## Exocet 2014_09 Discussion #1

Advanced methods and approaches for solving Sudoku puzzles

### Exocet 2014_09 Discussion #1

I decided to separate my discussion from champagne's post announcing his latest analysis of his "hardest puzzles" collection. I also decided to start "easy" and compare my solver's results with puzzles from the 03_E5_exo_others.txt and the 03_E6_exo_others_extended.txt files. I didn't find any QExocet patterns in the E5 file. That was expected. However, I was surprised to find three patterns in the E6 file that did not match champagne's results.

These patterns appear in a chute, but they don't qualify as JExocets (IMO) because of the difficulty linking the target cells for some base cell candidates.

Code: Select all
`98.7..6..5...8..4...3.2...84.........6...72.....26...3.9..7.8....59.8.2.........1;858994;GP;13_03;1;r8c5 r9c5 r1c6 r1c8;;   c6b2  Locked Candidate 1              <> 9    r46c6   c1b7  Locked Candidate 2              <> 2    r7c3,r9c23 +--------------------------------------------------------------------------------+ |  9       8       124     | Q7      Q1345    1345    |  6       135     25      | |  5       127     1267    |  136     8       1369    |  1379    4       279     | |  167     147     3       |  1456    2       14569   |  1579    1579    8       | |--------------------------+--------------------------+--------------------------| |  4       12357   12789   |  1358    1359   B135     |  1579    156789  5679    | |  138     6       189     |  13458   13459   7       |  2       1589    459     | |  178     157     1789    |  2       6      B145     |  14579   15789   3       | |--------------------------+--------------------------+--------------------------| |  1236    9       146     |  13456   7       123456  |  8       356     456     | |  1367    1347    5       | R9      R134     8       |  347     2       467     | |  23678   347     4678    |  3456    345     23456   |  34579   35679   1       | +--------------------------------------------------------------------------------+ # 160 eliminations remain ### -1345- QExocet   Base = r46c6   Target = r1c5,r8c5   aligned   no direct elims`

Code: Select all
`98.7..6..5..9..7....7.64...7......43.4.5..8....8..7.6..9.....2...56..4.......1...;1273827;GP;13_12;1;r6c1 r6c2 r1c6 r7c6;;   c3b1  Locked Candidate 1              <> 4    r79c3 r1  b2  Locked Candidate 1              <> 5    r1c89 +-----------------------------------------------------------------------------------------+ |  9        8        1234     |  7        1235     235      |  6        13       124      | | Q5       Q1236     12346    |  9        1238     238      |  7        138      1248     | |  123     S123      7        |  1238     6        4        |  12359    13589    12589    | |-----------------------------+-----------------------------+-----------------------------| |  7        1256     1269     |  128      1289     2689     |  1259     4        3        | | R1236    R4        12369    |  5        1239     2369     |  8        179      1279     | | S123      1235     8        |  1234     12349    7        |  1259     6        1259     | |-----------------------------+-----------------------------+-----------------------------| |  13468    9       B136      |  348      34578    358      |  135      2        15678    | |  1238     1237     5        |  6        23789    2389     |  4        13789    1789     | |  23468    2367    B236      |  2348     2345789  1        |  359      35789    56789    | +-----------------------------------------------------------------------------------------+ # 168 eliminations remain ### -1236- QExocet   Base = r79c3   Target = r2c2==r6c1,r5c1==r3c2   no direct elims *** value to be eliminated from base/target/secondary cells = <6>`

Code: Select all
`98.76.5..5..4..7.......5.936...3.4...9...6....385.....3....49...2..7............1;1293369;GP;13_12;1;r5c4 r5c5 r3c1 r6c1;;   c6b2  Locked Candidate 1              <> 3    r89c6 r1  b3  Locked Candidate 1              <> 4    r1c3 +-----------------------------------------------------------------------------------------+ |  9        8        123      |  7        6        123      |  5        124      24       | |  5        16       1236     | Q4       Q1289     12389    |  7        1268     268      | |  1247     1467     12467    |  128     S128      5        |  1268     9        3        | |-----------------------------+-----------------------------+-----------------------------| |  6        157      1257     | R1289    R3        12789    |  4        12578    25789    | |  1247     9        12457    | S128      1248     6        |  1238     123578   2578     | |  1247     3        8        |  5        1249     1279     |  126      1267     2679     | |-----------------------------+-----------------------------+-----------------------------| |  3        1567     1567     |  1268     1258     4        |  9        25678    25678    | |  148      2        14569    |  13689    7       B189      |  368      34568    4568     | |  478      4567     45679    |  23689    2589    B289      |  2368     2345678  1        | +-----------------------------------------------------------------------------------------+ # 168 eliminations remain ### -1289- QExocet   Base = r89c6   Target = r2c5==r5c4,r4c4==r3c5   no direct elims *** value to be eliminated from base/target/secondary cells = <9>`

