## exocet pattern in hardest puzzles

Advanced methods and approaches for solving Sudoku puzzles

### Re: bi bi pattern in hardest puzzles

champagne, thanks for the 2051 analysis, but it was ronk who questioned it first. Anyway it's nice to know my sanity's not completely gone.

ronk, I've just checked daj95376's three other problem puzzles and find them all to be valid JExocets
The 2 covering lines for each member digit are:
00035 (1234)JExocet:r3c12,r1c7,r2c4 c347 (1)r48, (2)r68, (3)r69, (4)r58
12120 (1236)JExocet:r12c3,r4c2,r7c1 r347 (1)c48, (2)c49, (3)c58, (6)c69
14596 (1236)JExocet:r12c3,r4c2,r7c1 r347 (1)c48, (2)c48, (3)c59, (6)c69

In practice looking for the JExocet pattern first, and only going into deeper analysis if that fails, would cut out the need to consider degeneracy in the base and target cell inferences until it was necessary.

Regarding XSUDO I expected that if you put an entire pattern into it the derived inference it produces would pop out but:
Firstly that must be a bit long winded and make it difficult to pick out what other pattern(s) are being combined with it.
Secondly I didnâ€™t know what would happen if as a result of combining two patterns the same candidate was covered in different ways a multitude of times.
David P Bird
2010 Supporter

Posts: 1040
Joined: 16 September 2008
Location: Middle England

### Re: bi bi pattern in hardest puzzles

champagne wrote:
ronk wrote:
champagne wrote:On my side, I have to add a filter in the program to clean naked quads
I'll assume you're referring to the hidden quads I mentioned ...
I was in fact speaking of naked quads covering the full region
box 4 and column 3 are reduced to a quad generating the most degenerated form of exocet;
This brings nothing and should be eliminated from the list

Sounds like you weren't applying basic techniques before the exocet search. I've fallen into that trap several times too.

After doing so, I'll be interested in knowing what is left on "the list"?
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: bi bi pattern in hardest puzzles

Last edited by daj95376 on Sun Apr 22, 2012 9:57 pm, edited 1 time in total.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: bi bi pattern in hardest puzzles

[Withdrawn: Champagne discusses the same puzzle in a few post.]
Last edited by daj95376 on Sun Apr 22, 2012 9:58 pm, edited 1 time in total.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: bi bi pattern in hardest puzzles

ronk wrote:Sounds like you weren't applying basic techniques before the exocet search. I've fallen into that trap several times too.

After doing so, I'll be interested in knowing what is left on "the list"?

basic techniques would not change the fact that a region has only four cells -> giving by construction a naked quad and nothing else
but it's true that currently, I don't apply all basic techniques before starting the search for exocets

In the related puzzle, these exocet would not be affected by the filter I have in mind.

..3..6...4.67...3..7....5...6...597..3...7.4.9............2......8.....1.4...3.5.;6519;elev;3594;
r2c7 r2c9 r1c1 r1c2;
r2c7 r2c9 r1c2 r3c6;
r3c1 r3c3 r1c8 r2c6;
r3c1 r3c3 r2c5 r2c6;

champagne
champagne
2017 Supporter

Posts: 6609
Joined: 02 August 2007
Location: France Brittany

### Re: bi bi pattern in hardest puzzles

An idle thought regarding future areas for exploration:
Single Exocets only produce exclusions in two cells while double Exocets are far more productive. So it may be worth looking next in the single Exocet collection for any that are Almost Double Exocets.

To spell this out; compare the exclusions that would follow if a disrupting digit is true against those that the Double Exocet would produce if that digit was false and eliminate those that would result in either case.
David P Bird
2010 Supporter

Posts: 1040
Joined: 16 September 2008
Location: Middle England

### Re: bi bi pattern in hardest puzzles

champagne wrote:
ronk wrote:In the related puzzle, these exocet would not be affected by the filter I have in mind.

