## JExocet Compendium

Advanced methods and approaches for solving Sudoku puzzles

### Re: JExocet Compendium

Leren wrote:
David P Bird Wrote : Your grid has (167)r1c1 which should be (127), and (35)r6c1 which should be (357) according to me.

Corrected r1c1 typo. r6c1 <> 7 is correct. You'll find it further up in your own notes : r4c368,r6c1 <> 7 (base digits in non-'S' cells).

Leren

Yes, so that's one all between us!

I've succeeded in reducing the JE4 Examples #4 a bit more but I'm still struggling with it.

DPB
David P Bird
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### Re: JE4 Ex 2 with embedded 0-rank logic

David P Bird wrote:JE4 Example 2 with 3 Cross-lines
Code: Select all
`..1....96...1.....57....1....798.6....67..5..4......3...56.89......2.........1... *--------------------------*--------------------------*--------------------------* | 238 b   2348 b  <1>      | 23458 T 3457    23457    | 23478   <9>     <6>      |  | 23689   234689  23489 T  | <1>     3479    23479    | 23478 t 24578   234578   |  | <5>     <7>     23489    | 2348 t  3469    23469    | <1>     248 B   2348 B   |  *--------------------------*--------------------------*--------------------------* | 123     1235    <7>      | <9>     <8>     2345     | <6>     124     124      |  | 12389   12389   <6>      | <7>     134     234      | <5>     1248    12489    |  | <4>     12589   289      | 25      156     256      | 278     <3>     12789    |2  *--------------------------*--------------------------*--------------------------* | 1237    1234    <5>      | <6>     347     <8>      | <9>     1247    12347    |  | 136789  134689  3489     | 345     <2>     34579    | 3478    145678  134578   | 34  | 236789  234689  23489    | 345     34579   <1>      | 23478   245678  234578   |234  *--------------------------*--------------------------*--------------------------*                    8                                     8                   CLb         CL1                       CLB                           JE4 (2348)R1c12,r3c4,r2c7, (2348)r3c89,r2c3,r1c4       (cover houses for (8) are c3 c7)=> r1c4<>5, r2c3<>9, r2c7 <> 7            (non-base digits in the target cells)=> r2c3<>8, r2c7 <> 8               (base digit in a target cell is that has one of its cross lines as a cover house) => r1c56 <>7, r2c12 <> 9, r2c89<>7, r3c56 <> 9       (locked digits in mirror cells exclude others of same type)=> r1c7 <> 2348, r3c3 <> 2348, r2c5 <> 34, r2c6 <> 234   (known base digits seen by all base cells or all target cells)=> r6c269,r9c 1289<> 2,                 (known base digits in non-'S' cells in their cover houses)=> r8c1269,r9c1259 <> 3                (known base digits in non-'S' cells in their cover houses)=> r8c2689,r9c2589 <> 4                (known base digits in non-'S' cells in their cover houses)`

As David shows, both r1c7 and r3c3 see all four base cells. Therefore naked singles r1c7 = 7 and r3c3 = 9 result in an embedded 10-truth 0-rank logic pattern in c347. The pattern consists of three almost-hidden-sets (AHS) for the same three digits (c4 has a fourth), each mutually weakly-linked to the other two.

____

Code: Select all
`10 Truths = {234C347 8C4}10 Links = {2r6 34r8 29n37 139n4}17 Eliminations --> r8c1269<>3, r8c2689<>4, r6c269<>2, r29c37<>8, r19c4<>5`

The observant will appreciate the impact of the r9c37 <> 8 exclusions.
ronk
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### Re: JExocet Compendium

Ronk, As I was working through the examples for JE4s with 3 cross-lines I realised that in each of the cross-lines two base digits had to be true in the parallel bands. If the cover houses for the different base digits then coincide, a rank 0 pattern will be created using the cross-lines and cover houses as you have shown. However I came to the conclusion that the rank 0 pattern eliminations would always be duplicates of those from the JE4 pattern, and when the cover houses don't coincide so nicely they may not all be available, and so didn't mention this at this point in the overall write-up.

