exocet pattern in hardest puzzles

Advanced methods and approaches for solving Sudoku puzzles

Re: The hardest sudokus (new thread)

Postby champagne » Sat Jul 21, 2012 9:06 am

Leren wrote: I also found Exocet's in puzzles 35, 14596 and 12120.


I checked that point with my latest code.
I find 2 exocets (classical ones, not twin) in puzzles
243 => Jexocet r7c1 r7c2 r9c5 r9c9 2345
and 35 => Jexocet r3c1 r3c2 r2c4 r1c7 1234

nothing for puzzles 14596 and 12120

could you give more information on your findings

PS I see clearly why my old code did not find the second one, for the first one, I likely had a filter to use different rows at that time.

EDIT : I checked puzzles 14956 and 12120, no doubt that there is an exocet (the same), so this is a bug to fix in my fresh code;
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Re: bi bi pattern in hardest puzzles

Postby ronk » Sat Jul 21, 2012 1:39 pm

Mostly bogus post, withdrawn
Last edited by ronk on Sat Jul 21, 2012 6:28 pm, edited 1 time in total.
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Re: The hardest sudokus (new thread)

Postby Leren » Sat Jul 21, 2012 2:00 pm

The Exocets I found were:

35 => r3c1 r3c2 r2c4 r1c7 1234

14596 => r1c3 r2c3 r4c2 r7c1 1236

12120 => r1c3 r2c3 r4c2 r7c1 1236

I didn't find an exocet for 243 as I have had trouble understanding the posts on Jexocets

Perhaps you can clarify the definition for me.

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Re: bi bi pattern in hardest puzzles

Postby champagne » Sat Jul 21, 2012 2:33 pm

ronk wrote:
here champagne wrote:nothing for puzzles 14596 and 12120

could you give more information on your findings

PS I see clearly why my old code did not find the second one, for the first one, I likely had a filter to use different rows at that time.

EDIT : I checked puzzles 14956 and 12120, no doubt that there is an exocet (the same), so this is a bug to fix in my fresh code;

champagne, this would require IMO a welcomed generalization of your definition, as I understand it.

For base cell pair B = B1 & B2 and target cell pair T = T1 & T2, there exists an exocet:
  1. If, for each individual candidate j = a, b, c, ... of B, B1 = j or B2 = j causes either T1 = j or T2 = j (as now)
  2. If, for each candidate pair jk = ab, ac, ad, bc, ... of B, there exists the strong inference (jk)B = (jk)T (if generalized)
[edits: umpteen times, tried to phrase the "as now" unambiguously]


to avoid confusion, I intend to maintain only the definition of the thread "Exotic pattern a resume".

The current definition is the following


The reduced definition uses

. A base of 2 unassigned cells in the same region (row, column, box)
. A target of 2 unassigned cells in other regions

having the following property (whatever is the process used to prove it.)

if for any digit solution of the base
one at least of the target is occupied by the same digit

then the target can not contain any other digit than the base.



The property is the same as your point one.

But then, we don't need any more property. Your point 2 is always valid if the puzzle has at least one solution.
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Re: The hardest sudokus (new thread)

Postby champagne » Sat Jul 21, 2012 2:41 pm

Leren wrote:The Exocets I found were:

35 => r3c1 r3c2 r2c4 r1c7 1234

14596 => r1c3 r2c3 r4c2 r7c1 1236

12120 => r1c3 r2c3 r4c2 r7c1 1236

I didn't find an exocet for 243 as I have had trouble understanding the posts on Jexocets

Perhaps you can clarify the definition for me.

Leren


The generic definition for the exocet is

here

it is a very simple one.

Problems are coming out of limitations set in the search process.

My old code added as constraint that any cell of the target should have all the digits of the base
My fresh code limits the search to the band/stack of the base and I have other constraints to be closer to the Jexocet definition. Clearly, I have one constraint in excess.

here after the definition you will find if you follow the link
============================================================
The reduced definition uses

A base of 2 unassigned cells in the same region (row, column, box)
A target of 2 unassigned cells in other regions

having the following property (whatever is the process used to prove it.)

if for any digit solution of the base
one at least of the target is occupied by the same digit

then the target can not contain any other digit than the base.


The logic is trivial and is just requiring that the puzzle has at least one solution.

