## JExocet Pattern Definition

Advanced methods and approaches for solving Sudoku puzzles

### Re: JExocet Pattern Defintion

Hi David,

Out of the four base candidates only the two that are true in the base cells will be subject to the pattern constraints when everything is resolved. This means that the other ones can occupy r1c4 and also r23c3 so the fish requirements won't apply to them.

This will probably be my last (relatively) quick reply for a time ...

It's like this: There are still the two distinct base cell values -- maybe one is '2', maybe not -- it doesn't matter.
From the fish requirements, each base cell value, is ultimately forced into at least one of the three cells, r23c4,
and r3c7. Since the two base cells values will differ from each other, in fact, they must occupy at least two of
those cells. Since only one of them can go in r3c7, at least one of them must go in r23c4. That, with what I said
before, rules out the possiblity of 2r3c5 being true ... again, since it would force r23c4 to contain an 89 ... and
since neither of those is a base digit.

Does it make more sense this time around ?

The situation isn't quite like it would be for a more general "exocet with AHS target(s)" scenario.
Here, you also know that the base cell values are forced into particular subsets of the AHS cell sets.

I guess It's time for me to run ... sorry. I'll leave it to you, to divine what the subsets are. In the most general case that still keeps with the "partial fish" idea ... a target AHS could intersect both fish columns (... making it a "row" AHS). As long as the AHS cell sets are disjoint, that isn't a problem.

Best Regards,
Blue.
blue

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Joined: 11 March 2013

### Re: JExocet Pattern Defintion

blue wrote:
Code: Select all
`+------------------+-------------------+-------------------+| 24    134  5     | 1234    6    7    | 1234  8     9     || 2468  9    1234  | 12348   5    1234 | 7     136   12346 || 2468  78   12347 | 123489  289  1234 | 1234  136   5     |+------------------+-------------------+-------------------+| 1     56   234   | 2468    278  9    | 345   357   348   || 7     56   49    | 1468    3    146  | 1459  2     148   || 249   34   8     | 5       27   124  | 6     1379  134   |+------------------+-------------------+-------------------+| 589   78   79    | 2369    1    2356 | 239   4     236   || 3     2    19    | 69      4    8    | 159   1569  7     || 459   14   6     | 7       29   235  | 8     139   123   |+------------------+-------------------+-------------------+`

The base cells are r1c12, and the fish columns are c347.
r3c7 is a "normal" target cell, and the other target is the "box" AHS for 89 in r23c4+r3c5.
The only elimination is for 2r3c5, and it's kind of a special case, since it doesn't fit the
general description: "non-AHS, non-base-cell digit".

Hmmm! I believe there are two more eliminations besides r3c5<>2.

Code: Select all
` +--------------------------------------------------------------------------------+ |  24      134     5       |  1234    6       7       |  1234    8       9       | |  2468    9       1234    |  138-24  5       1234    |  7       136     12346   | |  2468    78      12347   |  123489  89-2    1234    |  1234    136     5       | |--------------------------+--------------------------+--------------------------| |  1       56      234     |  2468    278     9       |  345     357     348     | |  7       56      49      |  1468    3       146     |  1459    2       148     | |  249     34      8       |  5       27      124     |  6       1379    134     | |--------------------------+--------------------------+--------------------------| |  589     78      79      |  2369    1       2356    |  239     4       236     | |  3       2       19      |  69      4       8       |  159     1569    7       | |  459     14      6       |  7       29      235     |  8       139     123     | +--------------------------------------------------------------------------------+ # 119 eliminations remain`

If r2c4=8, then r2c4<>1234. Nothing special here.

However, if r2c4 is a base cells value, then the presence of r2c5=5 and r3c9=5 forces secondary equivalences: r3c7==r2c6 and r2c4==r3c8. But, since r3c8 contains only <13> from the base cells, then r2c4<>24 must follow.

In both cases, we have r2c4<>24.
daj95376
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### Re: JExocet Pattern Defintion

Hi Blue,

In checking the pattern we are only looking at the capacity of the cell sets to hold the base digits, not how they can be distributed between the cells. Likewise for the locked candidates in the AHS.

