Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

Exotic patterns a resume

Postby champagne » Mon Apr 02, 2012 7:02 am

Over the last years, several of us have worked on what has been called “exotic patterns. It's time to summarise all that work in appropriate threads.

In that point I share the views of David P Bird who just opened a new thread: "sharks a truth balancing method" focused on a player's view.

I intended for a while to open on my side a new thread more focused on the view of a program exploring all these "exotic patterns".

No question to be in competition. I"ll contribute to David's thread, but I think better to keep separate both topics and I am convinced David will agree and will contribute as well to that thread;

This thread should not integrate the symmetry of given, on which I have nothing to add, except in the post 2 (definitions)

As that thread intend to be a kind of memory in that field, I open several posts to be updated later with the following content


Post 2: definition of the most common patterns for each family
Post 3: why "exotic" patterns are not at all exotic. (in my opinion)
Post 4: extended (generic) definition of the "exotic patterns".
Post 5: Exploring a puzzle after direct effect of a SK loop
Post 6: Exploring a puzzle having an Exocet pattern
Post 7: reserved


some statistics

Those statistics are extracted from my data base of all "potential hardest" known. here

The selection criteria to enter that data base is the Sudoku Explainer rating (turning now to skfr rating).

after an analysis of the first 30 000 puzzles in that data base, I got the following results

Code: Select all
20952 puzzles have an Exocet pattern
 4954 have a double exocet, the most active tool
1259 have also a "shark" pattern (multi_fish)

4896 have one or more  shark pattern

 1700 have an SK loop

 68 only have a symmetry of given








References

I am missing a very important reference , the first use of the SK loop

If I am right, "steve k" posted it first in October 2007 on the Eureka forum.
At that time, my solver had produced one of these boring solutions using AIC's nets.
If the use of the SK loop as start did not make the puzzle trivial, it brought such simplifications that I immediately introduced it in my solver. (the infrastructure was ok for that).

The second important reference is the work done by Allan Barker. He first exposed the logic of the Exocet, he first built huge SLGs and it's program is an important tool to check the validity of an assumption and to summarise it with nice graphic presentations

Here some of the key references
Allan Barker site
and some key threads in that forum
http://forum.enjoysudoku.com/local-area-sets-and-three-dimensional-sudoku-t5912.html
http://forum.enjoysudoku.com/great-monster-loops-t6407.html
http://forum.enjoysudoku.com/almost-fishes-patterns-t6490.html
http://forum.enjoysudoku.com/set-logic-solns-top1465-77-easter-mons-golden-nugget-t6049.html
http://forum.enjoysudoku.com/the-illusion-of-fata-morgana-t6353.html

based on Allan Findings, the first Exocet work in that thread

http://forum.enjoysudoku.com/bi-bi-pattern-in-hardest-puzzles-t6546.html
Last edited by champagne on Fri Oct 19, 2012 2:14 pm, edited 5 times in total.
champagne
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Posts: 5576
Joined: 02 August 2007
Location: France Brittany

Exotic patterns practical definitions

Postby champagne » Mon Apr 02, 2012 7:02 am

definition of the most common patterns for each type

In that post,

Symmetry of given
"V loop" and it's special well known form, the SK loop
Exocet
Multi-fish (or shark)

Symmetry of given

Hidden Text: Show
If we look at the statistics, symmetry of given seems somehow anecdotal

68 puzzles out of 30 000 and in that case, I would say that this is a highly biased ratio

Nevertheless, it is a powerful “exotic” technique and with lower ratings, somebody using as sample the pattern game could find it with a higher frequency.

I, for example, use the generation of puzzles having the "symmetry of given" as one way to have various seeds. Some of them have been submitted;

The best I think, for anybody interested, is to go through that thread where most has been said

symmetry of given


V loop definition

Hidden Text: Show
The common (and up to now only) pattern for the V loop is very strict and easy to detect.
The elementary component is a box having the following appearance
Code: Select all
z b z 
a x a 
z b z

where
'x' is an assigned cell
'a' 'b' are non assigned cells
'z' plays no role in the pattern
'a' has in total 4 candidates
'b' has in total 4 candidates

Note: any additional constraint would not be part of the definition

Next requirement to have a "V loop" is to have four such boxes forming a rectangle

Code: Select all
z a z | z d z
b x b | c x c
z a z | z d z
-------------
z h z | z e z
g x g | f x f
z h z | z e z


Here, we also show how the loop will work. Just follow the sequence a;b;c;d;e;f;g;h

Last but key requirement, it must be possible to pair digits in a;b;c;d;e;f;g;h in such a way that
(a1;a2 are the 2 pairs in a )
a2 common to b1
b2 common to c1
...
h2 common to a1

The most common form of that pattern in hardest puzzles is the SK loop (see next definition).
I voluntarily take as example a puzzle having a different pattern.