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Re: The hardest sudokus (new thread)

Postby daj95376 » Sat Jul 21, 2012 4:03 pm

Leren wrote:I didn't find an exocet for 243 as I have had trouble understanding the posts on Jexocets

Puzzle 243 has the target's candidate cells "aligned" in [r9], and the Exocet doesn't produce any eliminations.

Code: Select all
.2.4.......7.8...6.....3.5...9.6...1.....23.....5...4...1...8..6...1...797.......

 #   243;elev;258;11.40;11.40;11.30;884

 +--------------------------------------------------------------------------------+
 |  1358    2       3568    |  4       579     15679   |  179     13789   389     |
 |  1345    13459   7       |  129     8       159     |  1249    1239    6       |
 |  148     14689   468     |  12679   279     3       |  12479   5       2489    |
 |--------------------------+--------------------------+--------------------------|
 |  234578  3458    9       |  378     6       478     |  257     278     1       |
 |  14578   14568   4568    |  1789    479     2       |  3       6789    589     |
 |  12378   1368    2368    |  5       379     1789    |  2679    4       289     |
 |--------------------------+--------------------------+--------------------------|
 | B2345   B345     1       |  23679   234579  45679   |  8       2369    23459   |
 |  6       3458    23458   |  2389   Q1       4589    |  2459    239    R7       |
 |  9       7       23458   |  2368   Q2345    4568    |  12456   1236   R2345    |
 +--------------------------------------------------------------------------------+
 # 181 eliminations remain

 ### -2345- QExocet   Base = r7c12   Target = r9c5,r9c9   aligned   no direct elims

Note: I use QExocet/qExocet labeling because i don't want to agrue that my results do/don't match the definition of an Exocet/JExocet.

[Edit: numerous edits.]
Last edited by daj95376 on Sun Jul 22, 2012 10:46 pm, edited 5 times in total.
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Re: bi bi pattern in hardest puzzles

Postby Leren » Sun Jul 22, 2012 2:13 pm

The above definition for a Jexocet is identical to what I was using for an Exocet, except that the Target cells had to occupy different rows (or columns).

I've now removed this restriction, so I now see a Jexocet ? in puzzle 243. This produces one elimination in the base <5> r7c1

In the definition of an Exocet I also include 2 other restrictions - (1) both base cells must have 3 candidates for a 3 base digit exocet (1) the Target cells don't have to have all the base digits individually but all the base digits must be represented in at least one Target cell.

I introduced these after I had a couple of failures during testing. Unfortunatley it was some time ago and I can't remember the relevent puzzle numbers.

Has anyone noticed the need for these or similar restrictions ?

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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Sun Jul 22, 2012 5:05 pm

Leren wrote:I've now removed this restriction, so I now see a Jexocet ? in puzzle 243. This produces one elimination in the base <5> r7c1

In the definition of an Exocet I also include 2 other restrictions - (1) both base cells must have 3 candidates for a 3 base digit exocet (2) the Target cells don't have to have all the base digits individually but all the base digits must be represented in at least one Target cell.

I'm only aware of a single Exocet pattern producing eliminations in the target's candidate cells. I don't get any eliminations for puzzle 243.

I believe you will find this puzzle an exception to constraint (1). The puzzle is flagged as "aligned" because my solver knows that the base candidates are in r4c1 and r9c1 -- even though it isn't apparent from the grid.

Code: Select all
98.7.....6.....5....4.6..8..9..3..2...3..74.....1......4...13....23....5....8..4.;18371

 +--------------------------------------------------------------------------------+
 |  9       8      *15      |  7       1245    2345    |  126     136     12346   |
 |  6       1237   *17      |  2489    1249    23489   |  5       1379    123479  |
 |  12357   12357   4       |  259     6       2359    |  1279    8       12379   |
 |--------------------------+--------------------------+--------------------------|
 |  157-48  9       15678   |  4568    3       4568    |  1678    2       1678    |
 |  1258    1256    3       |  25689   259     7       |  4       1569    1689    |
 |  24578   2567    5678    |  1       2459    245689  |  6789    35679   36789   |
 |--------------------------+--------------------------+--------------------------|
 |  578     4       56789   |  2569    2579    1       |  3       679     26789   |
 |  178     167     2       |  3       479     469     |  16789   1679    5       |
 |  1357    1357-6  15679   |  2569    8       2569    |  12679   4       12679   |
 +--------------------------------------------------------------------------------+
 # 182 eliminations remain

 #3# -157- qExocet   Base = r12c3   Target = r4c1,(SL=3)r9c12   aligned

I believe you will find this puzzle an exception to constraint (2).