..3..6...4.67...3..7....5...6...597..3...7.4.9............2......8.....1.4...3.5.;6519;elev;3594;
r2c7 r2c9 r1c1 r1c2;
r2c7 r2c9 r1c2 r3c6;
r3c1 r3c3 r1c8 r2c6;
r3c1 r3c3 r2c5 r2c6;

I thought this might be the list and reducing it from six (or even seven) to four is certainly an improvement. However, you still include two (I colored them red) which IMO should not be considered true exocets, but rather pseudo-exocets. This is because
• each depends upon a true exocet double, and
• after performing the exclusions of the exocet double, the exclusions of the pseudos may be performed by simpler moves, one naked single r2c2=5 in this case.
I wrote earlier, "I can't imagine a workable definition wider than what you have now." I now think your definition is too wide. One can take a basic pattern and keep adding links, or keep adding both truths and links which might yield additional target pairs. With your definition, there are no bounds on this process.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: bi bi pattern in hardest puzzles

David P Bird wrote:An idle thought regarding future areas for exploration:
Single Exocets only produce exclusions in two cells while double Exocets are far more productive. So it may be worth looking next in the single Exocet collection for any that are Almost Double Exocets.

This seems like a capital idea. However, except for the second pair of base cells, an exocet and an exocet-double (for the same three or four digits) share all the strong inference sets (truths), so the suggested search space might not be as productive as you expect.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: bi bi pattern in hardest puzzles

ronk wrote:
David P Bird wrote:An idle thought regarding future areas for exploration:
Single Exocets only produce exclusions in two cells while double Exocets are far more productive. So it may be worth looking next in the single Exocet collection for any that are Almost Double Exocets.

This seems like a capital idea. However, except for the second pair of base cells, an exocet and an exocet-double (for the same three or four digits) share all the strong inference sets (truths), so the suggested search space might not be as productive as you expect.

Now you've said that, I can see that the prospects inside the Exocet band will be slender. But in the two parallel bands there are loads of fin cell eliminations from the 4 Swordfishes produced by a Double Exocet, and I would think the chances should be better for hitting one or more of those.
David P Bird
2010 Supporter

Posts: 1040
Joined: 16 September 2008
Location: Middle England

### Re: bi bi pattern in hardest puzzles

ronk wrote:
champagne wrote:
ronk wrote:In the related puzzle, these exocet would not be affected by the filter I have in mind.

..3..6...4.67...3..7....5...6...597..3...7.4.9............2......8.....1.4...3.5.;6519;elev;3594;
r2c7 r2c9 r1c1 r1c2;
r2c7 r2c9 r1c2 r3c6;
r3c1 r3c3 r1c8 r2c6;
r3c1 r3c3 r2c5 r2c6;

I thought this might be the list and reducing it from six (or even seven) to four is certainly an improvement. However, you still include two (I colored them red) which IMO should not be considered true exocets, but rather pseudo-exocets. This is because
• each depends upon a true exocet double, and
• after performing the exclusions of the exocet double, the exclusions of the pseudos may be performed by simpler moves, one naked single r2c2=5 in this case.
I wrote earlier, "I can't imagine a workable definition wider than what you have now." I now think your definition is too wide. One can take a basic pattern and keep adding links, or keep adding both truths and links which might yield additional target pairs. With your definition, there are no bounds on this process.

for me, the greatest danger is the silence.

Limiting the noise as much as possible is better as long as you have no risk to kill information of value.

Another point is that the simplest is the code, the best chance you have to see it working properly.

I agree that the 2 exocets you marked in red here have a poor added value, but it's not that disturbing to have them in the list.
The 3 others I intend to kill have an easy and general definition. It will not be to hard to build the filter.

champagne
champagne
2017 Supporter

Posts: 6609
Joined: 02 August 2007
Location: France Brittany

### Re: bi bi pattern in hardest puzzles

ronk wrote:
champagne wrote:
ronk wrote:In the related puzzle, these exocet would not be affected by the filter I have in mind.

