exocet pattern in hardest puzzles

Advanced methods and approaches for solving Sudoku puzzles

Re: bi bi pattern in hardest puzzles

Postby David P Bird » Fri Apr 27, 2012 10:21 am

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Last edited by David P Bird on Sun Apr 29, 2012 5:51 pm, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby ronk » Fri Apr 27, 2012 10:48 am

daj95376 wrote:I believe David was looking for a productive example of this form of JExocet. I'm sorry if another example has already been posted.

Code: Select all
Puzzle:   182;elev;L14;1;2;r8c3 r9c3 r1c2 r5c2

1....6.8....7....3....2.4....5.4....6....8.5....3..2....8..1.9..1......796.......

David P Bird posted one that didn't produce an exclusion, so AFAIK yours is the first that does. Nice find daj95376, and nice contribution David.

Furthermore, I don't believe anyone has systematically filtered champagne's latest "03 E exocet seen.txt" file for this property, so there could be quite a few more. Here's another one:

Code: Select all
#8361;TkP;4473;1;2;r1c4 r1c6 r2c3 r2c7
000000000000281000002706100000009005006010800040000030001070200300000009250000040

+---------------------------+-----------------------+---------------------------+
| 1456789  136789  78(3459) | (3459)  (3459)  (345) | 67(3459)   256789  234678 |
| 45679    3679    -7(3459) | 2       8       1     | -67(3459)  5679    3467   |
| 4589     389     2        | 7       (3459)  6     | 1          589     348    |
+---------------------------+-----------------------+---------------------------+
| 178      12378   78(3)    | 3468    26(34)  9     | 67(4)      1267    5      |
| 579      2379    6        | 345     1       23457 | 8          279     247    |
| 15789    4       78(59)   | 568     26(5)   2578  | 67(9)      3       1267   |
+---------------------------+-----------------------+---------------------------+
| 4689     689     1        | 345689  7       3458  | 2          568     368    |
| 3        678     78(4)    | 14568   26(45)  2458  | 67(5)      15678   9      |
| 2        5       78(9)    | 13689   6(39)   38    | 67(3)      4       13678  |
+---------------------------+-----------------------+---------------------------+

     14 Truths = {3459C3 3459C5 3459C7 1N46}
     18 Links = {3459r1 34r4 59r6 45r8 39r9 2n37 3459b2}
     3 Eliminations --> r2c37<>7, r2c7<>6
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Fri Apr 27, 2012 5:15 pm

David P Bird wrote:Danny, Well done! You've proved that they can exist and that the target cells can see each other! Did you find the puzzle in one of champagne's collections?

Yes, the puzzle was in his "03 E ..." file. The file also contains many double Exocet puzzles with secondary dependencies. Each puzzle is listed as containing multiple occurrences of single Exocets.
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Re: bi bi pattern in hardest puzzles

Postby ronk » Fri Apr 27, 2012 6:04 pm

David P Bird wrote:It contains an Almost SK Loop that produces a set of eliminations that include the two JExcocet target cells.
r4c47,r6c59,r8c457 <> 2347, r1c23,r5c23,r9c68 <> 15689
but where exactly one of these elimination cells is invalid.

If you're envisioning a hidden-pair-loop ala Steve Kurzhals, wouldn't that be r15c23, r89c68<>15689 of which only two cells are applicable for the exocet (single)?
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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Fri Apr 27, 2012 7:51 pm

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Last edited by David P Bird on Sun Apr 29, 2012 5:51 pm, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Sat Apr 28, 2012 6:44 pm

I'm trying to categorize the different "single" (J)Exocet patterns that I've encountered in Champagne's latest "03 E ..." file. I'm also soliciting a request for any patterns that I might have missed.

Code: Select all
  (J)Exocet w/aligned  target cells and no eliminations
 |-------------------+-------------------+-------------------|
 |  B1234  .  B1234  |    .    .    .    |    .    .    .    |
 |    .    .    .    |    /    .    .    |    /    .    .    |
 |    .    .    .    |  T1234  .    .    |  T1234  .    .    |
 |-------------------+-------------------+-------------------|

Code: Select all
  (J)Exocet w/diagonal target cells and no eliminations
 |-------------------+-------------------+-------------------|
 |  B1234  .  B1234  |    .    .    .    |    .    .    .    |
 |    .    .    .    |  T1234  .    .    |    /    .    .    |
 |    .    .    .    |    /    .    .    |  T1234  .    .    |
 |-------------------+-------------------+-------------------|

