12348    <6>      <5>      | t1234-9  1389     1248     |
 | 2356    23456     t1234-6  | T234-18  9        1348     | <7>      1368     12468    |
 *----------------------------*----------------------------*----------------------------*
 | <4>      567      68       | 168      <3>      9        | 15       <2>      1567     |
 | 235678   <1>      2368     | 2468     2478     4678     | 345      3567     <9>      |
 | 2367     2367     <9>      | <5>      1247     1467     | <8>      1367     1467     |
 *----------------------------*----------------------------*----------------------------*
 | <1>      23679    2368     | 368      578      3678     | 259      <4>      2578     |
 | 2378     2347     <5>      | <9>      1478     13478    | <6>      178      1278     |
 | 678      4679     468      | 1468     14578    <2>      | 159      15789    <3>      |
 *----------------------------*----------------------------*----------------------------*
JE3:  (234)B=r2c12, T=r3c4, T=r1c7 => r3c4 <> 18, r1c7 <> 15
JE4: (1234)b=r1c56, t=r3c3, t=r2c7 => r3c3 <> 6,  r2c7 <> 9

Now either we have a single JExocet base digit pair that is common to both pairs of base cells or we have different base pairs in each. (This consideration has never struck me before because it's usually the first of these cases.) If they share the same digit pair then (1)r1c56,r2c7,r3c3 must be false making (1)r1c3 true and giving this chain
(1)r1c3 = (1)r3c3 &So (1)r1c56 = > r1c89 <> 1

But now we run out of eliminations using the JExocet inferences as far as I can see. To check if I missed anything I followed the effects of these two alternatives on tier 1 and arrived at these different versions.

Code: Select all

 *----------------------*----------------------*----------------------*
 | <9>    <8>    1      | <7>    2'4    34'    | 23'4   5'6    56'    |
 | 2'3    23'4   <7>    | 18'    <6>    <5>    | 234'   9      1'8    |
 | 5'6    56'    234'   | 23'4   9      1'8    | <7>    138'   12'48  |
 *----------------------*----------------------*----------------------*

 *----------------------*----------------------*----------------------*
 | <9>    <8>    2346   | <7>    124    134    | 234    356    2456   |
 | 23     234    <7>    | 2348   <6>    <5>    | 1234   9      1248   |
 | 2356   23456  1      | 234    9      348    | <7>    368    2468   |
 *----------------------*----------------------*----------------------*

The upper one is false but the tick markings show one of the ways the cells could be completed legitimately to satisfy the row and box constraints. The surprise is that in this case there are still two separate JE3 patterns with base pairs (23)r2c12 and (24)r1c56

Leren, it's clear that these assumptions about the two base digits repeating together in the different mini-lines can't be taken for granted, and there is still some more sorting out to be done!

[Edit As following posts reveal, I got this wrong. I didn't check that there could be 3 truths for each digit in the partial fish columns. The way the tick marks have been made in the wrong solution shows that (2) would be left unsatisfied.]

[eleven]

Sapphire and ruby are special forms of corundum

Its no loss for exocets, that Denis is no more interested in them

[blue]

For eleven (and all):

Here are some statistics for the puzzles in eleven's Grey and Green Zone puzzle lists.
The statistics include data for JExocets, and Exocets, and are presented in form used in this post.
(The A.3 and A.4 table entries are for JE3 and JE4 -- which is only a small part of the data represented here).

There are two sets of tables for each puzzle file.
The first set considers all exocets.
The second set (as per eleven's request) considers only exocets with "standard" eliminations.

Note: the "degenerate forms" of types A-D (where for some digits, not all of the S columns are used), can have eliminations that are not considered as "standard eliminations" for the purposes here. "Standard" eliminations (for this post) are defined as candidates for non-base digits in the target cells.

This is interesting: the "green zone" puzzles have a higher ratio of JExocets/Puzzles, than the "grey zone" puzzles.
(Actually they have more exocets per puzzle tested, for any of the exocet types).

Also interesting: compared with champagne's "potential hardest" list, these puzzles have a much larger ratio of general exocets to "JExocet-like" exocets.