This puzzle that I name VS (virus loop Sample) has been published first on a French forum. It is a relatively easy puzzle where usually the "V loop" is not searched.
The start is easy and the puzzle becomes difficult in that point

Code: Select all
.........1....72...7..84.6...8....93.6..4..7.93....6...9.73..8...59....2......... VS puzzle

24568 2458 2469  |1256 12569 3     |145789 145 145789
1     458  3469  |56   569   7     |2      345 4589   
235   7    239   |125  8     4     |1359   6   159   
-----------------------------------------------------
457   145  8     |1256 12567 1256  |145    9   3     
25    6    12    |3    4     9     |158    7   158   
9     3    147   |8    157   15    |6      2   145   
-----------------------------------------------------
246   9    1246  |7    3     1256  |145    8   1456   
34678 148  5     |9    16    168   |1347   134 2     
23678 128  12367 |4    1256  12568 |13579  135 15679 



the V Loop is not hard to see, although finding the sequence of common digits requires attention

Code: Select all
r3c13 r3c79 r12c8 r89c8 r7c79 r7c13 r89c2 r12c2
25   39    15    34    15    46    12    48    25   

As here, in some rows, columns or boxes, several possibilities exist to define a1;a2 b1,b2, but there is always a place where ambiguity disappears.


How does it work?

The logic is explained in the "extended definition", but the properties of the chain
a_b_c_d ... brings to the conclusion that,

as soon as we have a loop
any 'a2 common to b1' forces an exclusive or a2^b1


so in each row, column, box of the loop, extra candidates can be cleared;

eg, in box 3, 1;5 are locked in row 3 and column 8

This is the direct effect.
How to continue with a "V loop" is explained in a separate post.



SK loop definition


Hidden Text: Show
The SK loop is the original form of the "V" loop. It has been first shown by Steve Kurzhals in Easter Monster.
The original post has been lost, but here is a copy made by ronk including small additions
Code: Select all
 1      A478     34578   | 3567    3689    5678    | 3489   I369     2
L238     9      L378     | 4      K12368  K12678   |J138     5      J368
 23458  A248     6       | 1235    12389   1258    | 7      I139     3489
-------------------------+-------------------------+-----------------------
 2468    5       1478    | 9       1246    3       | 128    H1267    678
 234689 B12468   13489   | 126     7       1246    | 123589 H12369   35689
 2369   B1267    1379    | 8       5       126     | 1239    4       3679
-------------------------+-------------------------+-----------------------
 7      C148     14589   | 1235    12348   12458   | 6      G239     3459
D456     3      D145     |E12567  E1246    9       |F245     8      F457
 45689  C468     2       | 3567    3468    45678   | 3459   G379     1

(27)r13c2=(27-16)r56c2=(16)r79c2-(16)r8c13=(16-27)r8c45=(27)r8c79-
(27)r79c8=(27- 16)r45c8=(16)r13c8-(16)r2c79=(16-27)r2c56=(27)r2c13 -
loop


As one can see, that original form used a chain of AALS. The "V loop" and the virus chain logic can be applied as well.
As my solver look specifically for the "V loop" logic, the result does not tell if the pattern is a SK loop or not.
So in my statistic files, I have to use the generic "V loop" qualifier



Exocet definition

As for the SK loop, I reduce the pattern to what reasonably a player can find. The extended definition will cover other cases.
Hidden Text: Show
The reduced definition uses

Code: Select all
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.

Code: Select all
The solution of the base require 2 different digits
The target must contain the 2 digit and this forces each cell of the target to have one of them
So there is no room for other digit.


Nothing more is required to define an exocet (but a wider definition exits)

The definition is valid for any number of digits in the base, in fact non trivial example have 3 or 4 digits. (may be I should replace 'non trivial' by 'explored')
This is the direct effect of an exocet.


For a player the major problem will be
- how to detect that we have an exocet.
- what to do out of it


Exocet common pattern

Hidden Text: Show
The nearly exclusive pattern found so far has other very interesting properties

Let see the example of â"fata morgana" the first puzzle where that pattern was seen.

........3..1..56...9..4..7......9.5.7.......8.5.4.2....8..2..9...35..1..6........ fata morgana

Code: Select all
2458  2467  245678 |126789 16789 1678  |24589  1248  3     
2348  2347  1      |23789  3789  5     |6      248   249   
2358  9     2568   |12368  4     1368  |258    7     125   
----------------------------------------------------------
12348 12346 2468   |13678  13678 9     |2347   5     12467
7     12346 2469   |136    5     136   |2349   12346 8     
1389  5     689    |4      13678 2     |379    136   1679 
----------------------------------------------------------
145   8     457    |1367   2     13467 |3457   9     4567 
249   247   3      |5      6789  4678  |1      2468  2467 
6     1247  24579  |13789  13789 13478 |234578 2348  2457 


Here the base is r5c46 (136) and the target r4c2 ;r6c8.
Most identified exocet (nearly all) have as here the base and the target in the same band/stack.