Code: Select all
98.7..6....5.4.........9.7.4...3.....3.8....6..9.5....2.....8.1.1.2...6...3...2..;3811

 +--------------------------------------------------------------------------------+
 |  9       8       124     |  7       12      1235    |  6       12345   345-2   |
 |  1367    267     5       |  136     4       12368   |  139     12389   2389    |
 |  136     246     1246    |  1356    1268    9       |  1345    7       23458   |
 |--------------------------+--------------------------+--------------------------|
 |  4       2567    12678   |  169     3       1267    |  1579    12589   25789   |
 |  157     3       127     |  8       1279    1247    |  459-17  12459   6       |
 |  1678    267     9       |  146     5       12467   |  1347    12348   23478   |
 |--------------------------+--------------------------+--------------------------|
 |  2       45679   467     |  34569   679     34567   |  8      *3459    1       |
 |  578     1       478     |  2       789     34578   |  34579   6       34579   |
 |  5678    45679   3       |  14569   16789   145678  |  2      *459     4579    |
 +--------------------------------------------------------------------------------+
 # 178 eliminations remain

 #4# -3459- QExocet   Base = r79c8   Target = r1c9,r5c7

 *** found 3x3 base values in target cells for 4-value QExocet

[Edit: removed any inference to puzzles being JExocet.]
Last edited by daj95376 on Sun Jul 22, 2012 10:49 pm, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby ronk » Sun Jul 22, 2012 6:19 pm

daj95376 wrote:I believe you will find this puzzle an exception to constraint (1). However, it's an "extended" JExocet -- qExocet to my solver -- because r9c2 contains candidates from the base set. This is acceptable because there is a strong link/inference on <3> in r9c12.

Code: Select all
98.7.....6.....5....4.6..8..9..3..2...3..74.....1......4...13....23....5....8..4.;18371

 +--------------------------------------------------------------------------------+
 |  9       8      *15      |  7       1245    2345    |  126     136     12346   |
 |  6       1237   *17      |  2489    1249    23489   |  5       1379    123479  |
 |  12357   12357   4       |  259     6       2359    |  1279    8       12379   |
 |--------------------------+--------------------------+--------------------------|
 |  157-48  9       15678   |  4568    3       4568    |  1678    2       1678    |
 |  1258    1256    3       |  25689   259     7       |  4       1569    1689    |
 |  24578   2567    5678    |  1       2459    245689  |  6789    35679   36789   |
 |--------------------------+--------------------------+--------------------------|
 |  578     4       56789   |  2569    2579    1       |  3       679     26789   |
 |  178     167     2       |  3       479     469     |  16789   1679    5       |
 |  1357    1357-6  15679   |  2569    8       2569    |  12679   4       12679   |
 +--------------------------------------------------------------------------------+
 # 182 eliminations remain

 #3# -157- qExocet   Base = r12c3   Target = r4c1,(SL=3)r9c12   aligned

Nice counter-example, but allowing two prospective base cells to only have two candidates each must increase the search time. Did you notice a change?

BTW another term is the wrong way to handle this scenario IMO. David P Bird should expand the definition of "JExocet" to include strongly linked target cell pairs.

daj95376 wrote: The puzzle is flagged as "aligned" because my solver knows that the base candidates are in r4c1 and r9c1 -- even though it isn't apparent from the grid.

I interpret that to mean the solver knows the solution. IOW there's no way r9c1 is known to be the actual target from just ...
Code: Select all
     12 Truths = {157R349 3R9 12N3}
     15 Links = {1c379 5c346 7c379 49n1 9n2 157b1}
     3 Eliminations --> r4c1<>48, r9c2<>6
[edit 2: was 13 Truths with superfluous 3R3]

[edit 1: I first posted that I agreed that your second counter-example was beyond the scope of "JExocet", but now I don't see it anymore. Would you please fill me in?]
Last edited by ronk on Mon Jul 23, 2012 3:55 am, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Sun Jul 22, 2012 8:27 pm

Let me tidy up three points in one post.

ronk You didn't lose my post when you transferred this discussion – I deleted it because daj had corrected his previous post in line with my comment to him.