Here is the grid stripped down to the essential digits showing how 1' & 2' could be true and 3 & 4 false in the base cells with sufficient capacity in the other two tiers to hold their other instances in these columns.
Code: Select all
` *-------------------*---------------------*-------------------* | 2'4   1'34  .     | 123'4   .     .     | 1234' .     .     |  | 24    .     123'4 | 12348'  .     1234' | .     1'3   12'34 |  | 24    .     1234' | 123489' 2'89  1'234 | 123'4 13    .     |  *-------------------*---------------------*-------------------* | 1     .     234   | 24      2     .     | 34    3     34    |   | .     .     4     | 14      3     14    | 14    2     14    |  | 24    34    .     | .       2     124   | .     13    134   |  *-------------------*---------------------*-------------------* | .     .     .     | 23      1     23    | 23    4     23    |  | 3     2     1     | .       4     .     | 1     1     .     |  | 4     14    .     | .       2     23    | .     13    123   |  *-------------------*---------------------*-------------------*`

In tick marking the assumed true candidates I've had to consider legitimate digit distributions in part, but if that shouldn't be necessary in checking for the existence of the pattern.

I contend that what eliminates (2)r3c5 doesn't arise from the capacity elements of the JE pattern but because of distribution constraints that aren't part of the pattern definition. Although they could be added as conditions, I'm doubtful if they will be constant.

For there to be two possible fish columns in the middle stack they must both satisfy the capacity constraints when used together with columns 3 and 7. If one of them doesn't, as in this case, it becomes an escape route.

This is what I meant when
I wrote:In addition to this both columns must give equivalent results regarding how many instances of each base digit the partial fish pattern can contain. This has yet to be found for two columns in a stack, but again is another remote possibility.

You have the advantage over me in that you know the time zone I'm in but I don't know yours. I made my previous post at midnight here and stayed up a further an hour to see if you would reply. Checking the number of users on-line it appeared I was the only one, so I went to bed!

David
David P Bird
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Location: Middle England

### Re: JExocet Pattern Defintion

Hi David,

David P Bird wrote:For there to be two possible fish columns in the middle stack they must both satisfy the capacity constraints when used together with columns 3 and 7. If one of them doesn't, as in this case, it becomes an escape route.

This is what I meant when
I wrote:In addition to this both columns must give equivalent results regarding how many instances of each base digit the partial fish pattern can contain. This has yet to be found for two columns in a stack, but again is another remote possibility.

I was confused when I read this, but didn't have time to figure out what you were really saying.
Column 5 is not a fish column. It's only columns 3, 4 and 7 (like usual).
That's probably keeping you from "seeing" what I've been saying (?).

Code: Select all
` *-------------------*---------------------*-------------------* | 2'4   1'34  .     | 123'4   .     .     | 1234' .     .     |  | 24    .     123'4 | 12348'  .     1234' | .     1'3   12'34 |  | 24    .     1234' | 123489' 2'89  1'234 | 123'4 13    .     |  *-------------------*---------------------*-------------------* | 1     .     234   | 24      2     .     | 34    3     34    |   | .     .     4     | 14      3     14    | 14    2     14    |  | 24    34    .     | .       2     124   | .     13    134   |  *-------------------*---------------------*-------------------* | .     .     .     | 23      1     23    | 23    4     23    |  | 3     2     1     | .       4     .     | 1     1     .     |  | 4     14    .     | .       2     23    | .     13    123   |  *-------------------*---------------------*-------------------*`

If you pursue the 2's in c3 and c7 here, they lead to 2r4c3 and 2r7c7 being true.
That knocks out 2r4c4 and 2r7c4, leaving no place for a 2, in c3.

You should probably go back and read this part again: (no disrespect intended)
blue wrote:From the fish requirements, each base cell value, is ultimately forced into at least one of the three cells, r23c4,
and r3c7. Since the two base cells values will differ from each other, in fact, they must occupy at least two of
those cells. Since only one of them can go in r3c7, at least one of them must go in r23c4.

Notice, there has been no mention of c5, or r3c5, in any of that.
The "fish requirements" are the usual ones involving c3, c4 and c7 only.
The thing that makes r3c5 "special", is that it's in the AHS, and it isn't one of r23c4.

Regards,
Blue.
blue

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Joined: 11 March 2013

### Re: JExocet Pattern Defintion

daj95376 wrote:Hmmm! I believe there are two more eliminations besides r3c5<>2.

Yes. Very good.
blue

Posts: 840
Joined: 11 March 2013

### Re: JExocet Pattern Defintion

Blue,

Right! You can stop fretting now. Sorry to be so thick, I was concentrating on the capacity constraints for columns 358 (which have none) rather than for 247 which provide the constraints that matter, but where I convinced myself that the distribution of the truths could be wouldn't be predictable and weren't important.

I must now try to put the pattern definition and it's proof into words, which is going to be pretty tortuous.

My immediate reaction is to question what similar repercussions there may be on other patterns involving partial fish.

Thank you very much for your patience.

Regards, David
David P Bird
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Location: Middle England

### Re: JExocet Pattern Defintion

In my next post, I'm going to provide some statistics about JExocet's -vs- other kinds of exocets, in champagne's list of "potential hardest" puzzles from Oct 2012.