The direct effect is <24> r4c2
Several players have studied that pattern (see for example here )

- Giving simplified way to verify the basic property base => target.
- Assessing if I am right that cells equivalent to r6c2;r4c8 should always be empty.
That work will stay in the thread open by David P Bird


My point is to develop the basic property in that pattern

As the digits solution of r5c46 are also solution for r4c2 r6c8, we have in the central band one of these scenario

=========== scenario 1
Code: Select all
12348 13    2468   |678    678   9     |247    5     2467
7     246   2469   |13     5     13    |249    246   8     
89    5     689    |4      678   2     |379    13    1679 


=========== scenario 2
Code: Select all
12348 16    2468   |378    378   9     |2347   5     247
7     234   249    |16     5     16    |2349   234   8     
389   5     89     |4      378   2     |379    16    1679 


=========== scenario 3
Code: Select all
12348 36    2468   |178    178   9     |247    5     1247
7     124   249    |36     5     36    |249    124   8     
189   5     89     |4      178   2     |379     36   1679 


Usually, this is enough to find new eliminations.
This will developed later





Extended exocet pattern

Hidden Text: Show
To prove that a digit must be in the target, we have used so far the one floor PM.
This makes sense for several reasons

1) usually it works
2) The proof is always easy, making the base true and the targets false.

In the logic of an exocet, any more complex proof can be used.
Usually, a short chain can provide the missing information to validate a digit.
The more complex will be the proof, the less attractive will be the solution.



Double exocet pattern

Hidden Text: Show
With the general definition we have, there is "a priori" no reason why we would not find several exocet in the same PM.
In fact, if we use the extended definition, it's always the case but with some redundancy.

In the 30000 first puzzles of my data base of "potential hardest puzzles" my solver detected 4954 puzzles having a "double exocet pattern" with the limitations used here.

This is much more that the puzzles having a SK loop in the same lot (1700).

I did not make an exhaustive check, but a quick overview shows that they (most of them if not all) have a very similar pattern

Code: Select all
They share the same band
They have the same digits in the base


May be somebody will explain one day why. For the time being, i's a fact.
Here the first puzzle in the list "03 EE" of my data base


1......8...71....6.9.....5...56....7..17.4..5......34.57.2.............2..2.61...;226;elev;91

Code: Select all
1     23456 346   |3459  234579 235679 |2479  8    349   
2348  23458 7     |1     234589 23589  |249   239  6     
23468 9     3468  |348   23478  23678  |1247  5    134   
--------------------------------------------------------
23489 2348  5     |6     12389  2389   |1289  129  7     
2389  238   1     |7     2389   4      |2689  269  5     
7     268   689   |589   12589  2589   |3     4    189   
--------------------------------------------------------
5     7     34689 |2     3489   389    |14689 1369 13489
34689 1     34689 |34589 345789 35789  |45689 369  2     
3489  348   2     |34589 6      1      |4589  7    3489 


First exocet base r7c56 target r8c3r9c9 digits 3489
Second exocet base r9c12 target r7c9r8c4 digits 3489

Note in that case some simple logic

The first target is under control of the second base
So the second solution is complementary (in digits) to the first one
Cells r7c3 and r9c4 are under control of the 2 bases
So r7c3=6 and r9c4=5

This is usually enough to solve the puzzle easily.
Here we have for example a pair 89 in row 6 => r6c9=1


The double exocet is a true killer.


Complementary AAHS pattern

Hidden Text: Show
This is easy to understand after the double exocet pattern.
If 2 AAHS are located as in the double exocet pattern, it is possible to check directly whether they must have complementary digits.

The process is exactly the same as for the proof of an exocet digit;
1) you make both AAHS true for the digits
2) you prove this is not valid.

As for exocets, this will usually work (when it is true) using the digit PM, but can require a more complex analysis

If the 4 digits are proven "not shared", all cells seen by the 2 AAHS can not contain the 4 digits.

That pattern has still some solving potential if it is established that 3 digits can not share both AAHS



Multi-fish definition Preliminary statement

Hidden Text: Show
Here we enter a more complex field.

Readers are supposed to have a reasonable knowledge of Allan Barker model, or of any similar approach of "Set/Link sets" constructions. (see reference links)

Anybody having studied Allan Barker approach could share my views:

The full rank 0 logic is quite simple to catch and can be applied without any restriction.

As soon as you introduce non rank 0 logic, the rules determining where eliminations can take place are more complex and it is very easy to make false conclusions.

Anyway, hand made SLG's should cautiously be controlled using XSUDO the very good program proposed by Allan Barker.

The general strategy followed here is to accept only fully rank 0.
Subject to deeper investigation, although I thought of accepting "nearly rank 0 logic", my solver does not recognise such SLG's.


Another point, coming from experience, is that a specific PM offers many possibilities to build SLGs leading to eliminations.

The general strategy will be to identify as much as possible the smallest “full rank 0” logic.
Here again, we have many examples that some puzzles offer several possibilities.

To be honest, my solver start a search of “fully rank 0” logic only if a multi-floors brute force analysis as shown some potential.

Then, the solver looks for specific patterns, so it will miss all non referenced patterns.

A player has also to rely on specific patterns, but can afford less precise definitions of theses patterns. This is an open field for creativity


So the general definition is that we are looking for "fully rank 0" patterns, accepting at the limit some specific "early rank 0" patterns.

The "operational" definition is reduced to a list of identified patterns that can be searched.

One more remark is what to search??
My solver explore only multi fish. The world of "full rank 0 logic" is open to any construction.