What you've identified is a case that I missed which happens when cross lines are used as cover houses for a digit. As a result you're able to show eliminations for (8)s in row 9 which aren't picked up by the JE4.

I did have to introduce Multi-Sector Locked Sets / rank 0 methods later on however when dealing with SK Loops and JE patterns in combination.

I've written this entirely from memory though so I may have left a few wrinkles out.

DPB
David P Bird
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### Re: JExocet Compendium

David P Bird wrote : Almost JE Examples Example 6 JE4 ..4..7.53....4...71.....4..........2.....8.3...3.1.5....1.3.7.....6...9.2.5.71.46 ;246934 (Morphed)

Hi David, I think there is a typo in this line : (357)HS:r345c4 => r3c4 <> 29, r4c4 <> 49, r5c7 <> 249 Should be (357)HS:r345c4 => r3c4 <> 29, r4c4 <> 49, r5c4 <> 249

Leren
Leren

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### Re: JExocet Compendium

Hi Leren, yes thanks, that's an obvious typo in the Almost JE Examples Example 6 which I've now corrected.

I now have a series of amended files to ready to substitute in the opening posts if I can work out the procedure. Can you tell me which of the files you have now completely scrutinised? I don't know if you are working methodically through them or just cherry-picking!

There's no rush as our recent exchanges give chapter and verse on the notation typos. I have also tried to improve the descriptions in the definition file on the topics which have raised comments and queries - principally Incompatible Base Pairs and Mirror nodes - but these changes aren't particularly earth shattering.

David
David P Bird
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### Re: JExocet Compendium

David P Bird wrote : Can you tell me which of the files you have now completely scrutinised?

Hi David, I've gone through files 01 - 08. I've cherry picked some of the files 09 - 14 as they are somewhat beyond the scope of my solver, so going through those in detail will take some considerable time.

I'd suggest that you reissue all the files with your amendments. I'll start at the beginning again to see if there is anything else I can pick up in files 01 - 08. That's a considerable body of work you've done, so it's not unexpected that you may go through several amendments before all issues are resolved.

Leren
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### Re: 5. JE2 Examples

David P Bird wrote:5. JE2 Examples

The JE2 examples provided either use 3-digits and/or require a special consideration. There is no "standard JE2" with 4-digits. Is this an oversight or do they exist elsewhere in the compendium?
ronk
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### Re: 5. JE2 Examples

ronk wrote:
David P Bird wrote:5. JE2 Examples

The JE2 examples provided either use 3-digits and/or require a special consideration. There is no "standard JE2" with 4-digits. Is this an oversight or do they exist elsewhere in the compendium?

Ronk
I've found that generally JE2s with 4 base digits are rather unproductive. We may be able to determine that certain digit pairings are incompatible but alone that won't provide immediate leverage into a puzzle – at least not for a manual solver. I don't have the tools or the skill to tailor puzzle grids to order so had to pick examples from those already published. My examples were chosen to illustrate a variety of possible openings which I hope explains the absence of JE2/4-digit examples (however there are a couple in the Almost JE examples).

As I don't use nets or forcing chains, I'm hardly qualified to describe how these techniques can be combined with JE inferences and so I must leave that to others (eg Sultan Vinegar was exploring rank 1 pattern openings.) Those avenues might be able to make more progress with these puzzles.

Leren
Sorry to keep you waiting for the amended compendium files but I picked up a few minor bits and pieces that needed editing, so am running through them all again in case there are others.

DPB
David P Bird
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### Re: JExocet Compendium

This puzzle was first discussed <here> It illustrates an interesting instance of a JExocet that must be false because of condition 4 - the afterthought condition because it occurs so rarely.
"4. It must be possible for at least two base digits to be true in one target cell and one non-target cell (a mirror cell) in the two target boxes in the JE band when each is true in the base cells. If the potential mirror cells in one of the target boxes can only hold non-base digits, the pattern can't be true"