Before I do, I want to introduce a new kind of JExocet-like pattern.
The basic idea behind why they are exocets in the general sense, will be familiar to daj95376, from his posts that note "equivalences" between cell values that can be observed (and exploited), once a JExocet has been found.

The basic pattern/patterns, look like this:

Code: Select all
` B B . | .  . .  | . . .          B B . | .  . .  | . . .  . . . | T1 \ T2 | \ . .          . . . | \  \ T2 | \ . .  . . . | \  . .  | * . .          . . . | T1 . .  | * . . -------+---------+-------        -------+---------+------- . . S | S  . .  | S . .          . . S | S  . .  | S . .  . . S | S  . .  | S . .          . . S | S  . .  | S . .  . . S | S  . .  | S . .          . . S | S  . .  | S . . -------+---------+-------        -------+---------+------- . . S | S  . .  | S . .          . . S | S  . .  | S . .  . . S | S  . .  | S . .          . . S | S  . .  | S . .  . . S | S  . .  | S . .          . . S | S  . .  | S . . `

The base cells and fish columns, are the same as for a normal JExocet.
The normal JExocet conditions are satisfied.
The T1 cell and the * cell, are normal exocet targets.
The \ cells, are supposed to be deviod of base digit candidates -- filled cells, usually.
It's the \ cell at r2c5 (in the diagrams), that's the essential ingredient.

It's possible for two patterns like this, to accompany a JExocet -- one for each target cell stack.

From the presence of the JExocet, we know that the T1 and * cells will contain the values that appear in the B cells.
From the \ at r2c5, we can see that the value in the * cell, will be forced into T2 (in box 2).
Danny would write (T2==*), as a "secondary equivalence", and note that there are bonus (base digit) eliminations in the T2 and * cells, when they don't have candidates for the same sets of base digits. Base digit candidates in T2, that don't occur in *, can be eliminated, and vica-versa.

Note: The * cell, can be filled, and the pattern is still valid. When that's the case, the * cell (must) contain a base digit, and we end up knowing what value to put in T2.

Like with JExocets, there is a possible extension, involving "box truths" in the box containing the target cells. If a base digit has candidates in box 2 (in this case), only in T1,T2, and the row containing the base cells, then if the digit appeared in a base cell, it would be forced into one of {T1,T2}, via the box constraint. When that's true, we can give that digit a "pass" on the usual requirement for the S cells/columns.

Those patterns -- JExocets and the ones above ... with the "box" extensions ... account for a very large percentage of the size 3 and 4 exocets in the puzzles in champagne's list

[ Note: there's an extension similar to the "box truths" extension but, using "row truths". For the puzzles in champagne's list, it's virtually never available. It's can be used to support only 8 patterns ... all like the one left above ... all "5-digit" exocets. ]

If anyone wants to put a name on these (David ?), feel free to do so.

Blue.
Last edited by blue on Wed May 22, 2013 1:08 am, edited 1 time in total.
blue

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### Frequencies

denis_berthier wrote:Speaking of frequencies, is there an estimate of the ratio JExocet/Exocet (in the "potential hardest" list if there's nothing less biased)?

This post, is meant to address that question.

Statistics for exocets in champagne's Oct 2012 "potential hardest" puzzle list.

The list contains 56448 puzzles.
Before searching for exocets, the PMs for puzzles were advanced as far as possible using singles, line/box eliminations, and eliminations from naked and hidden subsets, and basic fish.
No restrictions were placed on the number of base digits, or the positions of the base and target cells.
(Well OK, one restriction: no more than 8 base digits).
At that point, 47575 of the puzzles, contained exocets.
The total number of exocets was 162278.

[ That count, doesn't include exocets that are produced when two "locked quads" for the same digits, overlap in two cells. There were 182 of those. champagne likes to ignore them, and I'll stick with that approach.

Added: the original search was also restricted to cases with >= 3 base digits. After champagne noted that there wasn't a column for 2-digit exocets, I expanded the search to include those as well. Only 6 cases were found, 2 each in 3 puzzles. They were cases where a puzzle contained two non-intersecting locked pairs, for the same digit. If I run the search again, I'll include the 2-digit cases, and filter out any cases like that. ]

Below is 1) a breakdown of exocets, by size and type, and 2) a breakdown of puzzles by the "leading (exocet) type".
For the puzzle breakdown, a JExocet of any size, preceded any other kind of exocet, and so on -- then smallest to largest base digit count, for the same "types".

