The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |2..|..4|9.5|
 |...|...|...|
 |.49|.3.|21.|
 |---+---+---|
 |1.5|..9|4..|
 |8..|...|..3|
 |..6|3..|7.2|
 |---+---+---|
 |.72|.6.|34.|
 |...|...|...|
 |6.4|9..|..1|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 2       168     138      |B1678   B18      4        | 9       3678    5        |
| 357     T1-568  138      | 125678  9       125678   | 68      3678    4        |
| 57      4       9        | 5678    3       5678     | 2       1      T678      |
|--------------------------+--------------------------+--------------------------|
| 1       3       5        | 27      27      9        | 4       68      68       |
| 8       2       7        | 456     45      56       | 1       9       3        |
| 4       9       6        | 3       18      18       | 7       5       2        |
|--------------------------+--------------------------+--------------------------|
| 59      7       2        | 158     6       158      | 3       4       89       |
| 359     158     138      | 24578   45      2578     | 568     2678    6789     |
| 6       58      4        | 9       27      3        | 58      27      1        |
*--------------------------------------------------------------------------------*

Exocet : r1c4 r1c5 r2c2 r3c9 (1678) r3c8==r2c2: => - 568 r2c2; stte

or

Code: Select all

*--------------------------------------------------------------------------------*
| 2       168     138      | 1678    18      4        | 9       368-7   5        |
|b357     1568    138      | 125678  9       125678   |c68     c3678    4        |
|b57      4       9        | 5678    3       5678     | 2       1     ca678      |
|--------------------------+--------------------------+--------------------------|
| 1       3       5        | 27      27      9        | 4       68     a68       |
| 8       2       7        | 456     45      56       | 1       9       3        |
| 4       9       6        | 3       18      18       | 7       5       2        |
|--------------------------+--------------------------+--------------------------|
|b59      7       2        | 158     6       158      | 3       4      a89       |
| 359     158     138      | 24578   45      2578     | 568     2678    6789     |
| 6       58      4        | 9       27      3        | 58      27      1        |
*--------------------------------------------------------------------------------*

ALS XY Wing: (7=9) r347c9 - (9=3) r237c1 - (3=7) r2c78, r3c9 => - 7 r1c8; stte

Leren

[SteveG48]

Code: Select all

 *-----------------------------------------------------------------------------*
 | 2      h168    h138     |h1678   h18      4       | 9       3678    5       |
 | 357     168-5   138     | 125678  9       125678  | 68      3678    4       |
 |a57      4       9       | 5678    3       5678    | 2       1      b678     |
 *-------------------------+-------------------------+-------------------------|
 | 1       3       5       |g27     f27      9       | 4       68      68      |
 | 8       2       7       | 456     45      56      | 1       9       3       |
 | 4       9       6       | 3       18      18      | 7       5       2       |
 *-------------------------+-------------------------+-------------------------|
 | 9-5     7       2       | 158     6       158     | 3       4       89      |
 | 39-5   i158    i138     | 24578   45      2578    | 568     2678   c6789    |
 | 6      i58      4       | 9      e27      3       | 58     d27      1       |
 *-----------------------------------------------------------------------------*


(5=7)r3c1 - r3c9 = r8c9 - r9c8 = r9c5 - r4c5 = r4c4 - (7=1368)r1c2345 - (3=158)r8c23,r9c2 => -5 r2c2,r78c1 ; stte

[pjb]

Code: Select all

 2       168    f138    | 1678   18     4      | 9     a3678   5     
e357     1568    138    | 125678 9      125678 | 68     3678   4     
 57      4       9      | 5678   3      5678   | 2      1     b678   
------------------------+----------------------+---------------------
 1       3       5      | 27     27     9      | 4      68     68     
 8       2       7      | 456    45     56     | 1      9      3     
 4       9       6      | 3      18     18     | 7      5      2     
------------------------+----------------------+---------------------
 59      7       2      | 158    6      158    | 3      4      89     
d359     158     138    | 24578  45     2578   | 568    2678  c6789   
 6       58      4      | 9      27     3      | 58     27     1     


Discontinuous loop:
(7)r1c8 - r3c9 = (7-9)r8c9 = (9-3)r8c1 = r2c1 - r1c3 = r1c8 => -7 r1c8; stte

Phil

[gurth]

[gurth]