..3..6...4.67...3..7....5...6...597..3...7.4.9............2......8.....1.4...3.5.;6519;elev;3594;
r2c7 r2c9 r1c1 r1c2;
r2c7 r2c9 r1c2 r3c6;
r3c1 r3c3 r1c8 r2c6;
r3c1 r3c3 r2c5 r2c6;

I thought this might be the list and reducing it from six (or even seven) to four is certainly an improvement. However, you still include two (I colored them red) which IMO should not be considered true exocets, but rather pseudo-exocets. This is because
• each depends upon a true exocet double, and
• after performing the exclusions of the exocet double, the exclusions of the pseudos may be performed by simpler moves, one naked single r2c2=5 in this case.
I wrote earlier, "I can't imagine a workable definition wider than what you have now." I now think your definition is too wide. One can take a basic pattern and keep adding links, or keep adding both truths and links which might yield additional target pairs. With your definition, there are no bounds on this process.

Hmmm!!! Okay, let's remove the presence of double exocets and see how your use of pseudo-exocets works?

Here's a puzzle with one JExocet IMO, and a secondary dependency, as I call it.

Code: Select all
`Puzzle:   #61;elev;31;2BN....56.8..5.7....3..8......2.....9...4.5....7....92.6.3.4.....15..1..4...1.....7. after Locked Candidate 1 +--------------------------------------------------------------------------------+ |  1479    2379    12379   |  2349    5       6       |  127     8       249     | |  1469    5       1269    |  7       1248    1489    |  126     1249    3       | |  14679   23679   8       |  2349    1234    1349    |  12567   12459   24569   | |--------------------------+--------------------------+--------------------------| |  2       368     1356    |  3468    134678  13478   |  9       1345    458     | |  1689    4       1369    |  5       1368    138     |  1238    123     7       | |  178     378     1357    |  348     9       2       |  1358    6       458     | |--------------------------+--------------------------+--------------------------| |  3       26789   4       |  29-68   2678    5789    |  2568    259     1       | |  5       26789   2679    |  1       23678   3789    |  4       29-3    2689    | |  689     1       269     |  234689  23468   34589   |  23568   7       25689   | +--------------------------------------------------------------------------------+ # 177 eliminations remain <2689> JExocet:   Base = r9c13   Target = r7c4(==r8c8 secondary dependency),r8c9 direct    JExocet eliminations: -none- secondary JExocet eliminations: r7c4<>68, r8c8<>3`

How do you explain the secondary eliminations using "simpler moves".
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: bi bi pattern in hardest puzzles

daj95376 wrote:How do you explain the secondary eliminations using "simpler moves".

I see no simple alternative move for that. However, I thought I limited my conjecture to the exocet double environment.

[edit: Despite this, even here I'm not comfortable with the notion of a second true exocet. After all, it is dependent upon the existence of another. Whatever pair of digits is ultimately placed in base r9c13 is replicated in [r7c4, r8c9], that's a true exocet. That digit pair is excluded from r8b7 (because of the base cells) and excluded from r8b8 (because of the target cells), and must be in the remaining mini-row r8b9. If all possible digits of the base occur only in two cells of this mini-row, other candidate values in these two cells may be validly excluded. In my book, this is a consequence of the first independent exocet, not of a second exocet.]

BTW for your example, r7c4<>68 may be considered due to two 3-digit almost exocets, the truths for which are ...
Code: Select all
`     12 Truths = {6R8 2C249 8C249 9C249 9N13} --> r7c4<>6       12 Truths = {8R8 2C249 6C249 9C249 9N13} --> r7c4<>8`

That would leave r8c8<>3 as the sole additional exclusion of the "secondary dependent."
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: bi bi pattern in hardest puzzles

ronk wrote:
daj95376 wrote:How do you explain the secondary eliminations using "simpler moves".