Code: Select all
`       size                           Exocets      +------------+-------------------------+      |  3       4 |     5      6     7    8 |  +---+------------+-------------------------+t | A |  6   52869 |     7      -     -    - |  52882y | B |  -    2066 |  1655   3937   452   45 |   8155p | C |  1   47413 |    20      -     -    - |  47434e | D |  2    5335 | 14987   1177     -    - |  21501  +---+------------+-------------------------+  | G |  -     185 |  9811   5574   164    - |  15734  | H |  -     135 |    29      -     -    - |    164  | K |  1    4905 |  4587   6642   135    1 |  16271  | O | 27      40 |    69      1     -    - |    137  +---+------------+-------------------------+        37  112948   31165  17331   751   46   162278`

Code: Select all
`       size               Puzzles      +------------+-------------+      |  3       4 |    5      6 |  +---+------------+-------------+t | A |  6   43471 |    2      - |  43479y | B |  -    2022 |  937      1 |   2960p | C |  -       9 |   16      - |     25e | D |  -     686 |  138      1 |    825  +---+------------+-------------+  | G |  -      59 |    8      3 |     70  | H |  -      56 |    2      - |     58  | K |  -     139 |   18      1 |    158  | O |  -       - |    -      - |  +---+------------+-------------+         6   46442   1121      6    47575`

"Type" definitions:

---- JExocet-like
A) Standard JExocet (with the allowances for "degenerate cases")
B) Like (A), but with the "box singles" extension.
C) Patterns from by previous post, with JExocet conditions satisfied for all digits.
D) Like (B), but with "box extensions" (see previous post).
---- "hard core" exocets
G) Base cells in a mini-row/col, target cells in the base band/stack, targets in different boxes.
H) Base cells in a mini-row/col, target cells in the base band/stack, targets the same box.
K) Base cells in a mini-row/col, at least one target outside the base band/stack.
O) Unrestricted, none of the above.

The counts for some of the "hard core" types, and the size > 4 cases, while accurate, are somewhat of a distortion. A lot of them end up being cases where a template analysis, shows that one of the target cells needs to contain a particular base digit. When that's true, there can be several cells that end up forced to contain that digit, and usually any one of them can be designated as a "replacement" target cell, for the first target. There's nothing wrong with them, as exocets, but they're sort of unsatisfying, once you see what's going on. I filtered out two classes of exocets, and used the results to produce another pair of tables like the ones above. Whether that was the best idea ... who knows. It is what it is.

The classes that were filtered out, were:
1) cases where one of the target cells, only contains a candidate for one base digit.
2) cases where (single digit) template analysis, shows that for all but one of the base digits, if the digit appeared in the base, it would be forced to occupy a particular (common) target cell. When that's the case, only one of those values could appear in the base, and (assuming the exocet is valid), the remaining digit, must go in the 2nd base, and 2nd target cells.

Code: Select all
`Filtered:       size                           Exocets      +------------+-------------------------+      |  3       4 |     5      6     7    8 |  +---+------------+-------------------------+t | A |  6   51780 |     7      -     -    - |  51793y | B |  -    2036 |   170      -     -   45 |   2251p | C |  1   46313 |     4      -     -    - |  46318e | D |  2    5326 | 14976   1177     -    - |  21481  +---+------------+-------------------------+  | G |  -      56 |    21    265   164    - |    506  | H |  -      62 |    26      -     -    - |     88  | K |  1    3072 |    29      3     3    1 |   3109  | O | 27      40 |    69      1     -    - |    137  +---+------------+-------------------------+        37  108685   15302   1446   167   46   125683`

Code: Select all
`Filtered:       size               Puzzles      +------------+-------------+      |  3       4 |    5      6 |  +---+------------+-------------+t | A |  6   42393 |    2      - |  42401y | B |  -    1996 |   58      - |   2054p | C |  -     135 |    -      - |    135e | D |  -    1582 |  328     17 |   1927  +---+------------+-------------+  | G |  -      40 |    2      3 |     45  | H |  -       4 |    -      - |      4  | K |  1     157 |   19      1 |    178  | O |  -       7 |   39      - |     46  +---+------------+-------------+         7   46314    448     21    46790`

A note about the "type O" cases: I didn't place any restrictions on the positions of the base cells, but I did require that when they can't see each other, a single digit template analysis shows that the two cells can't hold the same digit. I'll check whether cases like that, ever came up. It doesn't seem likely. (Edit: no, it didn't happen).

Blue.
Last edited by blue on Wed May 22, 2013 1:14 am, edited 1 time in total.
blue

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### Re: JExocet Pattern Defintion

Hi Blue,

In between other things I'm slowly building an illustrated piece containing the pattern requirements and walk-throughs for the various types.
Following our exchanges I'm limiting the JE+ term to object cells that contain a single locked digit, and calling those with larger AHSs JE++ with a note saying they're included only for completeness.