Ronk recently (see some posts after that one) came with a "full rank 0 logic" where sets were exclusively cells.

As soon as we will have some experience of new solving potential with such logic, a new chapter will be open.

As a start, I post examples of the main patterns
Addition will come after some more selection work will have been done in the data base

Note: examples are given here in the simplest form
I'll prepare on my website a more attractive form, but this requires more time.


A typical row based or column based pattern

Hidden Text: Show
In such puzzles, sets are exclusively made of a collection of rows (or columns)
Link sets are a mix of columns (or rows) and cells
At the end, it works if we find a 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
Code: Select all
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     


Code: Select all
sets
2789R2 2789R4 2789R5 2789R7
linksets
89C2 79C6 79C8 28C9 r2c4 r2c5 r4c3 r4c5 r5c1 r5c7 r7c1 r7c3



The most useful seen rectangle pattern

Hidden Text: Show
Rectangle patterns are often found in puzzles having other exotic tools.

I assume that if a SK loop exists it will be found first
I assume also that many players will search first rows or columns based multi-fish

Then, we are interested in rectangle patterns

- Either appearing as the only available tool
- Or linked to an exocet (I'll explain why in the chapter describing what to do after an exocet has been found)

Going through the files of "potential hardest"  puzzles, it appears that the main and nearly exclusive pattern found with such restrictions is the following

.....67...5.1...3...9.2...42..........8.4...29.46..........7.6....3..1..8.......5;11.30;1.20;1.20;elev;318;G3

Code: Select all
13+   13+   13+   |X     3+    X     |X     1+    1+   
67+   X     67+   |X     7+    X     |6+    X     6+   
1367  1367+ X     |7+    X     3+    |6+    1+    X     

X     1367  1367+ |7+    137+  13+   |36+   17+   1367+
1367+ 1367  X     |7+    X     13+   |36+   17+   X     
X     137   X     |X     137+  X     |3+    17+   137+ 

13+   13+   13+   |X     1+    X     |3+    X     3+   
67+   67+   67+   |X     6+    X     |X     7+    7+   
X     1367+ 1367+ |X     16+   1+    |3+    7+    X     


Code: Select all
sets
1367R3 1367R9 1367C5 1367C9 r4c2 r5c2 r6c2
linksets
1367C2 37B2 16B3 16B8 37B9 r3c1 r4c5 r4c9 r6c5 r6c9 r9c3 r9c5

The most important is the sets structure.

We have the 2 rows and 2 columns, here r39 c59
And we have a mini row or mini column, here r456c2
The rectangle is located in the 2 bands 2 stacks that does not contain the mini row.

This has been the only pattern in the lot of puzzles having also an exocet.
A very small number of puzzles have only one or 2 cells as sets
No puzzle has been found with no cell as set and no alternative tool (SK loop or multi-fish)


A row or column based SLG plus cells


Hidden Text: Show
It is relatively frequent to have a rank 0 logic based on rows or columns requiring additional cells.
Here is an example

..1...5...2.4...6.3....7....6.28........9..2.......4.65.....1...9.8...4...7.....3;54;col;H2;G13

Code: Select all
7+    7+    X     |3+    3+    3+    |X     37+   7+   
7+    X     5+    |X     135   135+  |37+   X     17+   
X     5+    5+    |15+   15+   X     |X     1+    1+   

17+   X     35+   |X     X     135+  |37+   1357+ 157+ 
17+   1357+ 35+   |1357+ X     135+  |37+   X     157+ 
17+   1357+ 35+   |1357  1357  135   |X     1357+ X     

X     3+    3+    |37+   37+   3+    |X     7+    7+   
1+    X     3+    |X     1357+ 135+  |7+    X     57+   
1+    1+    X     |15+   15+   15+   |X     5+    X     



Code: Select all
sets
1357R2 1357R4 1357R5 1357R8 r6c6
linksets
17C1 35C3 135C6 37C7 157C9 r2c5 r4c8 r5c2 r5c4 r8c5


That SLG has clearly a row base for sets (rows r2458)
But the cover set has one link set in excess.

Happily, we find in one of the linksets (column 5) a cell
. outside the row sets (generating no triple point)
. having no extra digit.

We can use it as set and the system is now balanced.

We have here only one cell, we can have more.
Last edited by champagne on Sun Sep 22, 2013 9:54 am, edited 15 times in total.
champagne
2017 Supporter
 
Posts: 5576
Joined: 02 August 2007
Location: France Brittany

no so exotic

Postby champagne » Mon Apr 02, 2012 7:03 am

Why "exotic" patterns are not at all exotic. (in my opinion)

Let me start with that example
Here 5 puzzles.

Try to solve them in Sudoku Explainer without the fish pattern rule.

Code: Select all
1.......2.3..4..5...25.67....89.15......7......74.52....16.79...6..9..1.9.......8
1.......2.3..4..5...67.81....12.34.............28.46....74.63...1..8..7.9.......4
..........12..3..4.94..1..7....6..2....9..7...29..7..1....5.8.....3...4..31..4..2
...........47.32...125.937..97...14...........65...93..391.742...12.85...........
..1...2...3.4.5.6.6.......4.5.6.2.7...........2.7.3.4.8.......9.6.2.7.3...3...6..