_
daj95376
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### Re: Exocet 2014_09 Discussion #1

Hi Danny,

3 interesting case to study on my side ASAP.
With 2 cells targets, it should at minimum have been in the "band" files.
Mismatching puzzles with targets of more than 2 cells are expected.

Another interesting test would be to see if you find something in the puzzles where I did not find any exocet pattern.

I did not publish that file, but I can add it in my google drive if you don't have an easy tool to produce it.
champagne
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### Re: Exocet 2014_09 Discussion #1

For the moment, I'm still trying to interpret champagne's results. My current stumbling block:

champagne wrote:The set of rules used in "extended mode" is the following :

the base is set to true for the digit
the target is set to false for the digit
contradiction is looked for using so far basic rules plus embedded pair triplets ... Xwing swordfish .. and all kinds of X chains

All of my QExocet/qExocet logic is based on single-digit constraints. The following puzzle is from 03_E4_exo_bande_extended.txt. My solver found your first exocet, but missed your second exocet because the target cells were in the same box. For the "fun" of it, I decided to try and verify your second exocet using single-digit constraints. I failed when I tested <3>. What contradiction did you encounter for it?

Code: Select all
`98.76.5..75...9............8...4..3.6..........5..89..26..1..7..1.2.76....7..68..;1675066;GP;14_09;3;r3c1 r3c2 r1c6 r1c9;r3c1 r3c2 r1c6 r2c4; r9  b9  Hidden Pair                     =  12   r9c89 +--------------------------------------------------------------------------------------------------+ |  9         8         1234      |  7         6        Q1234      |  5         124      R1234      | |  7         5         12346     | R1348      238       9         |  1234      12468     123468    | | B134      B234       12346     |  13458     2358      12345     |  12347     124689    12346789  | |--------------------------------+--------------------------------+--------------------------------| |  8         279       129       |  1569      4         125       |  127       3         12567     | |  6         23479     12349     |  1359      23579     1235      |  1247      12458     124578    | |  134       2347      5         |  136       237       8         |  9         1246      12467     | |--------------------------------+--------------------------------+--------------------------------| |  2         6         3489      |  34589     1         345       |  34        7         3459      | |  345       1         3489      |  2         3589      7         |  6         459       3459      | |  345       349       7         |  3459      359       6         |  8         12        12        | +--------------------------------------------------------------------------------------------------+ # 165 eliminations remain ### -1234- QExocet   Base = r3c12   Target = r1c9,r1c6   aligned   no direct elims`

My results for <3> in your second exocet:

Code: Select all
` r3c12=3, r1c6<>3, r2c4<>3 -> r1c9=3, r2c5=3 -> r7c7=3 -> r5c6=3 -> r8c3=3, r9c4=3 -> X-Wing r36\c12`

No single-digit contradiction that I could find.

[Edit: made typo correction r1c5<>3 to r1c6<>3]

_
Last edited by daj95376 on Mon Sep 15, 2014 3:33 pm, edited 1 time in total.
daj95376
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### Re: Exocet 2014_09 Discussion #1

daj95376 wrote: However, I was surprised to find three patterns in the E6 file that did not match champagne's results.

These patterns appear in a chute, but they don't qualify as JExocets (IMO) because of the difficulty linking the target cells for some base cell candidates.