I describe the JE pattern theorem as providing a) the immediate eliminations and b) the immediate inference that the two target cells can't hold the same base digit. There are also the fish fin eliminations lying in wait for when the true base digits are identified.

Most of what you describe in your fist post today is what I would class as 'utilising the JE inferences when a pattern is found'. Depending on the positions of the givens and any AHSs, there are many possible eliminations in the JE band. These aren't confined to base digits restricted to the target cells either. They can also lie in wait until other cells in the JE band are reduced. Then when a double (as I should properly call it) JExocet is found they mushroom!

As all of these only consist of AIC chain segments using the JE theorem inferences, I intend to pick illustrative examples showing the type of thinking required and leave it there. This will leave it open for anyone else to catalogue all the many permutations later if they want.

I'm sorry if this sounds dismissive to you, but there are a lot of possibilities to cover and I must draw a line somewhere.

you wrote:[ Note: there's an extension similar to the "box truths" extension but, using "row truths". For the puzzles in champagne's list, it's virtually never available. It's can be used to support only 8 patterns ... all like the one left above ... all "5-digit" exocets. ]

Now here, 5-digit JExocets are new to me! Would you post one of these rarities here please so I can see what they involve?

I also picked up before that you had identified that AHSs in the rows within the JE band can also be part of a JE++ pattern. At the moment I just have that as an action point for further investigation, so if you have an example I'd be very grateful for that too.

I'll leave your frequency analysis post for later study, but my knee-jerk reaction is to wonder if patterns with more than 4 base digits are within the scope of a manual solver to find.

David
David P Bird
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### Re: JExocet Pattern Defintion

Hi David,

David P Bird wrote:I describe the JE pattern theorem as providing a) the immediate eliminations and b) the immediate inference that the two target cells can't hold the same base digit. There are also the fish fin eliminations lying in wait for when the true base digits are identified.

Most of what you describe in your fist post today is what I would class as 'utilising the JE inferences when a pattern is found'.
As all of these only consist of AIC chain segments using the JE theorem inferences, I intend to pick illustrative examples showing the type of thinking required and leave it there. This will leave it open for anyone else to catalogue all the many permutations later if they want.

I'm sorry if this sounds dismissive to you, but there are a lot of possibilities to cover and I must draw a line somewhere.

I don't disagree. The base and target cells, actually do satisfy the exocet property, though, and the presence of the "extended" pattern, guarantees it. The only reason that I brought them up, is that they account for the bulk of the non-JExocet exocets in champagne's "potential hardest" list, and they are describable as instances of a well defined pattern.

On the other hand, if you include the "box extensions", then the JExocet pattern can be "broken" for a digit that uses the box extension ... leaving a situation that doesn't fit the 'utilising the JE inferences when a pattern is found' characterization.

There was an example in the other exocet thread. Here's another(?) one from in champagne's list:

Code: Select all
`#3049 1.34............36.8..2.4............7..4.5.....6.1..8..2.9...4.9.....5.8....79..+------------------------+---------------------+-----------------------+| 1       256     3      | 4      5678   5689  | 278     2789    2579  || 24579   245     4579   | 15789  1578   589   | 1278    3       6     || 5679    8       5679   | 13579  2      3569  | 4       179     1579  |+------------------------+---------------------+-----------------------+| 234569  123456  145689 | 35789  3578   23589 | 12367   124679  12379 || 2369    7       1689   | 389    4      2389  | 5       1269    1239  || 23459   2345    459    | 6      357    1     | 237     2479    8     |+------------------------+---------------------+-----------------------+| 3567    1356*    2     | 1358   9      3568  | 13678   1678    4     || 367     9       167    | 123-8  136-8  4     | 123678  5       1237  || 8       13456   1456   | 1235   1356   7     | 9       126(B)  123(B)|+------------------------+---------------------+-----------------------+          S                       S              Sbase: r9c89, targets: r8c45, * cell: r7c2`

David P Bird wrote:
you wrote:[ Note: there's an extension similar to the "box truths" extension but, using "row truths". For the puzzles in champagne's list, it's virtually never available. It's can be used to support only 8 patterns ... all like the one left above ... all "5-digit" exocets. ]

Now here, 5-digit JExocets are new to me! Would you post one of these rarities here please so I can see what they involve?

All of them in champagne's list, needed the "degenerate cases" extension(s) for JExocet.
This puzzle has with two 5-digit JExocets, and three (5-digit) of the type from my 1st post.
One needs the "box extension". All 5, use the same S columns.