You should see ratings in the range 8.3 to 8.5
I suspect the last proposed rating tool would lead to equivalent rating.

I would not say these puzzles are "easy", but they surely would not be classified as hard in many newspapers.

These puzzles are pure jellyfish. A pattern that chains have difficulties to crack.

Most of the rating tools are deeply "chain oriented" as soon as the basic patterns have been applied.

Consequently, all patterns having a "global approach" potential are over rated.

This has been shown through the tools exposed in that thread for "potential hardest", but there is no reason to exclude a continuous potential of such patterns.

In the common way we solve puzzles, we start using chains just after we have applied basic"global patterns" (locked sets, fishes); No surprise if at that point chains are generally the best way to go ahead.

On top of it, for a player, following the assumption of a candidate "true" in chain mode open many doors.

But as soon as "simple chains" are not found, a player should look for other "global" tools.

A well balanced solving (and rating) system should in fact use both ways.

Generally speaking, solving a global situation (fishes, SK loop and in some ways exocet) creates new strong inferences and chains like very much strong inferences.

There is no reason to think that chains would not in the same way create conditions for appearance of new "global" tools.

It's just that that field has not been seriously explored so far.

As a conclusion, I am surprised to read that a tool (exocet) visible in about 2/3 of all known potential hardest puzzles is not relevant. I would look in another direction.
Last edited by champagne on Mon May 28, 2012 8:53 am, edited 3 times in total.
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extended (generic) definition of the exotic patterns

Postby champagne » Mon Apr 02, 2012 7:03 am

V loop extended definition

Hidden Text: Show
The wider extension for the V loop is more or less what I described in that post

here

a post dated October 29 2007

In that wider definition, chaining was studied for any AAHS having 4 free digits.
I named at that time elementary links “virus pattern

I’ll keep that name here, but reducing the scope to the component we have seen in the definition of the V loop

So we will mainly see here the proof, based on “virus pattern” chaining, of the properties of the V loop and partial or other complete possible forms of the loop.

In the definition I wrote

The elementary component is a box having the following appearance
Code: Select all
z b z 
a x a 
z b z

where
'x' is an assigned cell
'a' ‘b’ are non assigned cells
‘z’ plays no role in the pattern
‘a’ has in total 4 candidates
‘b’ has in total 4 candidates

Here
‘a’ is a “virus pattern”
‘b’ is a “virus pattern”

‘a’ and ‘b’ can be chained if

They belong to the same region
They share 2 digits

Eg: ‘a’:1234 ‘b’:3456 12’a’34 34’b’56


And we have the trivial implications

34’a’ => 56 ‘b’ 34’b’ => 12’a’

If we now can chain ‘b’ to ‘c’ using the 56’b’, we have for example

12’a’34 34’b’56 56’c’39

34’a’ => 56’b’ =>39’c’ 56’c’=>34’b’ =>12’a’


We can also write

12’a’(false)=>34’a’true=>39’c’ true.

In a solver using AAHS in the set of rules, this is an helpful implication.

As the relation is not symmetric, the use of such chains requires some attention.

Lets now assume we can form a loop, as in the V loop

12’a’34 34’b’56 56’c’39 39’d’12 12’a’34 …..

We have now 12’a’(false) =>12’d’ true
By construction ‘a’ and ‘d’ share the same regions. (loop)

So any other candidates 12 of the region can be eliminated.

This is the proof for the V loop effect using the virus chain property. One has just to cut the loop in any region crossed by the loop to have the full effect.

If we reduce “virus pattern” component to row or column pairs of cells (other have a poor interest in practice), we have in fact a very limited possibility to create loop.

One is the well known V loop formed of 4 boxes
Another one crosses 6 boxes with the following appearance

Code: Select all
X _ X
X X_
_ X X


Up to now, that loop has not been seen.
As it has not really been searched, it could be seen one day.
But my solvers (old and new) would accept that loop and have never found it.




Exocet extended definition


Hidden Text: Show
we keep in mind the generic definition of an exocet

========================

Code: Select all
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.

Code: Select all
The solution of the base require 2 different digits
 The target must contain the 2 digit and this forces each cell of the target to have one of them
 So there is no room for other digit.


=========================


In fact, here we can go in 3 directions

extending the scope of the search
reducing the scope of the search

Mixing both to define new patterns



Extension of the definition to any AAHS

This is possible, and works,
As far as I could see when I did that in my solver, the results are highly redundant with the first definition



Partial Exocets

We have a partial exocet if the exocet digit per digit rule is verified for 2 or more digits.
It can be verified
for 2 digits in a 3 digits base giving one "standard" pair
for 2 or three digits in a 4 digits base giving one or three "standard" pairs

In a partial exocet, we have no direct elimination,
but the scenario study can be applied to the pairs of digits verifying the rule.
(for example, the ABI loop can work for that pair)

Jexocet

The Jexocet is by far the most common exocet pattern.
I take "David P Bird"'s presentation for that specific pattern