_

I quickly checked that first lot. I did not started with the same PM, I have to explain why. I am missing some easy eliminations. As that code has been modified after I entered the zhou process, this can be the reason.
champagne
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### Re: Exocet 2014_09 Discussion #1

daj95376 wrote:For the moment, I'm still trying to interpret champagne's results. My current stumbling block:

No single-digit contradiction that I could find.

_

It's ok for a single digit. For the same reason as above, the first exocet is valid after eliminations not done by my solver;

The second one requires the extended mode, so the digit '3' has a full expansion using all rules (in fact not more than pairs and Xwings).

In fact, a third exocet
base r3c1r3c2
targets r1c9r2c7
has been seen in extended mode by the solver, and in that one, each digit required the extended mode

Checking these examples, I have seen several problem in the eliminations done before the search (linked to all recent changes I made in the process), I'll adjust the code for the next run.
champagne
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### Re: Exocet 2014_09 Discussion #1

Here are my Extended Exocet pattern search results for this puzzle: 98.76.5..75...9............8...4..3.6..........5..89..26..1..7..1.2.76....7..68..

r3c1 r3c2 r2c4 r2c7 1234
r7c7 r7c9 r8c3 r9c4 3459
r8c1 r8c3 r9c5 r7c9 3459
r8c8 r8c9 r9c2 r7c6 459
r9c4 r9c5 r8c1 r7c7 345
r1c6 r3c6 r5c4 r9c4 134
r8c1 r8c3 r9c4 r7c7 345

They all appear to be correct ie whatever 2 digits are in the base cells, the same two digits are in the taget cells.

I think that there needs to be some agreement on what constitutes a "reasonable" set of rules for an expansion process.

Leren
Leren

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### Re: Exocet 2014_09 Discussion #1

Leren wrote:Here are my Extended Exocet pattern search results for this puzzle: 98.76.5..75...9............8...4..3.6..........5..89..26..1..7..1.2.76....7..68..

r3c1 r3c2 r2c4 r2c7 1234
r7c7 r7c9 r8c3 r9c4 3459
r8c1 r8c3 r9c5 r7c9 3459
r8c8 r8c9 r9c2 r7c6 459
r9c4 r9c5 r8c1 r7c7 345
r1c6 r3c6 r5c4 r9c4 134
r8c1 r8c3 r9c4 r7c7 345

They all appear to be correct ie whatever 2 digits are in the base cells, the same two digits are in the target cells.

I think that there needs to be some agreement on what constitutes a "reasonable" set of rules for an expansion process.

Leren

Hi Leren,

The Exocet pattern and all derived patterns are for sure a key property for puzzles resisting to a set of rules based on chains.

Many points must be specified to take the benefit of it.

My start PM for the search is the following

Code: Select all
`9   8     1234  |7     6     1234  |5     124    1234     7   5     12346 |1348  238   9     |1234  12468  123468   134 234   12346 |13458 2358  12345 |12347 124689 12346789 ---------------------------------------------------------8   279   129   |1569  4     125   |127   3      12567    6   23479 12349 |1359  23579 1235  |1247  12458  124578   134 2347  5     |136   237   8     |9     1246   12467    ---------------------------------------------------------2   6     3489  |34589 1     345   |34    7      3459     345 1     3489  |2     3589  7     |6     459    3459     345 349   7     |3459  359   6     |8     12     12    `

clearly, it's not the same as yours r8c1 r8c3 for example has 5 digits you have four

So the first key property is the start PM. How do you come to it. What set of rule is applied for preliminary eliminations.
This is somehow an upstream condition. I would not use the word extended for that.

The second point is the exocet property itself.
Let's keep a 2 cell target here to keep it simple.

The definition I gave for an exocet derived from "fata morgana" is :

if any digit is true in the base forces it to be true in the target, then this is an exocet pattern.
In the first definition, the proof is done using a "digit pm"

from there, we can have several "extensions" (I continue to keep a 2 cells target)

- the proof can use the full pm with a given set of rules
- as in your wording, we can also rewrite the definition using all pairs in the base
They all appear to be correct ie whatever 2 digits are in the base cells, the same two digits are in the target cells.
and then, we can have specific conditions to make the proof
. either using the corresponding 2 digits pm
. or using the full PM

Using more cells in the target with locked candidates is another extension that you can combine with the previous one.