One more note: For both puzzle lists, there were puzzles containing 100-200 exocets (of general type).
This didn't happen for champagne's "potential hardest" list.
For the grey zone puzzles, it was rare: nothing with >= 100 exocets, in the "filtered" tables, 8 with >= 100 in the "all" tables.
For the green zone, it happens often enough to effect the "exocets per 'puzzle with an exocet'" ratio -- 39 and 475 puzzles, respectively.

Code: Select all

Grey Zone, all exocets

282588 puzzles

       size                             Exocets
      +-------------------+--------------------+
      |    2     3      4 |     5      6     7 |
  +---+-------------------+--------------------+
t | A |    -   104     25 |     2      -     - |     131
y | B |    -   242   1387 |   371      3     - |    2003
p | C |    -    63     39 |     -      -     - |     102
e | D |    - 13956   3243 |   891      3     - |   18093
  +---+-------------------+--------------------+
  | G |    3  2419   1219 |   587     22     - |    4250
  | H |    1  8899   4328 |  1721     35     1 |   14985
  | K |  449 19237  11012 |  3926    222    12 |   34858
  | O | 3578 49186  20219 |  8069    224     6 |   81282
  +---+-------------------+--------------------+
        4031 94106  41472   15567    509    19    155704

       size                             Puzzles
      +-------------------+--------------------+
      |    2     3      4 |     5      6     7 |
  +---+-------------------+--------------------+
t | A |    -   104     25 |     2      -     - |     131
y | B |    -   237   1349 |   357      3     - |    1946
p | C |    -    58     31 |     -      -     - |      89
e | D |    -  7779   2086 |   544      1     - |   10410
  +---+-------------------+--------------------+
  | G |    1  2136   1053 |   519     21     - |    3730
  | H |    -  4620   2625 |  1070     30     1 |    8346
  | K |  293  9823   5970 |  2060    133     7 |   18286
  | O | 1121  6331   4063 |  1933    111     4 |   13563
  +---+-------------------+--------------------+
        1415 31088  17202    6485    299    12     56501


Code: Select all

Grey Zone, only exocets with standard eliminations

282588 puzzles

       size                             Exocets
      +-------------------+--------------------+
      |    2     3      4 |     5      6     7 |
  +---+-------------------+--------------------+
t | A |    -    38     13 |     -      -     - |     51
y | B |    -    80     40 |     1      -     - |    121
p | C |    -    42     13 |     -      -     - |     55
e | D |    -   263     79 |     6      -     - |    348
  +---+-------------------+--------------------+
  | G |    1   308    235 |    54      -     - |    598
  | H |    1   667    363 |    60      1     - |   1092
  | K |  159  4089   3444 |   760     66     4 |   8522
  | O |  699  3438   2096 |   307     24     1 |   6565
  +---+-------------------+--------------------+
         860  8925   6283    1188     91     5    17352

       size                             Puzzles
      +-------------------+--------------------+
      |    2     3      4 |     5      6     7 |
  +---+-------------------+--------------------+
t | A |    -    38     13 |     -      -     - |     51
y | B |    -    77     40 |     1      -     - |    118
p | C |    -    48     12 |     -      -     - |     50
e | D |    -   248     70 |     5      -     - |    323
  +---+-------------------+--------------------+
  | G |    1   292    216 |    50      -     - |    559
  | H |    1   576    310 |    53      1     - |    941
  | K |  134  2828   2447 |   587     47     3 |   6046
  | O |  207  1395   1091 |   189     15     - |   2897
  +---+-------------------+--------------------+
         860  8925   6283    1188     91     5    10985


Code: Select all

Green Zone, all exocets

582178 puzzles

       size                               Exocets
      +---------------------+--------------------+
      |     2      3      4 |     5      6     7 |
  +---+---------------------+--------------------+
t | A |     1    614    187 |    17      -     - |     819
y | B |     -   1230   6027 |  1396     10     - |    8663
p | C |     -    434    324 |    10      -     - |     768
e | D |     6  55719   9644 |  2265     13     - |   67647
  +---+---------------------+--------------------+
  | G |    24  10169   5706 |  2053     98     3 |   18053
  | H |    97  37445  16666 |  5786    152     4 |   60150
  | K |  7243 107787  64250 | 15315    876    20 |  195491
  | O | 68709 345185 142340 | 32760   1102    24 |  590120
  +---+---------------------+--------------------+
        76080 558583 245144   59602   2251    51    941711