Code: Select all
      v   v       v           
*-------*-------*-------*
| b b . | . . . | . . . |     b = base cell restricted to digits from [abc] or [abcd]
| . . . | / . . | t . . |     t = target cell (at first will contain every base digit)
| . . . | t . . | / . . |     / = companion empty cell unable to hold any base digit
*-------*-------*-------*     v = cross line pointers


In reference to this pattern, a three step system for recognising one-band Exocets is:
1: Find two base cells in a mini-line.
2: Look for two companion empty cells in the other two boxes in the two other lines.
3: Check that in the 3 cross lines each base digit is confined to 2 rows in the 2 parallel bands.


here applied to "fata morgana"
base r5c46 target r4c2 r6c8
cells r6c2 r4c8 empty
cross lines are colums 2 5 8
one occurrence of digits in columns 26
1 confined in rows 1;9
3 confined in rows 2;9
6 confined in rows 1;8
Code: Select all
     v                v              v
X    6+   6+   |16+  16+  16+  |X    1+   3g
3+   3+   1g   |3+   3+   X    |6g   X    X 
3+   X    6+   |136+ X    136+ |X    X    1+   

13+  136+ 6+   |136+ 136+ X    |3+   X    16+
X    136+ 6+   |136  X    136  |3+   136+ X
13+  X    6+   |X    136+ X    |3+   136  16+

1+   X    X    |136+ X    136+ |3+   X    6+ 
X    X    3g   |X    6+   6+   |1g   6+   6+ 
6g   1+   X    |13+  13+  13+  |3+   3+   X 




Twin Jexocets


In the former diagram, we can still have a pattern with the same properties with one of the 2 cells r4c8 r6c2 having the digits of the base.
The necessary condition seems to be that the pair of cells r4c2;r6c2 or r4c8;r6c8 is an AHS

An example is given in Platinum Blonde where the base is in r12c7

Code: Select all
35678 34589 34679 |4679   5689   4578   |679    1      2     
15678 14589 4679  |124679 125689 124578 |679    56789  3     
15678 1589  2     |3      15689  1578   |4      56789  6789 
----------------------------------------------------------
237   2349  1     |8      236    234    |23679  234679 5     
235   6     349   |124    7      12345  |8      2349   149   
23578 23458 347   |1246   1235b6 9      |12367  23467  1467 
----------------------------------------------------------
1236  123   8     |5      1239   1237   |123679 234679 14679
9     123   36    |127    4      12378  |5      23678  1678 
4     7     5     |129    12389  6      |1239   2389   189   


the target is here made of
cell r4c8
AHS r7c8 r7c9 (digit 4 is locked in the AHS)

This works as an exocet if we keep in mind the basic rules

the target is reduced to
679 in r4c8
4679 in r7c89

for each pair in the base
other digits are excluded from the target
the digits of the base are erased form the cells seeing all the target cells
and the ABI loop can be applied where it is valid;
Last edited by champagne on Sat Oct 20, 2012 9:31 am, edited 4 times in total.
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what to do after a V loop has been seen

Postby champagne » Mon Apr 02, 2012 7:03 am

What to do after a V loop has been seen

This is a first shot to be improved later

In my database

Code: Select all
1700 puzzles have an identified V loop (out of 30 000)
. 1652 have also an exocet or a multi fish pattern
. among them 195 have an exocet pattern



A multi fish pattern, usually, does not bring more elimination. At least this is what has been seen in analysed examples
One more interesting point is to detect SK loop having also an exocet pattern.
This has not been seriously investigated so far,

so I developed



V loop + exocet a complete solution for the first in my list, puzzle #160


Without exocet, the right way is to work in priority in the V loop
Rating program continue to over rate the puzzle after eliminations from the V loop have been done due to the fact that they are ignoring the properties of that loop.

However, the puzzle can still offer a good resistance.
Easter Monster stays somewhere on the high side. It is still a difficult puzzle, but not the worse.
Other puzzles will collapse applying the right process.

As far as I remember, Easter Monster has the same eliminations using the V loop or one of the 2 identified multi fish patterns;

As a first approach on "how to fight against the V loop", I suggest to have a look at the solution for Easter Monster as I described it 2 years ago

EasterMonster

One important point is that the solution, apart of the SK loop properties, don't use more than chains rated around 9.0 by serate.

For sure, that solution of Easter Monster remains something boring. A player will have more fun fighting against a mix "V loop + Exocet" as above.

Possibly the path for Easter Monster could be improved with chains including objects as XWings, Pairs .. My old solver can't do that but Sudoku Explainer does it.
I intend, in the new solver to include that possibility and I'll then run again such puzzles.
Last edited by champagne on Sat Oct 20, 2012 9:36 am, edited 6 times in total.
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what to do after an exocet has been seen

Postby champagne » Mon Apr 02, 2012 7:04 am

what to do after an exocet has been seen

we are assuming here that we have only one exocet and no rank 0 logic, no sk loop.

Having shown recently that most exocets are Jexocets, I’ll introduce in that post the “abi” loop, a tool as useful as the SK loop if not more (we have many more exocets than SK loops.