Code: Select all
`#44084 98.7..6..5.46..7......8..3.6..4..9...4.....5...2..5...1....9..7...1...9.....761..+---------------------+--------------------+----------------------+| 9      8      13    | 7     12345  1234  | 6      124    1245   || 5      123    4     | 6     1239   123   | 7      128    1289   || 27     1267   167   | 259   8      124   | 245    3      12459  |+---------------------+--------------------+----------------------+| 6      1357   13578 | 4     123    12378 | 9      1278   1238   || 378    4      13789 | 2389  12369  12378 | 238    5      12368  || 378    1379   2     | 389   1369   5     | 348    14678  13468  |+---------------------+--------------------+----------------------+| 1      2356   3568  | 2358  2345   9     | 23458  2468   7      || 23478  23567  35678 | 1     2345   2348  | 23458  9      234568 || 2348   2359   3589  | 2358  7      6     | 1      248    23458  |+---------------------+--------------------+----------------------+  S                     S                    SJExocets:base: r8c56, targets: r7c7 r9c1 (no eliminations)base: r9c89, targets: r7c4 r8c1The others:base: r7c23, targets: r8c79 (needs the box extension)base: r8c56, targets: r7c78base: r9c89, targets: r7c45`

Here is another one I made on the fly a day or two ago.
It's a normal JExocet, in an SER 9.1 ouzzle.

Code: Select all
`+--------------------+---------------------+-------------------------+| 345   1245  12345  | 123458  23489  7    | 123459  134689  1235689 || 9     6     12345  | 12345-8 2348   1258 | 7       1348    12358   || 3457  8     123457 | 6       2349   1259 | 12345-9 1349    12359   |+--------------------+---------------------+-------------------------+| 3457  457   8      | 9       247    12   | 6       137     1357    || 1     479   3467   | 48      5      68   | 39      2       3789    || 2     579   567    | 18      678    3    | 159     1789    4       |+--------------------+---------------------+-------------------------+| 456   1245  9      | 7       236    256  | 8       1346    1236    || 467   247   247    | 238     1      2689 | 2349    5       23679   || 8     3     1257   | 25      269    4    | 129     1679    12679   |+--------------------+---------------------+-------------------------+base: r12c4, targets: r2c4, r3c7`

David P Bird wrote:I also picked up before that you had identified that AHSs in the rows within the JE band can also be part of a JE++ pattern. At the moment I just have that as an action point for further investigation, so if you have an example I'd be very grateful for that too.

I don't have anything on hand. I'll try to come up with one.
Maybe I'll try to reconstruct my code to search for them, and check champagne's list again.

I'll leave your frequency analysis post for later study, but my knee-jerk reaction is to wonder if patterns with more than 4 base digits are within the scope of a manual solver to find.

My opinion would be biased -- I don't think the size 4 cases are "within the scope".

Regards,
Blue.
blue

Posts: 840
Joined: 11 March 2013

### Re: Frequencies

blue wrote:
denis_berthier wrote:Speaking of frequencies, is there an estimate of the ratio JExocet/Exocet (in the "potential hardest" list if there's nothing less biased)?

This post, is meant to address that question.

Statistics for exocets in champagne's Oct 2012 "potential hardest" puzzle list.

Blue.

Hi Blue,

your post(s) require a lot of work to cover all the field.

I did not work yet in details on them, partly because I am moving currently all my code in a new infrastructure, what lock me on necessary recoding, re testing and cleaning tasks.

I have seen some new patterns, but I have the feeling that the main part are identified ones that I should find with existing code. In due time, a comparison of our results would point out what is old and what is new.

You opened widely the door considering Exocets with more than 4 digits. One reason why I did not go in that way is that it is less attractive for solving. A 4 digit exocets has already 6 possible pairs of digits, a 5 digits exocet has 10 and the chances to have the "abi loop" are decreasing.

Reversely, I don't see the exocet of 2 digits entry. I know this is very special, but it could have more solving power than the 5 digits one. But with the sample file you had, it could be that it would not show anyway.

I have in hands an old data base of puzzles built with a much lower cut off than the "potential hardest" file.
I checked a file of about 170 K puzzles where I look for exocet with a very old definition excluding down graded forms of exocets.

In that file, I found years ago 52493 puzzles having an exocet and among them 51083 having the 3 digits form of exocet.
That's why I am expecting for a sample file in the grey zone (say SER 9 to 10.5) a large majority of exocets having 3 digits.

I think it would be interesting to build a sample file in that area (I don't care whether it is biased or not) and work on a common file.
I could do that within one or two weeks.