LerenA bit of history: The provisional definition of an JExocet was much tighter and as we researched it, we found it could be relaxed to increase its frequency of occurrence. Of course the problem with that has been to extend the effort needed to code and run the search routine in a solver. If I remember correctly, we found cases for every option the final definition covers.

daj In your puzzle 18371 there are two JExcocets that are strongly linked through the non-member digit in the two potential target cells. champagne coined the "twin" descriptor for this situation.

When such a situation exists it is valid to make any eliminations common to both outcomes using JExocet logic. But (6)r9c2 is NOT a common elimination and requires some other justification.
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Re: bi bi pattern in hardest puzzles

Postby ronk » Sun Jul 22, 2012 9:09 pm

David P Bird wrote:daj In your puzzle 18371 there are two JExcocets that are strongly linked through the non-member digit in the two potential target cells. champagne coined the "twin" descriptor for this situation.

When such a situation exists it is valid to make any eliminations common to both outcomes using JExocet logic. But (6)r9c2 is NOT a common elimination and requires some other justification.

r9c2=6 implies r9c1=3 which leaves no room for base digits 1, 5, or 7 in r9c12 of this "JExocet" (with a twin target). This faulty common outcome argument by itself seems sufficient reason to a discard the twin "JExocet" POV.
Last edited by ronk on Sun Jul 22, 2012 9:39 pm, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Sun Jul 22, 2012 9:31 pm

David P Bird wrote:daj In your puzzle 18371 there are two JExcocets that are strongly linked through the non-member digit in the two potential target cells. champagne coined the "twin" descriptor for this situation.

When such a situation exists it is valid to make any eliminations common to both outcomes using JExocet logic. But (6)r9c2 is NOT a common elimination and requires some other justification.

Hmmm. I listed the only Exocet pattern that my analyzer found. I don't recall champagne using the term "twin", but I do recall him using the term "double". My solver indicates the presence of a "double" Exocet when it realizes there are two Exocets present and under the right conditions.

I manually locate eliminations after my Exocet analyzer outputs the presence of one or more Exocets. Given the fact that puzzle 18371 is an "extended" Exocet, the elimination r9c2<>6 still appears to be accurate to me. One of r9c12=3 and the other cell must contain a candidate from the base set.
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Sun Jul 22, 2012 9:51 pm

ronk wrote:Nice counter-example, but allowing two prospective base cells to only have two candidates each must increase the search time. Did you notice a change?

BTW another term is the wrong way to handle this scenario IMO. David P Bird should expand the definition of "JExocet" to include strongly linked target cell pairs.

I interpret that to mean the solver knows the solution. IOW there's no way r9c1 is known to be the actual target from just ...

As for execution time, I don't process millions of puzzles like others are known to do. So, my solvers and analyzers are written based on my hap-hazzard logic and not to save milliseconds. My Exocet analyzer took roughly a minute to process the 31,804 puzzles in "02 index.txt". That's acceptable to me.

[Edit: withdrew comment on JExocet.]

Yes, the analyzer knows and uses the solution to perform cross-checks on the logic it's performing. Since it's an analyzer, I take "liberties" with the information it reports.
Last edited by daj95376 on Sun Jul 22, 2012 11:01 pm, edited 1 time in total.
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Re: bi bi pattern in hardest puzzles

Postby David P Bird » Sun Jul 22, 2012 10:31 pm

ronk wrote: r9c2=6 implies r9c1=3 which leaves no room for base digits 1, 5, or 7 in r9c12 of this "JExocet" (with a twin target). This faulty common outcome argument by itself seems sufficient reason to a discard the twin "JExocet" POV.

Yes I jumped a bit too quickly with that answer. We only get a twin JExocet if we can eliminate (6)r9c2 first, but the point stands it can't be eliminated because of any JExocet pattern.

daj wrote: Yes, the analyzer knows and uses the solution to perform cross-checks on the logic it's performing. Since it's an analyzer, I take "liberties" with the information it reports.

What you do in the privacy of you’re your own home is entirely up to you! However, is it right to describe that as a JExocet elimination to a newcomer?
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Re: bi bi pattern in hardest puzzles

Postby daj95376 » Sun Jul 22, 2012 10:36 pm

ronk wrote:[edit: I first posted that I agreed that your second counter-example was beyond the scope of "JExocet", but now I don't see it anymore. Would you please fill me in?]