I guess any reader knows what are the direct eliminations that can be done in the target cells once an exocet has been seen.
In that post, we will focus mainly on the reduction of the authorized pairs in the base.
I also added an example for puzzles having a high potential for eliminations in the floors of the exocet

First example will be the start of "fata morgana", where the “abi”loop has full effect
Next example will be the start of Golden Nugget done using again the “abi”loop. Unhappily, this is far from solving the puzzle, but the step done is important.
Last example is not an exocet, but a puzzle having a pattern close to an exocet and a very high potential for eliminations using the corresponding floor


Fata morgana is the puzzle in which the exocet pattern has been found.

Several proofs have been done that the true value in the base is 36r5c46 (“ttt” and others)
In that example, the path is done using the “abi” loop

fata morgana

The second example is the start of Golden Nugget
Golden Nugget has no potential for elimination in floors 1247 out of the exocet direct effect.

Golden nugget


The third example is the complete solution of a puzzle (number 12177 in the data base) with a large potential for elimination in the floors of a “nearly” exocet.
That example shows how, using the exocets properties (even partial as in that example) side eliminations can be done.
I did not find use of the "abi" loop in that example


puzzle 12177
Last edited by champagne on Mon May 21, 2012 2:30 pm, edited 4 times in total.
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Re: Exotic patterns for manual solvers

Postby champagne » Mon Apr 02, 2012 7:04 am

Post 7: reserved
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7658;GP;H1521

Postby champagne » Mon Apr 02, 2012 3:04 pm

a very interesting pattern posted by ronk to day in another thread

here

98.7.....7.6...8...54......6..8..3......9..2......4..1.3.6..7......5..9......1..4 # 7658;GP;H1521

that pattern proves 16 eliminations.

16 Truths = {5689N47 47N5689}
16 Links = {7r4 8r7 3c4 6c7 125b5 459b6 249b8 125b9}
16 Eliminations --> r4c23<>7, r5c69<>5, r7c13<>8, r8c69<>2, r23c4<>3, r69c5<>2, r13c7<>6,
r69c8<>5

we have exactly the same results with another pattern which is not purely rank 0
that pattern is within the multi fish concept

17 Truths = {3R5689 6R5689 7R5689 8R5689 3B5}
15 Links = {3c4 6c7 69n5 58n6 69n8 58n9 78b4 678b7}
16 Eliminations --> r4c23<>7, r5c69<>5, r7c13<>8, r8c69<>2, r23c4<>3, r69c5<>2, r13c7<>6,
r69c8<>5,


it would be interesting to see if ronk's findings can be replicated in other puzzles.
This is another way to come to eliminations and I prefer by far a pure rank 0 logic.

champagne

EDIT I made a mistake when I defined the SLG in xsudo.
You have a pure rank 0 logic if you replace the truth 3B5 by the link 3b4
Last edited by champagne on Wed Apr 04, 2012 7:53 am, edited 1 time in total.
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Re: Exotic patterns for manual solvers

Postby David P Bird » Mon Apr 02, 2012 8:04 pm

champagne wrote:Over the last years, several of us have worked on what has been called “exotic patterns. It’s time to summarise all that work in appropriate threads.

In that point I share the views of David P Bird who just opened a new thread: “sharks – a truth balancing method” focused on a player’s view.

I intended for a while to open on my side a new thread more focused on the view of a program exploring all these “exotic patterns”.

No question to be in competition. I’ll contribute to David’s thread, but I think better to keep separate both topics and I am convinced David will agree and will contribute as well to that thread;

Not really competition but more a meeting of minds where we have common ground. You're interested in patterns that suit computerised methods and I'm interested in picking out bits of them that a manual solver with enough patience could apply.

Cut-down versions of Exocets, Multi-Fish and so on, will never enable a player to match a program's capabilities. Nevertheless I hope that sometimes they might provide new insights into the way they can be coded, and possibly reveal some additional inferences that could be exploited. In this way I hope to pay you back for the work you've done on exotic patterns.

Our two approaches therefore produce similar but different methods for handling the same pattern. I agree it's therefore right that they should be in separate threads. We must also be careful about our choice of terms to avoid confusion.

It will always be an unequal partnership though, as working one puzzle at a time on a spreadsheet, I can't run through a set of reference puzzles as quickly as you can.

I've got one query however, why did you choose that thread title – it doesn't seem to match your contents! It implies that you are providing rules for manual player to recognise your patterns but your descriptions don't do that. Perhaps you should ask ronk to change it to something better.

DPB
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Re: Exotic patterns for manual solvers

Postby ronk » Mon Apr 02, 2012 8:29 pm

David P Bird wrote:I've got one query however, why did you choose that thread title – it doesn't seem to match your contents! It implies that you are providing rules for manual player to recognise your patterns but your descriptions don't do that. Perhaps you should ask ronk to change it to something better.

The thread "owner" might be able to change the thread title by editing the subject line of his/her opening post.
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Re: Exotic patterns for manual solvers

Postby champagne » Mon Apr 02, 2012 9:19 pm

David P Bird wrote:
We must also be careful about our choice of terms to avoid confusion.

DPB


Sure, but as you are the native English speaker, warn me as often as necessary when you feel something has to be changed.