Code: Select all
  (J)Exocet w/aligned  target cells and    eliminations
 |-------------------+-------------------+-------------------|
 | B1234   .  B1234  |    .    .    .    |    .    .    .    |
 |    .    .    .    |    /    .    .    |    /    .    .    |
 |    .    .    .    |  T12345 .    .    |  T12346 .    .    |
 |-------------------+-------------------+-------------------|
  r3c4<>5, r3c7<>6

Code: Select all
  (J)Exocet w/diagonal target cells and    eliminations
 |-------------------+-------------------+-------------------|
 |  B1234  .  B1234  |    .    .    .    |    .    .    .    |
 |    .    .    .    |  T12345 .    .    |    /    .    .    |
 |    .    .    .    |    /    .    .    |  T12346 .    .    |
 |-------------------+-------------------+-------------------|
  r2c4<>5, r3c7<>6

Code: Select all
  (J)Exocet w/diagonal target cells and 1x secondary dependency
 |-------------------+-------------------+-------------------|
 |  B1234  .  B1234  |    .    .    .    |    .    .    .    |
 |    .    .    .    |  T12345 /  S1237  |    /    .    .    |
 |    .    .    .    |    /    .    .    |  T12346 .    .    |
 |-------------------+-------------------+-------------------|
  r2c4<>5, r3c7<>6  ;  r2c6<>7, r3c7<>4

Code: Select all
  (J)Exocet w/diagonal target cells and 2x secondary dependency
 |-------------------+-------------------+-------------------|
 |  B1234  .  B1234  |    .    .    .    |    .    .    .    |
 |    .    .    .    |  T12345 /  S1237  |    /    .    .    |
 |    .    .    .    |    /    .    .    |  T12346 /  S2348  |
 |-------------------+-------------------+-------------------|
  r2c4<>5, r3c7<>6  ;  r2c6<>7, r3c7<>4  ;  r2c4<>1, r3c9<>8

If only one of these "single" (J)Exocet patterns exist in a chute, and it's one w/o any eliminations, is it a noteworthy (J)Exocet? The reason I ask is because I plan to filter puzzles from Champagne's file into a file for each category -- except those w/o eliminations, which I plan to discard.

I don't plan to categorize the double (J)Exocet patterns (in a chute) that I find, but I do intent to place them into a separate file as well.
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Re: bi bi pattern in hardest puzzles

Postby ronk » Sat Apr 28, 2012 8:55 pm

daj95376 wrote:
Code: Select all
  (J)Exocet w/diagonal target cells and no eliminations
 |-------------------+-------------------+-------------------|
 |  B1234  .  B1234  |    .    .    .    |    .    .    .    |
 |    .    .    .    |  T1234  .    .    |    /    .    .    |
 |    .    .    .    |    /    .    .    |  T1234  .    .    |
 |-------------------+-------------------+-------------------|
If only one of these "single" (J)Exocet patterns exist in a chute, and it's one w/o any eliminations, is it a noteworthy (J)Exocet? The reason I ask is because I plan to filter puzzles from Champagne's file into a file for each category -- except those w/o eliminations, which I plan to discard.

I hope champagne doesn't discard them just yet. It might be worthwhile to look for "horizontal" strong inferences. For example, if (4)r3c123=(4)r3c7, then r2c4=123, r3c7=1234, r1c2<>4, and r2c123<>4.

Also, I wonder if his search allowed for one of the exocet digits to be missing from both target cells. For example, if r2c4<>4 and r3c7<>4, then r1c12<>4 as well as r2c4=123, and r3c7=123.
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Re: bi bi pattern in hardest puzzles

Postby champagne » Thu May 03, 2012 5:46 am

daj95376 wrote:
Code: Select all
  (J)Exocet w/diagonal target cells and no eliminations
 |-------------------+-------------------+-------------------|
 |  B1234  .  B1234  |    .    .    .    |    .    .    .    |
 |    .    .    .    |  T1234  .    .    |    /    .    .    |
 |    .    .    .    |    /    .    .    |  T1234  .    .    |
 |-------------------+-------------------+-------------------|
If only one of these "single" (J)Exocet patterns exist in a chute, and it's one w/o any eliminations, is it a noteworthy (J)Exocet? The reason I ask is because I plan to filter puzzles from Champagne's file into a file for each category -- except those w/o eliminations, which I plan to discard.


As noticed ronk, direct elimination is one property of the exocet. I am missing time to prepare the posts for the "resume" thread, but we have already many examples showing what to do after direct eliminations.