98.7..6..7......8...6.5....5.....4...4...3.....95...6.3...2.1....8.....2..59...7. ;21774;GP;
Code: Select all
` *-----------------------*-----------------------*-----------------------* | <9>    <8>    1234    | <7>    134    124     | <6>    12345t 1345    |  | <7>    5      1234    | 12346t 13469  12469   | 239    <8>    1349    |  | 124b   123b   <6>     | 12348  <5>    12489   | 2379   12349  13479   |  *-----------------------*-----------------------*-----------------------* | <5>    12367  1237    | 1268   16789  126789  | <4>    1239   13789   | 123. | 1268   <4>    127     | 1268   16789  <3>     | 25789  1259   15789   | 12.. | 128    1237   <9>     | <5>    1478   12478   | 2378   <6>    1378    |  *-----------------------*-----------------------*-----------------------* | <3>    679    47      | 468    <2>    45678   | <1>    459    45689   | ...4  | 146    1679   <8>     | 1346   13467  14567   | 359    3459   <2>     | 1.34 | 1246   126    <5>     | <9>    13468  1468    | 38     <7>    3468    |  *-----------------------*-----------------------*-----------------------*                 CLB       CL1                             CL2`

This looks like an Almost JE2:(1234)r3c12,r2c4,r1c8 with (1) being a non-compliant digit for condition 3 as it could be true in three 'S' cells.
If either (1)r3c12 or (1)r8c4 were false then conditions 1 to 3 for the JE would be met and the target cells would be forced to hold two different base digits.
But a base digit in target r1c8 would force the mirror cells r1c79 to hold (56) which would make the JE false under condition 4.

Therefore both (1)r3c12 and (1)r8c4 must be true!

DPB
.
David P Bird
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### Re: JExocet Compendium

I have updated most of the files on the first page of this thread to correct reported errors & omissions, improve the wording in some sections, and to extend a few of the examples.

Thanks to Leren & ronk for their efforts when the files were first posted and again to Leren during the recent updating process.

David P Bird
.
David P Bird
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### Re: JExocet Compendium

Hi David,

I am making some progress with your compendium. It is a most valuable [and impressive!] addition to the Sudoku world. I have some small edits/typos/questions for you in:

2 JExocet Definition.
1) In Section 3, you list within [ ] abef which would suggest there could 6 base candidates: abcdef [is this possible?]
2) In Section 3.2 in JE2A I think r3c56 should be >
3) In Section 3.2 I am unsure why A B are uppercase
4) In Section 4, Add 'after' in: Immediately after a pattern is confirmed
5) In Section 8, I am unsure of the notation a# b#
6) In Section 8.4, the need for the mix of uppercase and lower case letters is unclear to me
7) In Section 10.5 I am unsure of the distinction between Junior and Senior. Am I right that some contributors do not make this distinction? Is there a definition of Senior Exocet?

Best
Gordon
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### Re: JExocet Compendium

Gordon, welcome to the forum and thanks both for the bouquet and your conscientious proof reading. I know I'm error-prone and welcome corrections so I hope you'll continue through the other files.

2 JExocet Definition.
1) In Section 3, you list within [ ] abef which would suggest there could 6 base candidates: abcdef [is this possible?]

Theoretically it might be possible. In a JE4 four of the base digits will be true in the target cells when the other two would be false in base cells. I'm not aware of an example though.

2) In Section 3.2 in JE2A I think r3c56 should be >
You're right - corrected.

3) In Section 3.2 I am unsure why A B are uppercase
Yes, there's no reason for that – corrected

4) In Section 4, Add 'after' in: Immediately after a pattern is confirmed
Accepted.

5) In Section 8, I am unsure of the notation a# b#
The #s differentiate the base and target cells which are known from the mirror instances of the digits which will be discovered.

6) In Section 8.4, the need for the mix of uppercase and lower case letters is unclear to me
It's simply because the base cells A&B occupy fixed positions in the series while the targets a & b move.

7) In Section 10.5 I am unsure of the distinction between Junior and Senior. Am I right that some contributors do not make this distinction? Is there a definition of Senior Exocet?
In a Junior Exocet the target cells always occupy the same band of boxes as the base cells, whereas for a Senior Exocet they don't. The senior pattern is only included for completeness as its search method is radically different and would require considerable effort from a human player. Its major disadvantage is that most of the derived inferences from the Junior pattern are lost so it's a lot of work for potentially little or no gain. It is covered in file 14 in the compendium and I'll add that fact to the final sentence.