       size                               Puzzles
      +---------------------+--------------------+
      |     2      3      4 |     5      6     7 |
  +---+---------------------+--------------------+
t | A |     1    612    186 |    16      -     - |     815
y | B |     -   1201   5796 |  1336      9     - |    8342
p | C |     -    386    289 |     8      -     - |     683
e | D |     5  29980   5970 |  1334      6     - |   37295
  +---+---------------------+--------------------+
  | G |    19   8017   4211 |  1584     68     3 |   13902
  | H |    57  17612   9537 |  3269    100     1 |   30576
  | K |  2899  37212  23100 |  5421    349    14 |   68995
  | O |  6748  23555  16559 |  5144    301     9 |   52316
  +---+---------------------+--------------------+
         9729 118575  65648   18112    833    27    212924


Code: Select all

Green Zone, only exocets with standard eliminations

582178 puzzles

       size                               Exocets
      +---------------------+--------------------+
      |     2      3      4 |     5      6     7 |
  +---+---------------------+--------------------+
t | A |     -    210     75 |     2      -     - |     287
y | B |     -    396    179 |     8      1     - |     584
p | C |     -    274     96 |     -      -     - |     370
e | D |     6   1467    518 |    50      -     - |    2041
  +---+---------------------+--------------------+
  | G |    20   1812   1715 |   274     10     1 |    3832
  | H |    97   4679   2965 |   414     13     1 |    8169
  | K |  3852  30329  20363 |  3120    194     5 |   57863
  | O | 36405  75502  30206 |  3432    129     1 |  145675
  +---+---------------------+--------------------+
        40380 114669  56117    7300    347     8    218821

       size                               Puzzles
      +---------------------+--------------------+
      |     2      3      4 |     5      6     7 |
  +---+---------------------+--------------------+
t | A |     -    210     75 |     2      -     - |    287
y | B |     -    390    174 |     8      1     - |    573
p | C |     -    253     87 |     -      -     - |    340
e | D |     5   1365    453 |    41      -     - |   1864
  +---+---------------------+--------------------+
  | G |    19   1657   1531 |   239      8     1 |   3455
  | H |    74   3880   2311 |   332     10     1 |   6608
  | K |  1817  15792  11013 |  1874    122     3 |  30621
  | O |  3246  12297   7782 |  1118     53     - |  24496
  +---+---------------------+--------------------+
         5161  35844  23426    3614    194     5    68244


Regards,
Blue

[Leren]

David,

You have missed a JE3 elimination r1c7 <> 2 because there is a JE secondary equivalence r1c7 == r3c6.

I'll put this another way: Suppose r1c7 = 2. So r1c5 <> 2. But also r3c4 <> 2 because it must resolve to another
JE3 base digit 3 or 4. So there is nowhere for 2 to go in Box 2. That's bad ! r1c7 <> 2 !!

The situation is similar in r1c89. Suppose r1c89 = 56. Now suppose r1c7 = 3 . So neither 2 nor 4 is in r1c789.
But because of the JE3 either (1) one of r2c12 = 2 and r3c4 = 2 or (2) one of r12 = 4 and r3c4 = 4. If 2 applies then there is
nowhere for 2 to go in Box 3. If 4 applies there is nowhere for 4 to go in Box 3

A similar argument applies if r1c7 = 4. The net result of all this is that r1c89 <> 6 because 1 of r1c89 = 5.

So the concept of an Exocet secondary equivalence is extended to 2 cells that are linked by a SIS digit.

For the JE3 we could write the secondary equivalences as r1c7== r3c6 and r4c3 == r1c89 (6).