Code: Select all

*--------------------------------------------------------------------------------*
| 2       168     138      |B1678   B18      4        | 9       3678    5        |
| 357     T1-568  138      | 125678  9       125678   | 68      3678    4        |
| 57      4       9        | 5678    3       5678     | 2       1      T678      |
|--------------------------+--------------------------+--------------------------|
| 1       3       5        | 27      27      9        | 4       68      68       |
| 8       2       7        | 456     45      56       | 1       9       3        |
| 4       9       6        | 3       18      18       | 7       5       2        |
|--------------------------+--------------------------+--------------------------|
| 59      7       2        | 158     6       158      | 3       4       89       |
| 359     158     138      | 24578   45      2578     | 568     2678    6789     |
| 6       58      4        | 9       27      3        | 58      27      1        |
*--------------------------------------------------------------------------------*

Exocet : r1c4 r1c5 r2c2 r3c9 (1678) r3c8==r2c2: => - 568 r2c2; stte

Leren

Leren,
Searching the literature for a clear explanation of Exocet is like looking for a needle in a haystack: I haven't found one. I am hoping you could give some idea of what it is all about, some idea of the logic that you use in this technique.

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 2       168     138      |B1678   B18      4        | 9       3678    5        |
| 357     T1-568  138      | 125678  9       125678   | 68      3678    4        |
| 57      4       9        | 5678    3       5678     | 2       1      T678      |
|--------------------------+--------------------------+--------------------------|
| 1       3       5        | 27      27      9        | 4       68      68       |
| 8       2       7        | 456     45      56       | 1       9       3        |
| 4       9       6        | 3       18      18       | 7       5       2        |
|--------------------------+--------------------------+--------------------------|
| 59      7       2        | 158     6       158      | 3       4       89       |
| 359     158     138      | 24578   45      2578     | 568     2678    6789     |
| 6       58      4        | 9       27      3        | 58      27      1        |
*--------------------------------------------------------------------------------*

Exocet : r1c4 r1c5 r2c2 r3c9 (1678) r3c8==r2c2: => - 568 r2c2; stte

Leren

Leren,
Searching the literature for a clear explanation of Exocet is like looking for a needle in a haystack: I haven't found one. I am hoping you could give some idea of what it is all about, some idea of the logic that you use in this technique.

Hi Gurth, I'm afraid there's no way around saying this but Exocets are one of the most advanced solving techniques and explaining them would take a long long time, far too long for a puzzle thread,

Two of the most relevant threads for learning about this technique can be found here http://forum.enjoysudoku.com/exotic-patterns-a-resume-t30508.html and here http://forum.enjoysudoku.com/jexocet-pattern-defintion-t31133.html

Be prepared for a long and tortuous slog, but if you stick it out for a few months (as I and several others have done) you may become as adept as anyone. You really gotta love Sudoku to learn this technique.

Leren

[SteveG48]

Leren, once you learn it, how difficult is it to apply? Is it usable for most manual solvers?

[daj95376]

Code: Select all

*--------------------------------------------------------------------------------*
| 2       168     138      |B1678   B18      4        | 9       3678    5        |
| 357     T1-568  138      | 125678  9       125678   | 68      3678    4        |
| 57      4       9        | 5678    3       5678     | 2       1      T678      |
|--------------------------+--------------------------+--------------------------|
| 1       3       5        | 27      27      9        | 4       68      68       |
| 8       2       7        | 456     45      56       | 1       9       3        |
| 4       9       6        | 3       18      18       | 7       5       2        |
|--------------------------+--------------------------+--------------------------|
| 59      7       2        | 158     6       158      | 3       4       89       |
| 359     158     138      | 24578   45      2578     | 568     2678    6789     |
| 6       58      4        | 9       27      3        | 58      27      1        |
*--------------------------------------------------------------------------------*

Exocet : r1c4 r1c5 r2c2 r3c9 (1678) r3c8==r2c2: => - 568 r2c2; stte

I don't see it.

