## exocet pattern in hardest puzzles

Advanced methods and approaches for solving Sudoku puzzles

### Re: bi bi pattern in hardest puzzles

[Withdrawn: found missing logic in my program.]
Last edited by daj95376 on Tue Mar 20, 2012 6:40 pm, edited 1 time in total.
daj95376
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### Re: bi bi pattern in hardest puzzles

daj95376 wrote:You might change your parameters to use <14678> (if possible). Templates like them a lot.
...
No, I don't know if this has anything to do with the Exocet or not.

Thanks. Don't you get about 31 of those eliminations with just <1678>-templates?
ronk
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### Re: bi bi pattern in hardest puzzles

ronk wrote:Thanks. Don't you get about 31 of those eliminations with just <1678>-templates?

[Withdrawn: planning replacement response to be posted soon.]
Last edited by daj95376 on Tue Mar 20, 2012 4:34 pm, edited 1 time in total.
daj95376
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### Re: bi bi pattern in hardest puzzles

daj95376 wrote:Ron,

You might change your parameters to use <14678> (if possible). Templates like them a lot.

No, I don't know if this has anything to do with the Exocet or not. _ _

this and the following posts are nice findings.
I am more interested in ronk exercice if he finds the shortest SLG showing the exocet.

The pattern described by David is exactly the same logic as the usual SLG drawn for an exocet.
It is just expressed in other words, fitting with a player approach.

I'll check ronk's last SLG to-day in that sense,

champagne

EDIT: I checked ronk's SLG floor per floor.

I can find any shorter logic to prove the exocet, so we have a good chance that he got the shortest logic.

For David, as long as it appears as an isolated pattern, it is of a poor interest to players.

In that case

1 in the base gives 1 in r7c5
8 in the base gives 8 r2c9

the situation for 6 and 7 is somehow symmetric, but uses a kind of XWing induced effect
(in row 5 in both cases, what can be seen in ronk's diagram)
champagne
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### Re: bi bi pattern in hardest puzzles

I discovered that a test was missing for N-template logic in my templates solver. Reviewing this puzzle:

Code: Select all
`...4....94....923..8..2...4..6..3...8..59...2.......7.3..9....5..8..21...1...5... +--------------------------------------------------------------------------------+ |  12567   23567   12357   |  4       135678  1678    |  5678    1568    9       | |  4       567     157     |  1678    15678   9       |  2       3       1678    | |  15679   8       13579   |  1367    2       167     |  567     156     4       | |--------------------------+--------------------------+--------------------------| |  12579   24579   6       |  1278    1478    3       |  4589    14589   18      | |  8       347     1347    |  5       9       1467    |  346     146     2       | |  1259    23459   123459  |  1268    1468    1468    |  345689  7       1368    | |--------------------------+--------------------------+--------------------------| |  3       2467    247     |  9       14678   14678   |  4678    2468    5       | |  5679    45679   8       |  367     3467    2       |  1       469     367     | |  2679    1       2479    |  3678    34678   5       |  346789  24689   3678    | +--------------------------------------------------------------------------------+ # 180 eliminations remain`

My logic thought this combination for <1678>-templates was acceptable because all four values are assigned to every unit/house.

Code: Select all
`16...7.8...718...6.8.6..71...671...8871..6........8671....7186.6.8...1.771.86.... +-----------------------+ | 1 6 . | . . 7 | . 8 . | | . . 7 | 1 8 . | . . 6 | | . 8 . | 6 . ~ | 7 1 . | |-------+-------+-------| | . . 6 | 7 1 . | . . 8 | | 8 7 1 | . . 6 | . . . | | . . . | . . 8 | 6 7 1 | |-------+-------+-------| | . . . | . 7 1 | 8 6 . | | 6 . 8 | . . . | 1 . 7 | | 7 1 . | 8 6 . | . . . | +-----------------------+`

It's only when I examined the unassigned cells that I realized the candidates in r3c6 were eliminated.

Correcting for this oversight, my templates solver now returns the following eliminations when limited to 4-template patterns for the first step.

Code: Select all
` <1678>   <>1  r1c356,r2c39,r3c346,r4c18,r5c68,r6c136,r7c5 <1678>   <>3  r5c3 <1678>   <>4  r5c3,r7c56 <1678>   <>6  r7c6 <1678>   <>7  r2c24,r5c3,r7c6,r8c2 <1678>   <>8  r1c5,r6c9,r7c56,r9c789`

My apologies for any inconvenience caused!!!