The requirements of the extended secondary equivalence are the same as for the ordinary type:

1. The JE Target cells must occupy 2 different rows.
2. The equivalence (opposing) Target cell must definitely resolve to a base digit (so can't be part of a twin Exocet with an AHS linking 2 Target cells in the same box)

Leren

[daj95376]

And in a jiffy Leren finds this one
98.7.......7.65.........7..4...3..2..1......9..95..8..1......4...59..6.......2..3
After basic eliminations:

Code: Select all

 *----------------------------*----------------------------*----------------------------*
 | <9>      <8>      12346    | <7>      b124     b134     | T234-15  1356     12456    |
 | B23      B234     <7>      | 12348    <6>      <5>      | t1234-9  1389     1248     |
 | 2356    23456     t1234-6  | T234-18  9        1348     | <7>      1368     12468    |
 *----------------------------*----------------------------*----------------------------*
 | <4>      567      68       | 168      <3>      9        | 15       <2>      1567     |
 | 235678   <1>      2368     | 2468     2478     4678     | 345      3567     <9>      |
 | 2367     2367     <9>      | <5>      1247     1467     | <8>      1367     1467     |
 *----------------------------*----------------------------*----------------------------*
 | <1>      23679    2368     | 368      578      3678     | 259      <4>      2578     |
 | 2378     2347     <5>      | <9>      1478     13478    | <6>      178      1278     |
 | 678      4679     468      | 1468     14578    <2>      | 159      15789    <3>      |
 *----------------------------*----------------------------*----------------------------*
JE3:  (234)B=r2c12, T=r3c4, T=r1c7 => r3c4 <> 18, r1c7 <> 15
JE4: (1234)b=r1c56, t=r3c3, t=r2c7 => r3c3 <> 6,  r2c7 <> 9

Now either we have a single JExocet base digit pair that is common to both pairs of base cells or we have different base pairs in each. (This consideration has never struck me before because it's usually the first of these cases.) If they share the same digit pair then (1)r1c56,r2c7,r3c3 must be false making (1)r1c3 true and giving this chain
(1)r1c3 = (1)r3c3 &So (1)r1c56 = > r1c89 <> 1

But now we run out of eliminations using the JExocet inferences as far as I can see. ...

More eliminations can be deduced based on the double JExocet.

I'm going to combine previous observations by DPB, Leren, and champagne ... plus add something champagne forgot to add.

First are the eliminations by DPB and Leren's secondary eliminations.

Code: Select all

 +--------------------------------------------------------------------------------+
 |  9       8       12346   |  7      b124    b134     | T34-125  1356    12456   |
 | B23     B234     7       |  12348   6       5       | t1234-9  1389    1248    |
 |  2356    23456  t1234-6  | T234-18  9      E34-18   |  7       1368    12468   |
 |--------------------------+--------------------------+--------------------------|
 |  4       567     68      |  168     3       9       |  15      2       1567    |
 |  235678  1       2368    |  2468    2478    4678    |  345     3567    9       |
 |  2367    2367    9       |  5       1247    1467    |  8       1367    1467    |
 |--------------------------+--------------------------+--------------------------|
 |  1       23679   2368    |  368     578     3678    |  259     4       2578    |
 |  2378    2347    5       |  9       1478    13478   |  6       178     1278    |
 |  678     4679    468     |  1468    14578   2       |  159     15789   3       |
 +--------------------------------------------------------------------------------+
 # 167 eliminations remain

 ### - 234- QExocet   Base = r2c12   Target = r1c7==r3c6,r3c4

 ### -1234- QExocet   Base = r1c56   Target = r2c7,r3c3


Then there's champagne's eliminations -- r1c3<>1234, r3c89<>234 -- based on the double JExocet. There's also r2c4<>1234. Here's how:

Code: Select all

 assume the following assignments for the B/T/E cells
 and the eliminations forced in       the b     cells
 +-------------------------------------------------+
 |   .   .   .   |   . 1c-ab 1c-ab |   a   .   .   |
 |  ab  ab   .   |   .   .    .    |   .   .   .   |
 |   .   .   .   |   b   .    a    |   .   .   .   |
 |---------------+-----------------+---------------|
 |   .   .   .   |   .   .    .    |   .   .   .   |
 |   .   .   .   |   .   .    .    |   .   .   .   |
 |   .   .   .   |   .   .    .    |   .   .   .   |
 |---------------+-----------------+---------------|
 |   .   .   .   |   .   .    .    |   .   .   .   |
 |   .   .   .   |   .   .    .    |   .   .   .   |
 |   .   .   .   |   .   .    .    |   .   .   .   |
 +-------------------------------------------------+