Meantime, I would have cleaned the moved coded (and introduced your quick filter based on the solution)

Code: Select all
`     B B . | .  . .  | . . .          B B . | .  . .  | . . .     . . . | T1 \ T2 | \ . .          . . . | \  \ T2 | \ . .     . . . | \  . .  | * . .          . . . | T1 . .  | * . .    -------+---------+-------        -------+---------+-------     . . S | S  . .  | S . .          . . S | S  . .  | S . .     . . S | S  . .  | S . .          . . S | S  . .  | S . .     . . S | S  . .  | S . .          . . S | S  . .  | S . .    -------+---------+-------        -------+---------+-------     . . S | S  . .  | S . .          . . S | S  . .  | S . .     . . S | S  . .  | S . .          . . S | S  . .  | S . .     . . S | S  . .  | S . .          . . S | S  . .  | S . .`

may be one question about that pattern.
Don't you have an exocet using T1 and the star cell

regards
champagne
champagne
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### Re: Frequencies

Hi Blue,

Great work!

If my interpretation of all your results is correct, considering JExocets (types A B C D) on the one hand and all Exocets (types A B C D G H K O) on the other hand, something strange appears with the percentages JExocets/Exocets:

- (43479+2960+25+825)/47575 = 47289/47575 = 99.4 % for puzzles [99.4 % of the puzzles having an Exocet have a JExocet];
- (52882+8155+47434+21501)/162278 % = 129972/162278 = 80.1 % for instances [80.1 % of the Exocet instances are JExocets].

Moreover, there are, in the mean:
- 162278/47575 = 3.41 Exocets per puzzle having at least one Exocet
- 129972/47289 = 2.75 JExocets per puzzle having at least one JExocet

I wonder how much multiple Exocets/JExocets in a puzzle overlap. This is only part of the question but (if this is not too much work) it would be interesting to have a similar table for the number of different eliminations.
Last edited by denis_berthier on Tue May 21, 2013 10:48 am, edited 1 time in total.
denis_berthier
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Location: Paris

### Re: Frequencies

Hi champagne,

champagne wrote:Reversely, I don't see the exocet of 2 digits entry. I know this is very special, but it could have more solving power than the 5 digits one. But with the sample file you had, it could be that it would not show anyway.

I didn't actually look for them, it turns out. I'll edit the post, to reflect that.
I've changed the code to look for them now, and it only finds 6 -- 2 each, in 3 puzzles.
Unfortunately, they're like the "overlapping locked quads" case, but even less interesting -- two disjoint locked pairs for the same digit set. I would filter them out, just like the locked quads.

I can't think of a reason why an interesting case couldn't exist.
There is this: for a JExocet instance, the base pair would be a naked pair, and knock out all of the other candidates in the base row, and the candidates in intersection of the base cell box, and the (1st) S column. At that point, the "fish" requirements in the S columns, would yield a "multi-fish" pattern that would justify the target cell eliminations by itself (i.e. without the argument needing to depend on the presence of the base cells). It would also justify eliminations in the "covering rows" for the fish patterns (in bands 2 & 3). Still, it seems like any of those eliminations, would rate fairly high, in SE. Then there's the possiblity for non-JExocet instances, where the presence of the base cells would be important.

You opened widely the door considering Exocets with more than 4 digits. One reason why I did not go in that way is that it is less attractive for solving. A 4 digit exocets has already 6 possible pairs of digits, a 5 digits exocet has 10 and the chances to have the "abi loop" are decreasing.

Just a few comments. I knew that 5-digit JExocets were possible, and on a whim, I decided to look for 5,6,7, and 8 in the field of general exocets. I was surprised by what I saw. I included them in the statistics, just to satisfy any curiosities that others might have. There are many reasons for not being interested in anything larger than 5, say.

About the "abi loop": I understand now they work, and so on. I'm not a great fan of uniqueness techniques, though. I always feel like I'm cheating if I use one in solving a puzzle by hand. It's just a personal opinion. I remember a topic in your "Exotic Patterns, a Resume" thread: "What to do after you've found an exocet". I waited with baited breath, for you to answer the question. When the answer turned out to be "use it with a uniqueness assumption", I was crushed. Oh well. I like better, the kinds of eliminations that daj95376 notes, when "secondary equivalences" are apparent. Again, it's just a personal opinion.

I have in hands an old data base of puzzles built with a much lower cut off than the "potential hardest" file.
I checked a file of about 170 K puzzles where I look for exocet with a very old definition excluding down graded forms of exocets.

In that file, I found years ago 52493 puzzles having an exocet and among them 51083 having the 3 digits form of exocet.
That's why I am expecting for a sample file in the grey zone (say SER 9 to 10.5) a large majority of exocets having 3 digits.

I think it would be interesting to build a sample file in that area (I don't care whether it is biased or not) and work on a common file.
I could do that within one or two weeks.

That does sound interesting. Please do.