If we keep in mind that the exocet property must be used only to find easier paths to solve a puzzle, It should not be too hard to see what is reasonable.

For that specific puzzle, could you clarify what is your start PM and what rules you applied to establish the exocet property from that PM
champagne
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### Re: Exocet 2014_09 Discussion #1

Hi Champagne, the Exocets I quoted result from sequential eliminations using only Exocet moves plus a few other basic moves in between Exocet eliminations.

The first 2 Exocets are evident from the same PM as you have. The 3rd Exocet is made apparent following eliminations from these first 2, which reduces r8c13 to 4 digits.

Exocets 4 and 5 may be evident from the original PM, I'd have to check further, in any event they make no eliminations. The 6th Exocet arises from prior eliminations in a similar fashion to the 3rd Exocet.

With my current code the 7th Exocet no longer arises since the puzzle is completely solved using only the first 6.

As to what methods I used to prove the Exocet properties, prior to you releasing your 03 E2 exo je extended.txt file I was only using S cell Truth counts as for Jexocets, plus some simple single digit chains in the Exocet band. To replicate the results in your file I have employed some general purpose scenario testing code, which is a full PM expansion. I'm getting reasonably good agreement with your results but this is possibly because the scenario testing code is overly complex for the purpose of discovering Exocets.

Leren
Leren

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### Re: Exocet 2014_09 Discussion #1

Leren wrote:Hi Champagne, the Exocets I quoted result from sequential eliminations using only Exocet moves plus a few other basic moves in between Exocet eliminations.

The first 2 Exocets are evident from the same PM as you have. The 3rd Exocet is made apparent following eliminations from these first 2, which reduces r8c13 to 4 digits.

Exocets 4 and 5 may be evident from the original PM, I'd have to check further, in any event they make no eliminations. The 6th Exocet arises from prior eliminations in a similar fashion to the 3rd Exocet.

With my current code the 7th Exocet no longer arises since the puzzle is completely solved using only the first 6.

As to what methods I used to prove the Exocet properties, prior to you releasing your 03 E2 exo je extended.txt file I was only using S cell Truth counts as for Jexocets, plus some simple single digit chains in the Exocet band. To replicate the results in your file I have employed some general purpose scenario testing code, which is a full PM expansion. I'm getting reasonably good agreement with your results but this is possibly because the scenario testing code is overly complex for the purpose of discovering Exocets.

Leren

Hi leren,

more details will help.

My solver produces from that pm 3 exocets

r3c1 r3c2 r1c6 r1c9 ;
r3c1 r3c2 r1c6 r2c4 ;
r3c1 r3c2 r1c9 r2c7

none of these is in your list.

I only checked your second r7c79 r8c3 r9c4.
I don't see an easy way to establish it from the PM.
How do you prove it from the PM

regarding the "sequence", this is perfect in a "solver view".

In the files I produced, I only looked for the "easiest exocet" giving priority to the JExocet. The aim was to detect puzzles having an exocet solving potential.
champagne
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### Re: Exocet 2014_09 Discussion #1

Hi Champagne,

For the Exocet r7c7 r7c9 r8c3 r9c4 3459 none of the 4 digits has an S cell count of <=2 so each has to be proven to be true in a target cell if it is true in the base.

Digit 4 is easy to prove true in r9c4 if true in the base because of the Strong link in Box 8.

For the other 3 digits (call them X) there are no obvious links of this type so a full PM expansion is done based on Scenario testing where a contradiction is looked for in the following cases:

- X is true in a base cell (if it's there) and false in both target cells

- X is false in both base cells and true in a target cell (if it's there)

- X is true in a base cell (if it's there) and true in both target cells (if they are both there)

The PM expansion code I have uses singles, pointing & claiming pairs and triples, naked & hidden pairs, triples and quads, Skyscrapers, Kites, basic 2, 3 and 4 fish, finned 2 and 3 fish, XY wings, W wings and M wings.

If that's not enough to produce a contradiction there is a multilevel trial and error procedure where a digit that is one of 2 in a row or column is guessed at a higher level and depending on the results, that digit is resolved at the lower level.

For the Exocets in your extended file and for this puzzle I'm using one guessing level.