On my website, there is an old (2 years old) description of a solution for fata morgana
giving some details on that possible strategy.



ronk wrote:Also, I wonder if his search allowed for one of the exocet digits to be missing from both target cells. For example, if r2c4<>4 and r3c7<>4, then r1c12<>4 as well as r2c4=123, and r3c7=123.


The program as it is requires that the union of the potential target studied contains all the base digits.

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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Thu May 03, 2012 6:10 am

champagne wrote:The program as it is requires that the union of the potential target studied contains all the base digits.

Have you a logical reason for that requirement?

DPB
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Re: bi bi pattern in hardest puzzles

Postby champagne » Thu May 03, 2012 6:35 am

David P Bird wrote:
champagne wrote:The program as it is requires that the union of the potential target studied contains all the base digits.

Have you a logical reason for that requirement?

DPB


My first requirement was that both potential targets had all the base digits.

After our discussions and some examples, I opened the search to downgraded patterns and the requirement is now

. minimum one in each cell
. union covers all

I surely can reduce the second condition to union has a minimum of 2.

The only reasons to ask for a full cover are

. a good chance to be in that position
. a lowest number of combinations to study

Seen the speed of the new process, it would not be a big problem to open the search.

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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Thu May 03, 2012 7:11 am

champagne wrote:Seen the speed of the new process, it would not be a big problem to open the search.

I think that would be worth doing - it might be similar to targets seeing each other which seems to be rare but possible.

This statement is false - see follwowing posts
If the base digits hold (abcd) and the targets hold (abx) and (bcx), then if JExcocet condition 3) holds for [abc] then (d) can be eliminated from the base cells.

DPB
Last edited by David P Bird on Thu May 03, 2012 9:00 am, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby champagne » Thu May 03, 2012 8:08 am

David P Bird wrote:
champagne wrote:Seen the speed of the new process, it would not be a big problem to open the search.

I think that would be worth doing - it might be similar to targets seeing each other which seems to be rare but possible.

If the base digits hold (abcd) and the targets hold (abx) and (bcx), then if JExcocet condition 3) holds for [abc] then (d) can be eliminated from the base cells.

DPB


I thought a little more about that.

If we don't have the rule for all digits of the base (requiring the union condition), then we can not conclude.

In your example, just assume the base is ok for a;d
then the target will contain 'a' + any of the other digits.

I don't see that we have established more.

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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Thu May 03, 2012 8:58 am

champagne wrote:In your example, just assume the base is ok for a;d
then the target will contain 'a' + any of the other digits.

I don't see that we have established more.

Yes you're right. After I wrote that I was considering how to build the inference into a chain and realised the same thing.

In fact it's possible for both targets to contain (a).

The only inference that exists (when (abc) all pass condition 3) is that the two target cells can't both hold non-members.

DPB
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Re: bi bi pattern in hardest puzzles

Postby ronk » Thu May 03, 2012 10:05 am

David P Bird wrote:The only inference that exists (when (abc) all pass condition 3) is that the two target cells can't both hold non-members.

My scenario above was for "when (abcd) all pass condition 3" and 'd' is missing from both target cells. However, such a pattern is probably impossible.

champagne wrote:... direct elimination is one property of the exocet ..., but we have already many examples showing what to do after direct eliminations.

On my website, there is an old (2 years old) description of a solution for fata morgana

What does a total solution to Fata Morgana have to do with this topic? We don't even know if the few exclusions, the very few exclusions, produced by an exocet pattern [ed: usually] lowers the Explainer difficulty rating.
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Re: bi bi pattern in hardest puzzles

Postby champagne » Thu May 03, 2012 2:40 pm

ronk wrote:
champagne wrote:... direct elimination is one property of the exocet ..., but we have already many examples showing what to do after direct eliminations.

On my website, there is an old (2 years old) description of a solution for fata morgana

What does a total solution to Fata Morgana have to do with this topic? We don't even know if the few exclusions, the very few exclusions, produced by an exocet pattern [ed: usually] lowers the Explainer difficulty rating.


The start for that solution is elimination of possibilities 1;6 1;3 for the exocet, leaving 3;6 as possible solution

This is done using exocet properties.

After 3;6 has been established, the puzzle is rated 9.0 by Sudoku Explainer.

I have not yet checked if this covers all potential eliminations in fata morgana for the floors 1;3;6, but it could be.

Generally speaking, elimination of possibilities for the base (what I commonly call a scenario) is a good way to continue after direct eliminations.

This can also be seen, although not so efficient in Golden Nugget.

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