Code: Select all

 BB=16  =>  =1 r2c23      &  =6  r2c2,r3c9  =>  possible contradiction:  =1 r2c3  &  =6 r2c2,r3c9

 BB=17  =>  =1 r2c23      &  =7       r3c9  =>  possible contradiction:  =1 r2c3  &  =7      r3c9

 BB=18  =>  =1 r2c23      &  =8       r3c9  =>  possible contradiction:  =1 r2c3  &  =8 r2c2,r3c9

 BB=68  =>  =6 r2c2,r3c9  &  =8       r3c9  =>           contradiction   in                  r3c9

 BB=78  =>  =7      r3c9  &  =8       r3c9  =>           contradiction   in                  r3c9


Two combinations are invalid, and the remaining three combinations have possible contradictions to your assertion.

_

[Leren]

Hi Danny, I think that the difference between your view and mine may stem from the way that an Exocet is detected.

My way is to demonstrate that, for each digit, it must appear in at least one of the target cells if it's in the base cells. I assume that this has been automatically proven if the digit satisfies the <= 2 line rule in the S cells.

Let's look at each digit.

1 has to be covered by 4 rows : Rows 6, 7 and 8 as candidates and Row 9 as a solved (actually a given) cell.

6 can be covered by 2 orthogonal lines : Row 5 and Column 9, or 2 rows, Rows 4 and 5.

7 can be covered by 2 parallel lines : Row 7 as a solved (actually a given) cell and Row 8 as candidates, or 2 orthogonal lines : Column 3 as a solved (actually a given) cell and Row 8 as candidates.

8 has to be covered by 5 rows : Rows 4, 6, 7, 8 and 9 as candidates.

Now let's look at how each digit is proven to occupy at least one target cell if it's in the base cells.

1 has to be proven by a multi-digit expansion process more or less equivalent to your template process - that's the hard one. But since there is no 1 in r3c9 it must be in r2c2.

6 and 7 are covered by the 2 line rule and are assumed to occupy at least one target cell with no further work.

Incidentally it's obvious for 6 since if 6 r1c4 => - 6 r1c2 => 6 r2c2. It's also obvious for 7 since if r1c4 = 7 and r3c9 <> 7 then r8c9 = 7, r8c6 <> 7 and there are no 7's in Column 6.

8 is proven by a short in-band chain : 8 r1c4 or r1c5 => - 8 r3c46 => 8 r3c9.

Having demonstrated that an Exocet exists, I now look for "bad" digits ie digits that would be forced into 2 target cells if they are in the base cells - this again by a similar multi-digit expansion process to the Exocet detection process.

As it turns out, both 6 and 8 are "bad digits" and can be removed from the base and target cells.

So my amended move is Exocet : r1c4 r1c5 r2c2 r3c9 1678 => - 8 r1c45, r2c2, r3c9, - 6 r1c4, r2c2, r3c9; stte

Code: Select all

*--------------------------------------------------------------------------------*
| 2       168     138      |B17-68  B1-8     4        | 9       3678    5        |
| 357    T15-68   138      | 125678  9       125678   | 68      3678    4        |
| 57      4       9        | 5678    3       5678     | 2       1      T7-68     |
|--------------------------+--------------------------+--------------------------|
| 1       3       5        | 27      27      9        | 4       68      68       |
| 8       2       7        | 456     45      56       | 1       9       3        |
| 4       9       6        | 3       18      18       | 7       5       2        |
|--------------------------+--------------------------+--------------------------|
| 59      7       2        | 158     6       158      | 3       4       89       |
| 359     158     138      | 24578   45      2578     | 568     2678    6789     |
| 6       58      4        | 9       27      3        | 58      27      1        |
*--------------------------------------------------------------------------------*

Now let's look at your possible contradictions / invalid cominations.

No's 1, 3, 4 and 5 involve the "bad" digits 6 and 8, which are shown to be false in the Exocet cells, so that's not surprising.

No 2 can't happen because it was shown in the Exocet detection process that 1 must be in r2c2 if it's in the base, although it has to be admitted that this is the hardest one to prove.

Finally I should say that an Exocet solution does exist as described, ie in the solution r1c4 = 7, r1c5 = 1, r2c2 = 1 and r3c9 = 7.

Hopefully, as a reward for my efforts, I may be credited with adding a new term to the Sudoku lexicon : a "bad" digit is one that is shown to occupy at least one target cell if it's in the base during an Exocet detection process,
but is subsequentially shown to occupy both target cells if it's in the base and can therefore be removed from the base and target cells. Well at least the term is short and snappy !

Phew, that was a long post, hopefully there are not too many typos or semantic blunders.