Code: Select all

 r1c3 and r2c4 see r1c56=1c and r2c12=ab ... leading to: r1c3,r2c4<>1234
 also r1c56=1c forces r1c78<>1
 now, the only place left in [b1] for <c> is r3c123 ... leading to: r3c89<>234
 +--------------------------------------------------------------------------------+
 |  9       8       6-1234  |  7      b124    b134     | T34-125  356-1   2456-1  |
 | B23     B234     7       |  8-1234  6       5       | t1234-9  1389    1248    |
 |  2356    23456  t1234-6  | T234-18  9      E34-18   |  7       16-3    168-24  |
 |--------------------------+--------------------------+--------------------------|
 |  4       567     68      |  168     3       9       |  15      2       1567    |
 |  235678  1       2368    |  2468    2478    4678    |  345     3567    9       |
 |  2367    2367    9       |  5       1247    1467    |  8       1367    1467    |
 |--------------------------+--------------------------+--------------------------|
 |  1       23679   2368    |  368     578     3678    |  259     4       2578    |
 |  2378    2347    5       |  9       1478    13478   |  6       178     1278    |
 |  678     4679    468     |  1468    14578   2       |  159     15789   3       |
 +--------------------------------------------------------------------------------+
 # 167 eliminations remain


[Edit: updated statements to reflect eliminations only. Any Naked/Hidden Singles must be part of subsequent steps.]

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 9       8       6        | 7      b124    b134      |T34      35      245      |
|B23     B234     7        | 8       6       5        |t234     9       1        |
| 235     2345   t1        |T234     9       34       | 7       68-3    68-24    |
|--------------------------+--------------------------+--------------------------|
| 4       567     8        | 16      3       9        | 15      2       567      |
| 567-23  1       23       | 246     78-24   678-4    | 345     567-3   9        |
| 2367    2367    9        | 5       1247    1467     | 8       1367    467      |
|--------------------------+--------------------------+--------------------------|
| 1       679-23  23       | 36      578     678-3    | 259     4       578-2    |
| 2378    237     5        | 9       1478    13478    | 6       178     278      |
| 678     679     4        | 16      1578    2        | 159     1578    3        |
*--------------------------------------------------------------------------------*

                  S          S                          S

And now the fun begins: the JE3 and JE4 share the same S lines and the JE3 digits
are a subset of the JE4 digits, so double Exocet eliminations can be made for digits 234 as shown.

While I was preparing this post I noticed that Danny Jones has just posted on the same puzzle.

Obviously I haven't had a chance to look at this. It will be interesting to compare our 2 approaches.

Leren

[David P Bird]

Gentlemen, I realised my error when I went to bed. Without reading your replies in detail my logic goes like this

If the same digit is true in both sets of base digits it can't be true in any target cell, because each pair sees the targets for the other. But that is a requirement to complement the two truths in the partial fish. So no digit can be common to both base pairs. Furthermore the four target cells must each hold a different digit.

This means (1)r1c56 must be true, this in turn forces (1)r3c3 and (1)r2c9 etc etc.

[denis_berthier]

I have some difficulties to imagine what is the frequency of sapphire and ruby in the nature.
However, they are intensively searched.

But I've never heard anybody making such propaganda about their frequency as you have done for exocets.

[daj95376]

Code: Select all

*--------------------------------------------------------------------------------*
| 9       8       6        | 7      b124    b134      |T34      35      245      |
|B23     B234     7        | 8       6       5        |t234     9       1        |
| 235     2345   t1        |T234     9       34       | 7       68-3    68-24    |
|--------------------------+--------------------------+--------------------------|
| 4       567     8        | 16      3       9        | 15      2       567      |
| 567-23  1       23       | 246     78-24   678-4    | 345     567-3   9        |
| 2367    2367    9        | 5       1247    1467     | 8       1367    467      |
|--------------------------+--------------------------+--------------------------|
| 1       679-23  23       | 36      578     678-3    | 259     4       578-2    |
| 2378    237     5        | 9       1478    13478    | 6       178     278      |
| 678     679     4        | 16      1578    2        | 159     1578    3        |
*--------------------------------------------------------------------------------*

                  S          S                          S

And now the fun begins: the JE3 and JE4 share the same S lines and the JE3 digits
are a subset of the JE4 digits, so double Exocet eliminations can be made for digits 234 as shown.

Your grid is solvable with basics. So it's a poor example for such a complex set of deductions.