Note: I still had 252 combinations remaining after making the aforementioned correction.
daj95376
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### Re: bi bi pattern in hardest puzzles

daj95376 wrote:I still had 252 combinations remaining ...

That matches what I have. Didn't check each and every exclusion but that presumably matches too.
ronk
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### Re: bi bi pattern in hardest puzzles

champagne wrote:...4....94....923..8..2...4..6..3...8..59...2.......7.3..9....5..8..21...1...5...;1952;elev;1806

Code: Select all
`A     B     C      |D    E      F     |G      H     I    12567 23567 12357  |4    135678 1678* |5678   1568  9    4     567   157    |1678 15678  9     |2      3     1678* 15679 8     13579  |1367 2      167*  |567    156   4    --------------------------------------------------------12579 24579 6      |1278 1478   3     |4589   14589 18   8     347   1347   |5    9      1467  |346    146   2    1259  23459 123459 |1268 1468   1468  |345689 7     1368 --------------------------------------------------------3     2467  247    |9    14678* 14678 |4678   2468  5    5679  45679 8      |367  3467   2     |1      469   367  2679  1     2479   |3678 34678  5     |346789 24689 3678 `

Here we have a valid exocet based on r13c6
the target is r2c9 r7c5

I'm beginning to understand ... sorta.

Reiterating part of your Exocet logic:

One of these patterns must be true for an Exocet in base cells r13c6 and target cells r2c9,r7c5.

Code: Select all
` +-----------------------------------+   +-----------------------------------+ |  .  .  .  |  .  .  A  |  .  .  .  |   |  .  .  .  |  .  .  A  |  .  .  .  | |  .  .  .  |  .  .  .  |  .  .  A  |   |  .  .  .  |  .  .  .  |  .  .  B  | |  .  .  .  |  .  .  B  |  .  .  .  |   |  .  .  .  |  .  .  B  |  .  .  .  | |-----------+-----------+-----------|   |-----------+-----------+-----------| |  .  .  .  |  .  .  .  |  .  .  .  |   |  .  .  .  |  .  .  .  |  .  .  .  | |  .  .  .  |  .  .  .  |  .  .  .  |   |  .  .  .  |  .  .  .  |  .  .  .  | |  .  .  .  |  .  .  .  |  .  .  .  |   |  .  .  .  |  .  .  .  |  .  .  .  | |-----------+-----------+-----------|   |-----------+-----------+-----------| |  .  .  .  |  .  B  .  |  .  .  .  |   |  .  .  .  |  .  A  .  |  .  .  .  | |  .  .  .  |  .  .  .  |  .  .  .  |   |  .  .  .  |  .  .  .  |  .  .  .  | |  .  .  .  |  .  .  .  |  .  .  .  |   |  .  .  .  |  .  .  .  |  .  .  .  | +-----------------------------------+   +-----------------------------------+`

Now, without getting buried in details, a general analysis of the base cells impact on the target cells.

Code: Select all
`r13c6=1  =>  r2c9=1 and r7c5=1r13c6=6  =>  r2c9=6 and r7c5=?r13c6=7  =>  r2c9=? and r7c5=7r13c6=8  =>  r2c9=8 and r7c5=?`

Code: Select all
`{16}  =>  not possible because r2c9=1 and r2c9=6{17}  =>  not possible because r7c5=1 and r7c5=7{18}  =>  not possible because r2c9=1 and r2c9=8{67}  =>      possible because r2c9=6 and r7c5=7{68}  =>  not possible because r2c9=6 and r2c9=8{78}  =>      possible because r2c9=8 and r7c5=7`

Conclusion: r13c6<>1, r2c9=68, and r7c5=7.
daj95376
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### Re: bi bi pattern in hardest puzzles

daj95376 wrote:Now, without getting buried in details, a general analysis of the base cells impact on the target cells.

Code: Select all
`r13c6=1  =>  r2c9=1 and r7c5=1r13c6=6  =>  r2c9=6 and r7c5=?r13c6=7  =>  r2c9=? and r7c5=7r13c6=8  =>  r2c9=8 and r7c5=?`

Hi daj95376,

I have to study more in details your post, but I have a problem here.