I see no simple alternative move for that. However, I thought I limited my conjecture to the exocet double environment.

[edit: Despite this, even here I'm not comfortable with the notion of a second true exocet. After all, it is dependent upon the existence of another. Whatever pair of digits is ultimately placed in base r9c13 is replicated in [r7c4, r8c9], that's a true exocet. That digit pair is excluded from r8b7 (because of the base cells) and excluded from r8b8 (because of the target cells), and must be in the remaining mini-row r8b9. If all possible digits of the base occur only in two cells of this mini-row, other candidate values in these two cells may be validly excluded. In my book, this is a consequence of the first independent exocet, not of a second exocet.]

To some degree, we are in agreement. You are against the idea of "a second true exocet". I accept that. I was trying to introduce the concept of a single Exocet that can contain an extension/secondary dependency whose eliminations are included in the Exocet. However, it would also mean that these additional eliminations would factor into a double Exocet when one or both of the Exocets have this property. Only after these eliminations would additional eliminations be attributed to the effect of the double Exocet.

ronk wrote:BTW for your example, r7c4<>68 may be considered due to two 3-digit almost exocets, the truths for which are ...
Code: Select all
`     12 Truths = {6R8 2C249 8C249 9C249 9N13} --> r7c4<>6       12 Truths = {8R8 2C249 6C249 9C249 9N13} --> r7c4<>8`

That would leave r8c8<>3 as the sole additional exclusion of the "secondary dependent."

Really!!! Are you actually proposing an alternative based on "two 3-digit almost exocets" that (ultimately) use the same four values as my single Exocet?
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: bi bi pattern in hardest puzzles

daj95376 wrote:However, it would also mean that these additional eliminations would factor into a double Exocet when one or both of the Exocets have this property. Only after these eliminations would additional eliminations be attributed to the effect of the double Exocet.

That sounds OK. I'll try it out in some actual 'exocet double' puzzles.

daj95376 wrote:
ronk wrote:BTW for your example, r7c4<>68 may be considered due to two 3-digit almost exocets, the truths for which are ...
Code: Select all
`     12 Truths = {6R8 2C249 8C249 9C249 9N13} --> r7c4<>6       12 Truths = {8R8 2C249 6C249 9C249 9N13} --> r7c4<>8`

That would leave r8c8<>3 as the sole additional exclusion of the "secondary dependent."

Really!!! Are you actually proposing an alternative based on "two 3-digit almost exocets" that (ultimately) use the same four values as my single Exocet?

As of now, I don't really know, but maybe. Just thought this was an opportune time to point out that r7c4<>68 was cannibalistic, and cannibalistic exclusions can (usually) be accomplished with a smaller set of strong inferences. It's also possible that r7c4<>68 could be true, even if the "secondary dependent" exocet didn't exist. It warrants further study.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: bi bi pattern in hardest puzzles

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 r5c21....6.8....7....3....2.4....5.4....6....8.5....3..2....8..1.9..1......796.......     b2  Naked  Quad                     <> 3459 r2c5,r3c4 +--------------------------------------------------------------------------------+ |  1      T2347-59 23479   |  459     359     6       |  579     8       259     | |  2458    24589   2469    |  7       18      459     |  1569    126     3       | |  3578    35789   3679    |  18      2       359     |  4       167     1569    | |--------------------------+--------------------------+--------------------------| |  2378    23789   5       |  1269    4       279     |  136789  1367    1689    | |  6      T2347-9  123479  |  129     179     8       |  1379    5       149     | |  478     4789    1479    |  3       15679   579     |  2       1467    14689   | |--------------------------+--------------------------+--------------------------| |  23457   23457   8       |  2456    3567    1       |  356     9       2456    | |  2345    1      B234     |  245689  35689   23459   |  3568    2346    7       | |  9       6      B2347    |  2458    3578    23457   |  1358    1234    12458   | +--------------------------------------------------------------------------------+ # 181 eliminations remain`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

PreviousNext