Code: Select all
`     B B . | .  . .  | . . .          B B . | .  . .  | . . .     . . . | T1 \ T2 | \ . .          . . . | \  \ T2 | \ . .     . . . | \  . .  | * . .          . . . | T1 . .  | * . .    -------+---------+-------        -------+---------+-------     . . S | S  . .  | S . .          . . S | S  . .  | S . .     . . S | S  . .  | S . .          . . S | S  . .  | S . .     . . S | S  . .  | S . .          . . S | S  . .  | S . .    -------+---------+-------        -------+---------+-------     . . S | S  . .  | S . .          . . S | S  . .  | S . .     . . S | S  . .  | S . .          . . S | S  . .  | S . .     . . S | S  . .  | S . .          . . S | S  . .  | S . .`

may be one question about that pattern.
Don't you have an exocet using T1 and the star cell

Almost always, yes. There are two exceptions.
I see I didn't state it clearly, but the JExocet conditions do need to be satisfied in the S columns. I'll make an edit to reflect that.
One exception, is that the * cell can be filled. It can only contain a base digit (if the puzzle has a solution). In that case, the T2 cell will be forced to contain the same value, (and one of the base cells as well). The other exception, has to do with the possiblity of using the "box extension". I mentioned it in my last post to David (using puzzle #3049 as an example).

Best Regards,
Blue.
blue

Posts: 840
Joined: 11 March 2013

### Re: Frequencies

Hi Denis,

denis_berthier wrote:If my interpretation of all your results is correct, considering JExocets (types A B C D) on the one hand and all Exocets (types A B C D G H K O) on the other hand, something strange appears with the percentages JExocets/Exocets:
(...)

One note: I don't think that David will like calling them all JExocets. (Maybe with the "types", it's OK ?)

You have slight error in your calculations: (43479+2960+25+825) is 47289
It's a correct interpretation of the results, though.

I wonder how much multiple Exocets/JExocets in a puzzle overlap. This is only part of the question but (if this is not too much work) it would be interesting to have a similar table for the number of different eliminations.

I'm not exactly sure what you're asking, but I'm sure it wouldn't be too much work.
Counting candidates eliminated by "some" type (A B C D) exocet, and only counting them once, then extending the count to include eliminations from the remaining exocets ?
Can you suggest a table layout (or layouts) ?

Regards,
Blue.
blue

Posts: 840
Joined: 11 March 2013

### Re: Frequencies

blue wrote:
champagne wrote:Reversely, I don't see the exocet of 2 digits entry. I know this is very special, but it could have more solving power than the 5 digits one. But with the sample file you had, it could be that it would not show anyway.

I didn't actually look for them, it turns out. I'll edit the post, to reflect that.
I've changed the code to look for them now, and it only finds 6 -- 2 each, in 3 puzzles.
Unfortunately, they're like the "overlapping locked quads" case, but even less interesting -- two disjoint locked pairs for the same digit set. I would filter them out, just like the locked quads.

I can't think of a reason why an interesting case couldn't exist.
There is this: for a JExocet instance, the base pair would be a naked pair, and knock out all of the other candidates in the base row, and the candidates in intersection of the base cell box, and the (1st) S column. At that point, the "fish" requirements in the S columns, would yield a "multi-fish" pattern that would justify the target cell eliminations by itself (i.e. without the argument needing to depend on the presence of the base cells). It would also justify eliminations in the "covering rows" for the fish patterns (in bands 2 & 3). Still, it seems like any of those eliminations, would rate fairly high, in SE. Then there's the possiblity for non-JExocet instances, where the presence of the base cells would be important.

The 2 digits exocet has no interest in that lot. The chances to find a pair at start are close to nil.
I agree on all your comments, I intend to restart that case if we work on files with lower ratings.

blue wrote:About the "abi loop": I understand now they work, and so on. I'm not a great fan of uniqueness techniques, though. I always feel like I'm cheating if I use one in solving a puzzle by hand. It's just a personal opinion. I remember a topic in your "Exotic Patterns, a Resume" thread: "What to do after you've found an exocet". I waited with baited breath, for you to answer the question. When the answer turned out to be "use it with a uniqueness assumption", I was crushed. Oh well. I like better, the kinds of eliminations that daj95376 notes, when "secondary equivalences" are apparent. Again, it's just a personal opinion.

For me the worst we are doing with computers is to produce these long, boring and indigestible paths using chains nets.
for a manual player, such paths are just not acceptable;
generally speaking, the uniqueness brings much shorter paths. with exocets and the "abi loop", the contrast is still bigger.

But as you say, this remains a matter of taste.

I started the generation of puzzles with no filter using the data base of potential hardest. It could be interesting to give the criteria for our "grey zone";

Regards,

champagne
champagne
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Joined: 02 August 2007
Location: France Brittany

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