The correct wording for me is

Code: Select all
`r13c6=1  =>                 r7c5=1r13c6=6  =>  r2c9=6 or r7c5=6  r13c6=7  =>  r2c9=7 or r7c5=7r13c6=8  =>  r2c9=8  `

but looking at the consequences for each possible pair of digits solution of the base is a classical way to continue after an exocet pattern has been found

champagne
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### Re: bi bi pattern in hardest puzzles

champagne, does your database of puzzles contain any instances of this twist on the classic one-band Exocet?

Code: Select all
`*------------*-----------*----------*| abc abc .  | .   .  .  | .   .  . || .   .   .  | /   .  .  | /   .  . |  / = (abc) excluded | .   .   .  | T1  .  .  | T2  .  . |  T1, T2 = target cells*------------*-----------*----------*| .   .   a  | a   .  .  | .   .  . |  | .   .   bc | b   .  .  | bc  .  . || .   .   .  | .   .  .  | .   .  . |*------------*-----------*----------*| .   .   ab | ab  .  .  | a   .  . || .   .   .  | .   .  .  | .   .  . || .   .   c  | c   .  .  | c   .  . |*------------*-----------*----------*`

Perhaps this form is trivial for your solver, but unless I've missed something, it would extend the scope of the pattern for manual solvers.

DPB
David P Bird
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### Re: bi bi pattern in hardest puzzles

champagne wrote:The correct wording for me is

Code: Select all
`r13c6=1  =>            r7c5=1r13c6=6  =>  r2c9=6 or r7c5=6r13c6=7  =>  r2c9=7 or r7c5=7r13c6=8  =>  r2c9=8  `

First, let me help update your table of cells assigned by r13c6=1.

Code: Select all
` r13c6=1           =>  <1> eliminated elsewhere in [b2] and [c6] r7c5=1 follows    =>  r46c5<>1 +-----------------------------------+ |  1  .  1  |  . -1 +1  |  .  1  .  | |  .  .  1  | -1 -1  .  |  .  .  1  | |  1  .  1  | -1  . +1  |  .  1  .  | |-----------+-----------+-----------| |  1  .  .  |  1 -1  .  |  .  1  1  | |  .  .  1  |  .  . -1  |  .  1  .  | |  1  .  1  |  1 -1 -1  |  .  .  1  | |-----------+-----------+-----------| |  .  .  .  |  . +1 -1  |  .  .  .  | |  .  .  .  |  .  .  .  |  1  .  .  | |  .  1  .  |  .  .  .  |  .  .  .  | +-----------------------------------+ -followed by- r2c9<>1 => r2c3=1 => r13c1<>1 => X-Wing r46c19 => r46c4<>1; [b5]<>1  =>  r2c9=1 r13c6=1  =>  r2c9=1 and r7c5=1   q.e.d.`

Second, I was looking for an alternate perspective that was more in line with my template solver's results for <1678>-template. As an additional benefit, I discovered that the alternate perspective uses the value-assigned cells to lock in where the target cells could exist. Leaving open the possibility that the target cells don't necessarily need to have all four candidates present -- i.e., r7c5=17 would be sufficient to still deduce some eliminations.
daj95376
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### Re: bi bi pattern in hardest puzzles

David P Bird wrote:champagne, does your database of puzzles contain any instances of this twist on the classic one-band Exocet?

Code: Select all
`*------------*-----------*----------*| abc abc .  | .   .  .  | .   .  . || .   .   .  | /   .  .  | /   .  . |  / = (abc) excluded | .   .   .  | T1  .  .  | T2  .  . |  T1, T2 = target cells*------------*-----------*----------*| .   .   a  | a   .  .  | .   .  . |  | .   .   bc | b   .  .  | bc  .  . || .   .   .  | .   .  .  | .   .  . |*------------*-----------*----------*| .   .   ab | ab  .  .  | a   .  . || .   .   .  | .   .  .  | .   .  . || .   .   c  | c   .  .  | c   .  . |*------------*-----------*----------*`

Perhaps this form is trivial for your solver, but unless I've missed something, it would extend the scope of the pattern for manual solvers.

DPB

Hi David,

I intend to review the entire file of Exocets to go in that direction, but it needs some fresh code.
My todo list is overloaded, so this is more or less a question of priorities.
In the top of the list, I have to update the public version of my data base, pushing up to about 20 000 thousands the number of exocets.

I forecast some action in the exocet characterisation by pattern in April.