Leren
Leren

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### Re: Exocet 2014_09 Discussion #1

Hi leren,

Now it is clear (in principles) I still don't catch why you did not find the exocets I have, but it can be due to the fact that you had already your first one.

Leren wrote:Hi Champagne,

based on Scenario testing where a contradiction is looked for in the following cases:

- X is true in a base cell (if it's there) and false in both target cells

- X is false in both base cells and true in a target cell (if it's there)

- X is true in a base cell (if it's there) and true in both target cells (if they are both there)

I use only the first one, but the second one is perfect.
IMO the third one is something slightly different. It can still be an exocet, but that digit can not be in the solution.

Leren wrote:The PM expansion code I have uses singles, pointing & claiming pairs and triples, naked & hidden pairs, triples and quads, Skyscrapers, Kites, basic 2, 3 and 4 fish, finned 2 and 3 fish, XY wings, W wings and M wings.

Leren

This is not yet stable on my side but very similar, having the serate expansion code, I can decide to include any process. I don't intend to use any guess.

but I also have a preliminary elimination phase with optional level of eliminations.

I was in trouble with that part of the process, so I restarted the exocet search having fixed several points.
champagne
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### Re: Exocet 2014_09 Discussion #1

champagne wrote:Now it is clear (in principles) I still don't catch why you did not find the exocets I have, but it can be due to the fact that you had already your first one.

Leren wrote:Hi Champagne,

based on Scenario testing where a contradiction is looked for in the following cases:

- X is true in a base cell (if it's there) and false in both target cells

- X is false in both base cells and true in a target cell (if it's there)

- X is true in a base cell (if it's there) and true in both target cells (if they are both there)

I use only the first one, but the second one is perfect.
IMO the third one is something slightly different. It can still be an exocet, but that digit can not be in the solution.

For either of you ... (Leren or champagne) ...

The first thing is relevant for the definition of an exocet.
The third thing, as champagne points out, can be used to eliminate X from the base and target cells, if the thing tests as being an exocet (i.e. if the 1st thing yields a contradiction for each X and choice of base cell).
What use is the 2nd kind of test ?
blue

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### Re: Exocet 2014_09 Discussion #1

blue wrote : What use is the 2nd kind of test ?

Based on some testing I've done this morning I'd say tests 2 and 3 are of no use at all - I'm still detecting the same Exocets without them.

In fact taking tests 2 and 3 out of service possibly increases my codes ability to detect Exocets - the reason being that the detection code is not perfect and there are fewer contradictions to be missed.

Leren
Leren

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### Re: Exocet 2014_09 Discussion #1

blue wrote:
- X is false in both base cells and true in a target cell (if it's there)

What use is the 2nd kind of test ?

my first reaction has been to think hat a solution to that would kill the possibility to have an exocet.
Looking more carefully, I rally your implicit position, It does not prove anything and has no interest
champagne
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### Re: Exocet 2014_09 Discussion #1

Exocet : ALS/AALS in 1 cell or 2 cells in a box-line [unit ?] giving rise to exclusion(s) by using NxM-Fishes only on the digits of the ALS/AALS [+ N-tuples, eventually].

First puzzle studied by Danny : 98.7..6..5...8..4...3.2...84.........6...72.....26...3.9..7.8....59.8.2.........1 ;858994;GP;13_03;1;r8c5 r9c5 r1c6 r1c8;;

Analysis of the puzzle from AALS(345)r9c5 :
Code: Select all
`r9c5=3 -> SF(3R157)-3r2c4,r4c6; HP(38-145)r45c4          JF(4R1567)-(4=1)r8c5r9c5=4 -> SF(4R157)-4r3c4,r6c6; HP(48-135)r45c4          JF(3R1457)-(3=1)r8c5r9c5=5 -> SF(5R157)-5r3c4,r46c6; HP(58-134)r45c4          JF(4R1567)-4r8c5          JF(3R1457)-(3=1)r8c5`
Conclusion : -1r45c6, +1r8c5 followed by C(C4)-1r123c6, SF(1R157)-1r2346c138

This is to be compared with Base=(1345)r89c5 and Target=(1345)r1c6.r5c4 !
JC Van Hay

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