I've made these changes to Version 3 of the file which I will hold for now and post after I've allowed time for any other necessary corrections to be spotted.

David
David P Bird
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### Re: JExocet Compendium

David P Bird wrote : In a Junior Exocet the target cells always occupy the same band of boxes as the base cells, whereas for a Senior Exocet they don't.

I thought my memory was playing tricks on me when I read this. I've always been under the impression that an Exocet was Junior when the pattern was contained in a single band and the proof that each digit must occupy at least one Target cell was done by showing that in the S cells, each digit can be covered by two straight lines. If any digit requires some other method of proof then the Exocet is not a Junior, it's just an Exocet in the more general sense (not a "Senior" - just an Exocet).

Well that's been the way I've been thinking for about 3 years. To see whether my memory was playing tricks one me, I've just made a search of the earliest reference to an Exocet being described as "Junior".

As far as I can see this was first made by one David P Bird on Thursday April 12th, 2012 AD at 7:47 pm. Here is a link to the relevant post http://forum.enjoysudoku.com/post216841.html?hilit=Junior%20Exocet#p216841

This seems to support my way of thinking. Perhaps your thinking has changed in the intervening years but I can't remember when/if you extended the use of the term "Junior" to cover any Exocet with Base and Target cells in a single band.

Not that this is important, it's only a label, but it's nice if we can agree on terminology. Maybe this history is worth a mention in the Compendium 02 definition file.

Leren
Leren

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### Re: JExocet Compendium

Hi Leren,
There is nothing wrong with your memory regarding the requirements for a Junior Exocet which has definite pattern criteria whereas an unqualified Exocet just requires two cells anywhere in the grid that will duplicate the contents of a pair of cells.

When Blue suggested that the target cells could be located outside the JE band in the cross lines we had an alternative pattern which needed to be qualified. Because the search method would be quite a bit more complicated than for the Junior pattern I chose to call them Senior Exocets. They still use the concept of 'S' cells covered by two houses but IMO they no longer qualify as humanly 'recognisable' for most of the population.

So the (current) family is:
Exocets - no pattern requirements.
Junior Exocets + various extensions – pattern based with base and target cells in the same band
Senior Exocets – pattern based with target cells anywhere in two cross lines.

David
David P Bird
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### Re: JExocet Compendium

Hi David, I note that Champagne still has the following information in the Exotic Patterns a Resume thread :

Jexocet

The Jexocet is by far the most common exocet pattern.
I take "David P Bird"'s presentation for that specific pattern

CODE: SELECT ALL
v v v
*-------*-------*-------*
| b b . | . . . | . . . | b = base cell restricted to digits from [abc] or [abcd]
| . . . | / . . | t . . | t = target cell (at first will contain every base digit)
| . . . | t . . | / . . | / = companion empty cell unable to hold any base digit
*-------*-------*-------* v = cross line pointers

In reference to this pattern, a three step system for recognising one-band Exocets is:
1: Find two base cells in a mini-line.
2: Look for two companion empty cells in the other two boxes in the two other lines.
3: Check that in the 3 cross lines each base digit is confined to 2 rows in the 2 parallel bands.

I've underlined point 3. As I now take it there are other methods for proving that a base digit must occupy at least one target cell and the Exocet pattern could still be regarded as a Junior.

These could be :

(a) Simple single digit in-band chains - simple transport being the most obvious example. A UR threat is another one.

(b) More complex single digit chains that may wander outside of the JExocet band but still end up on a Target cell (Danny Jones, wherever he is, was good at finding these).

(c) Even more complex multi-digit chains.

Somewhere in (b) and (c) a line of reasonableness is crossed where it is ridiculously complicated to prove that a JExocet exists - you might as well just solve the puzzle by other means.

I note with some amusement that in any single solution puzzle there are exactly 324 completed JExocets, but in the vast majority of cases you have to solve the puzzle by other means to identify them !

More seriously it might be worth looking at the Exotic Patterns thread to see that the terminology is up to date. People who are new to the forum might be confused by apparently conflicting terminology.

Leren
Leren

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