I have also in the highest part of my list a subject that could be of interest to you.

You worked on the exocets, may-be not much on the multi-fish pattern.

Everybody uses the basic fish patterns. Multi fish patterns have shown a high potential to crack hardest puzzles. I am convinced that we have a continuous potential for multi-fish patterns (bi fish tri fish ...) that offers nicer paths to puzzles solutions in between.

I am also preparing some code to perform a selection of puzzles of that kind and open in due time a specific thread with examples.

If you have worked in that field, I could open the thread earlier

champagne
champagne
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### Re: bi bi pattern in hardest puzzles

daj95376 wrote:
champagne wrote:The correct wording for me is

Code: Select all
`r13c6=1  =>            r7c5=1r13c6=6  =>  r2c9=6 or r7c5=6r13c6=7  =>  r2c9=7 or r7c5=7r13c6=8  =>  r2c9=8  `

First, let me help update your table of cells assigned by r13c6=1.

Code: Select all
` r13c6=1           =>  <1> eliminated elsewhere in [b2] and [c6]  r2c9<>1 => r2c3=1 => r13c1<>1 => X-Wing r46c19 => r46c4<>1; [b5]<>1  =>  r2c9=1`

Second, I was looking for an alternate perspective that was more in line with my template solver's results for <1678>-template. As an additional benefit, I discovered that the alternate perspective uses the value-assigned cells to lock in where the target cells could exist. Leaving open the possibility that the target cells don't necessarily need to have all four candidates present -- i.e., r7c5=17 would be sufficient to still deduce some eliminations.

1) OK and well done for your 1r13c6 => 1r2c9.
In an exocet pattern, if it's shown that one digit can occupy the 2 targets, it can not be in the final solution.
You can just see that this is not in ronk's diagram. what you did is one way to continue.
having shown 2r13c6 => 1r2c9 1r7c5 you can conclude that they all are false.

2) Most often, you can not catch in once the full potential of you "template review", unless you build complex structures.

3) For sure the exocet pattern is only one among other patterns and has downgraded forms.
The template analysis catches all possible patterns (as does my brute force algorithm).

champagne
champagne
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### Re: bi bi pattern in hardest puzzles

champagne, Thanks for your response and I await with interest for your analysis.

It seems to be a fundamental property that when two cells in a mini-line contain only digits that aren't givens in a band, there will be other cells in the band that contain all of them after simple exclusions for singles and tuples have been made. That seems to be the way that your solver recognises potential openings. As I see it however, the more important thing is to identify the pattern of cells where the Exocet digits are all excluded. This may identify other potential target cells where some member digits are missing when the search is made.

I'm interested in your multi-fish but I'm not sure what the term describes as it seems rather general. To be of most use to a manual solver, I think all the truths (or strong links) should be counted by rows and the weak links counted by columns or vice-versa - as in the one-band Exocet analysis I described. Looking at ronk's diagrams there are usually sub-patterns of this type. What I'm now looking for is either
a) a two-way inference from the pattern that can be carried forward or
b) two patterns that together give such an inference.
That is, I donâ€™t want to have to follow multiple cases.

<Here> You mention a multi-fish approach that reduces an SE 11.9 puzzle to 8.3, but I don't see it! Not wanting to go off topic, I'd be grateful if you (or perhaps ronk) would describe that either in a fresh thread or in a PM to me.

DPB
David P Bird
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### Re: bi bi pattern in hardest puzzles

David P Bird wrote:I'm interested in your multi-fish but I'm not sure what the term describes as it seems rather general. To be of most use to a manual solver, I think all the truths (or strong links) should be counted by rows and the weak links counted by columns or vice-versa -
<Here> You mention a multi-fish approach that reduces an SE 11.9 puzzle to 8.3, but I don't see it! Not wanting to go off topic, I'd be grateful if you (or perhaps ronk) would describe that either in a fresh thread or in a PM to me.

DPB

My solver, when applying Allan Barker model, is always looking for specific patterns having a pure rank o logic or a "nearly rank o" logic;

Up to now, 3 patterns of value have been identified

a row based or columns base pattern (the main sets are in rows or in column and sometimes additional sets are cells)
a rectangle pattern made of 2 rows and 2 columns.

a third pattern has been shown by ronk, downgrading one of the puzzle I put in my short list, but I did not work on it so far (it is in the hardest puzzle new thread).