David P Bird wrote:
It will always be an unequal partnership though, as working one puzzle at a time on a spreadsheet, I can't run through a set of reference puzzles as quickly as you can.

DPB


surely a program can do very fast what can be coded, but defining what has to be coded is a key point.
Experience of players is very important when the target (which is mine) is to simulate processes a player can apply


David P Bird wrote:I've got one query however, why did you choose that thread title – it doesn't seem to match your contents! It implies that you are providing rules for manual player to recognise your patterns but your descriptions don't do that. Perhaps you should ask ronk to change it to something better.

DPB


Choosing the title for a thread is not easy.

let see that one

"exotic patterns for manual solvers"

exotic is somehow provocative. I am convinced they are not exotic at all. I am not responsible for the first use of that word to qualify our common work.

"patterns for manual solver"

I was already convinced, but you came to reinforce my intimate conviction that manual players can find an use these tools.

On the other side, I don't want to duplicate your work (I am not sure I would do it in the proper way), so, you are right, that thread will focus on more theoretical and more general views.

I have no problem (if it is authorised for the "owner" of the thread to do it) to change the title, but I have no idea for a better one.

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Re: Exotic patterns for manual solvers

Postby David P Bird » Tue Apr 03, 2012 7:42 am

Champagne, thanks for your response.

What I meant when I mentioned being careful with out terms was that in a computer solver your patterns can be analysed far more deeply than would be possible for a player. Therefore if there are two versions of the same basic method they should be individually identified.

As far as we currently know, a player should be able make the eliminations for a one-band Exocet but not for the more complex ones, so it's not a so much of a problem. For multi-fish our approaches seem to be quite different though, which is why I coined the Shark term.

I would suggest "Exotic Patterns – a Résumé" or something similar as a thread title. As you started it, you are considered to be it's 'owner' and so may be able to change it by editing your opening post.

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7658;GP;H1521

Postby champagne » Tue Apr 03, 2012 1:37 pm

preparing some examples of a rectangle fish pattern, I found that oddity

98.7.....7.6...8...54......6..8..3......9..2......4..1.3.6..7......5..9......1..4;10.80;10.80;9.60;GP;H1521;G3

that puzzle has a 5 digits "full rank 0 logic"

Code: Select all
X      X      12+    |X      124+   25+    |1245+  145+   25+   
X      12     X      |12459+ 124+   259+   |X      145+   259+   
12+    X      X      |129+   12+    29+    |129+   1+     29+   

X      1249+  1259+  |X      12+    25+    |X      45+    59+   
145+   14+    15+    |15+    X      5+     |45+    X      5+     
25+    29+    259+   |25+    2+     X      |59+    5+     X     

1245+  X      1259+  |X      24+    29+    |X      15+    25+   
124+   124+   12+    |24+    X      2+     |12+    X      2+     
25+    29+    259+   |29+    2+     X      |25+    5+     X     

sets
12459R4 12459R7 12459C4 12459C7
linksets
125B5 459B6 249B8 125B9 r1c7 r2c4 r3c4 r3c7 r4c2 r4c3 r7c1 r7c3

what is very strange is that the complementary floors have a high potential for another multi-floors SLG
as in last ronk example, eliminations are the same if I am right

Code: Select all
X     X     3+    |X     36+   36+   |6+    36+   36+   
X     X     X     |3+    3+    3+    |X     3+    3+   
3+    X     X     |3+    368+  368+  |6+    367+  367+ 

X     7+    7+    |X     7+    7+    |X     7+    7+   
38+   7+    378+  |3+    X     367+  |6+    X     678+ 
38+   7+    378+  |3+    367+  X     |6+    678+  X     

8+    X     8+    |X     8+    8+    |X     8+    8+   
8+    67+   78+   |3+    X     378+  |6+    X     368+ 
8+    67+   78+   |3+    378+  X     |6+    368+  X     

The solver did not see the corresponding multi-fish (I suppose it exists).

EDIT

very strange. In fact, it is exactly the same puzzle as above, what I did not see first
so this is a third way to have the same eliminations

champagne
Last edited by champagne on Wed Apr 04, 2012 7:53 am, edited 1 time in total.
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Re: Exotic patterns a resume

Postby ronk » Tue Apr 03, 2012 4:12 pm

champagne wrote:very strange. In fact, it is exactly the same puzzle as above, what I did not see first
so this is a third way to have the same eliminations

There are at least four ways, with two pairs of complementary 0-rank logic sets. One pair is the 5-digit sk-loop in both its naked set and hidden set forms. The second pair are 4-digit fish, one using rows and one using columns. each having coincident [edit2: cover cells] at r58c69 and r69c58.

Realistically, I don't think there is a fifth way. [edit1: This guess is not true.]
Last edited by ronk on Fri Apr 06, 2012 12:31 pm, edited 2 times in total.
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Re: Exotic patterns a resume

Postby daj95376 » Tue Apr 03, 2012 5:55 pm

ronk wrote:each having coincident fins at r58c69 and r69c58.

I don't know the definition of "coincident fins", but my template solver says that these cells contain a candidate from every <3678>-template group, from which it found 224 acceptable combinations.
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