Leren

<edit> Added simple argument proving r1c4 = 7 => r3c9 = 7

Keren

[Leren]

Leren, once you learn it, how difficult is it to apply? Is it usable for most manual solvers?

Hi Steve, in my opinion, finding an Exocet is best done by a computer, although at least when it's found it's easy see and to understand the eliminations.

Some solvers, David P Bird for example (I think) can find Exocets manually, but they are much better manual solvers than me.

Good luck with learning about them. The 2 main Exocet threads run to 70 pages and they contain mistakes, because as they were being written, many new discoveries and clearing up of mistakes were being made. Fortunately for me I was in the middle of the process, so I was able to absorb it a bit at a time. As a result my Exocet routines have more spaghetti in them than you'll find in an Italian restaurant ! I'll bet that's true of most solvers.

Leren

[SteveG48]

Thanks, Leren!

OK, I'm back having scanned just the very tip of the iceberg in the first of the threads that you cited. The definition of the exocet seems pretty simple, as does the logic. However, I'm immediately lost when I look at your amended solution:

r1c4 r1c5 r2c2 r3c9 1678 => - 8 r1c45, r2c2, r3c9, - 6 r1c4, r2c2, r3c9; stte

Since neither of the base cells, r1c45, contains a 5, why are you no longer claiming -5 r2c2? That seems to be a basic elimination from an exocet.

[Leren]

Hi Steve, Yes I could have claimed -5 r2c2 because the base cells have been reduced to 17, I just didn't bother because it was unnecessary for an stte finish.

The reason for - 8 r1c45, r2c2, r3c9, - 6 r1c4, r2c2, r3c9 is a relatively recent (or maybe obscure) piece of Exocet reasoning.

When you detect an Exocet you have to prove that each of the 3 or 4 base digits must be in at least one target cell if it's in the base.

A somewhat counter-intuitive corollary of this logic is that if you can subsequently prove that if a digit is in the base => it must be in both target cells then this contradicts the Exocet detection logic. This then means that the digit can't be in the Exocet solution and can be removed from the base and target cells !

For this puzzle it was true for 6 and 8 but the proof was via a somewhat complex piece of logic - definitely a computer solution. I've since demoted the piece of code that does this so that the more basic Exocet eliminations can be done first, so I would now go back to my first move as the preferred one.

Even proving the existence of the Exocet involves some complex computer logic for one of the digits, which is why I posted another move that could be understood by a manual solver. The existence of the Exocet was something I found by accident when I was just playing around with my solver, so I posted it because it rarely comes up in Dan's daily puzzles. Curiously, in the puzzle for January 29th I detected 2 Exocets, but I couldn't claim it as a single move, so I didn't bother to mention it.

The lesson from all this is that you might have to read all 70 odd pages of the Exocet threads before you fully master Exocets. Also, Champagne publishes list of puzzles with various properties, and there's one where all the puzzles contain Exocets, so you can use this to practice on.

Leren

[David P Bird]

Steve, as you will probably have gathered, there are players who use a computer search to find Exocets and those who want to find them for themselves such as me. I could find them completely unaided (as I did at first) but it would be a long and tedious operation.

However I solve Sudokus on an Excel spreadsheet so I have a worksheet which shows me the digits that don't appear as givens in each tier and stack of boxes. These are the ones that will dominate the Exocet candidate choices. I then enter one of these sets into an input box and in a secondary grid the spreadsheet strips out all the other digits and colours those cells that have candidates that are confined to that set. (This grid has other uses too.)

If I want I can then add an additional digit that is a given in the band of interest. Using this I can generally scan for Junior Exocets in under 5 minutes (whereas computer searches take seconds). The pattern requirements for Junior Exocets are set so that most but not all Exocets will be identified. They can be extended when a near miss is found, but even then a few Exocets will be missed.

I believe Exocets are quite common in puzzles of all difficulties but are overkill when a starting grid has a plenty of strong links and are solvable using basic methods. The technique is best saved for the harder puzzles where strong links are scarce at the start.

I'm in the process of writing a Junior Exocet Compendium with examples taken from the different threads, which I will post in due course if I decide to continue as a contributor here.

DPB

[SteveG48]

Thanks Leren, David.

David, I hope you elect to stick around. You make valuable contributions. Hopefully the occasional satisfactions outweigh the frustrations.