In the following puzzle, we have a row based pure rank 0 logic.

12.3.....4.5...6...7.....2.6..1..3....453.........8..9...45.1.........8......2..7;5;elev;1;;;;;G1

Code: Select all
`__ A____ B_____ C____ |D___ E____ F____ |G____ H____ I____ 1||1____ 2_____ 689__ |3___ 46789 45679 |45789 4579_ 458__ 2||4____ 389___ 5____ |2789 12789 179__ |6____ 1379_ 138__ 3||389__ 7_____ 3689_ |689_ 14689 14569 |4589_ 2____ 13458 4||6____ 589___ 2789_ |1___ 2479_ 479__ |3____ 457__ 2458_ 5||2789_ 189___ 4____ |5___ 3____ 679__ |278__ 167__ 1268_ 6||2357_ 135___ 1237_ |267_ 2467_ 8____ |2457_ 14567 9____ 7||23789 3689__ 23789 |4___ 5____ 3679_ |1____ 369__ 236__ 8||23579 134569 12379 |679_ 1679_ 13679 |2459_ 8____ 23456 9||359__ 134569 139__ |689_ 1689_ 2____ |459__ 34569 7____ `

It's good, to work on multi-fish patterns to have a reliable slave producing a reduced PM as that one

here
'+' show any extra candidate
'X' is a cell either assigned or containing no candidates of the floors studied.

Code: Select all
`A____  B____ C____ |D___  E____  F___ |G___ H___ I____ X      X     89+   |X     789+   79+  |789+ 79+  8+  X      89+   X     |2789* 2789+* 79+  |X    79+  8+  <==89+    X     89+   |89+   89+    9+   |89+  X    8+ X      89+   2789* |X     279+*  79+  |X    7+   28+ <==2789*  89+   X     |X     X      79+  |278* 7+   28+ <== 27+    X     27+   |27+   27+    X    |27+  7+   X     2789+* 89+   2789+*|X     X      79+  |X    9+   2+  <==279+   9+    279+  |79+   79+    79+  |29+  X    2+ 9+     9+    9+    |89+   89+    X    |9+   9+   X           xx                         xx         xx   xx`

In that situation you have the simplest pattern you can look for

16 sets (or truths in the last version of AB model)
2789R2 2789R4 2789R5 2789R7
89C2 79C6 79C8 28C9 D2 E2 C4 E4 A5 G5 A7 C7

I could produce the XSUDO diagram, but I am not familiar with the process to show it in the post.

in the column marked 'xx' the '2789' must be exclusively in rows 2457
In all cells marked '*' extra candidates can be removed.

This gives in row 1 a pair and a triplet and this is the start for several assignments

champagne
champagne
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### Re: bi bi pattern in hardest puzzles

champagne wrote:In the following puzzle, we have a row based pure rank 0 logic.
12.3.....4.5...6...7.....2.6..1..3....453.........8..9...45.1.........8......2..7;5;elev;1;;;;;G1
...
I could produce the XSUDO diagram, but I am not familiar with the process to show it in the post.

Very nice find. I looked at this puzzle earlier, but didn't see your multi-digit fish. Here are clickable XSUDO graphics for it and its complement.

____ ____

XSUDO pastable truth/link solutions, where eliminations assume two locked-candidate steps were performed first.

Code: Select all
`     16 Truths = {2R2457 7R2457 8R2457 9R2457}     16 Links = {2c9 7c68 8c29 9c268 57n1 47n3 2n4 24n5 5n7}     18 Eliminations --> r138c6<>9, r1c68<>7, r7c13<>3, r9c28<>9, r13c9<>8, r1c8<>9, r2c5<>1,      r4c5<>4, r6c8<>7, r8c9<>2, r8c6<>7, r8c2<>9`

Code: Select all
`     20 Truths = {2C13457 7C13457 8C13457 9C13457}     20 Links = {2r68 7r168 8r139 9r1389 57n1 47n3 2n4 24n5 5n7}     18 Eliminations --> r138c6<>9, r1c68<>7, r7c13<>3, r9c28<>9, r13c9<>8, r1c8<>9, r2c5<>1,      r4c5<>4, r6c8<>7, r8c9<>2, r8c6<>7, r8c2<>9`
Last edited by ronk on Sun Apr 01, 2012 7:58 pm, edited 1 time in total.
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