I no longer compare my results to the possibility of a JExocet. (see edits to messages above) Below is the reason for my analyzer's results.

Hidden Text: Show
Code: Select all
 +--------------------------------------------------------------------------------+
 |  9       8       124     |  7       12      1235    |  6       12345   345-2   |
 |  1367    267     5       |  136     4       12368   |  139     12389   2389    |
 |  136     246     1246    |  1356    1268    9       |  1345    7       23458   |
 |--------------------------+--------------------------+--------------------------|
 |  4       2567    12678   |  169     3       1267    |  1579    12589   25789   |
 |  157     3       127     |  8       1279    1247    |  459-17  12459   6       |
 |  1678    267     9       |  146     5       12467   |  1347    12348   23478   |
 |--------------------------+--------------------------+--------------------------|
 |  2       45679   467     |  34569   679     34567   |  8      *3459    1       |
 |  578     1       478     |  2       789     34578   |  34579   6       34579   |
 |  5678    45679   3       |  14569   16789   145678  |  2      *459     4579    |
 +--------------------------------------------------------------------------------+
 # 178 eliminations remain

Code: Select all
 r7c8=3; r12c8,r7c46,r8c79<>3  =>

 r8c6=3; r1c6<>3; r1c9=3   q.e.d.
 +-----------------------------------+
 |  .  .  .  |  .  . -3  |  . -3  3  |
 |  3  .  .  |  3  .  3  |  3 -3  3  |
 |  3  .  .  |  3  .  .  |  3  .  3  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  3  .  |  .  .  .  |
 |  .  3  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  3  3  3  |
 |-----------+-----------+-----------|
 |  .  .  .  | -3  . -3  |  . =3  .  |
 |  .  .  .  |  .  . =3  | -3  . -3  |
 |  .  .  3  |  .  .  .  |  .  .  .  |
 +-----------------------------------+

Code: Select all
 r79c8=4; r1c8,r56c8,r8c79,r9c9<>4  =>

 r8c3=4; r1c3<>4; r1c9=4   -or-
 r8c6=4; r5c6<>4; r5c7=4          q.e.d.
 +-----------------------------------+
 |  .  . #4  |  .  .  .  |  . -4  4  |
 |  .  .  .  |  .  4  .  |  .  .  .  |
 |  .  4  4  |  .  .  .  |  4  .  4  |
 |-----------+-----------+-----------|
 |  4  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  . #4  |  4 -4  .  |
 |  .  .  .  |  4  .  4  |  4 -4  4  |
 |-----------+-----------+-----------|
 |  .  4  4  |  4  .  4  |  . =4  .  |
 |  .  . *4  |  .  . *4  | -4  . -4  |
 |  .  4  .  |  4  .  4  |  . =4 -4  |
 +-----------------------------------+

Code: Select all
 r79c8=5; r1c8,r45c8,r8c79,r9c9<>5  =>

 r8c1=5; r5c1<>5; r5c7=5   -or-
 r8c6=5; r1c6<>5, r1c9=5          q.e.d.
 +-----------------------------------+
 |  .  .  .  |  .  . #5  |  . -5  5  |
 |  .  .  5  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  5  .  .  |  5  .  5  |
 |-----------+-----------+-----------|
 |  .  5  .  |  .  .  .  |  5 -5  5  |
 | #5  .  .  |  .  .  .  |  5 -5  .  |
 |  .  .  .  |  .  5  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  5  .  |  5  .  5  |  . =5  .  |
 | *5  .  .  |  .  . *5  | -5  . -5  |
 |  5  5  .  |  5  .  5  |  . =5 -5  |
 +-----------------------------------+

Code: Select all
 r79c8=9; r2c8,r45c8,r8c79,r9c9<>9  =>

 r8c5=9; r5c5<>9; r5c7=9   q.e.d.
 +-----------------------------------+
 |  9  .  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  9 -9  9  |
 |  .  .  .  |  .  .  9  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  9  .  .  |  9 -9  9  |
 |  .  .  .  |  . -9  .  |  9 -9  .  |
 |  .  .  9  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  9  .  |  9  9  .  |  . =9  .  |
 |  .  .  .  |  . =9  .  | -9  . -9  |
 |  .  9  .  |  9  9  .  |  . =9 -9  |
 +-----------------------------------+
daj95376
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