Fireworks

Advanced methods and approaches for solving Sudoku puzzles

Re: Fireworks

Postby yzfwsf » Wed Dec 22, 2021 5:54 am

In the Chinese forum, there are related posts about this technique as early as 2018.
https://tieba.baidu.com/p/5547459565
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Re: Fireworks

Postby StrmCkr » Thu Dec 23, 2021 7:39 am

http://sudopedia.enjoysudoku.com/Almost_Locked_Candidates.html
looks like people started using this old technique and appreciating it with some advancement
aka http://forum.enjoysudoku.com/almost-hidden-set-xz-rule-t32268.html

Nice.
Last edited by StrmCkr on Sat Jan 08, 2022 3:16 am, edited 1 time in total.
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Re: Fireworks

Postby yzfwsf » Sat Dec 25, 2021 4:44 am

I have implemented the first five of the six firework techniques introduced by shye in my solver,
but firework MSLS has not been implemented. Then I used the batch generated puzzle module to test
the frequency of these techniques. I found that the frequency of these techniques in random puzzles is
very low, 1/1700 ~ 1000, of which 18% are dual w-wing and the rest are Firework Triple. Only one Fire Exocet
is not standard and is an extended type.Of course, my test results are for really effective steps.I put its priority
behind SDC. I searched more than a million puzzles to get the above statistics.

I think these puzzle examples must be specially designed.
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Re: Fireworks

Postby ghfick » Sat Dec 25, 2021 4:54 pm

So far, for me, I would say the FW Triple is easier to spot than SDC. Maybe the basic SDC is as easy as FW Triple. But the more elaborate SDC are tough to spot. imho Maybe I just need more practice finding SDC.
It will be great having the various FWs in YZF_Sudoku. Then, over time, we may see them pop up in solution paths. I think the FW ALP is 'attractive'.
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Re: Fireworks

Postby shye » Wed Dec 29, 2021 12:39 pm

yzfwsf wrote:In the Chinese forum, there are related posts about this technique as early as 2018.
https://tieba.baidu.com/p/5547459565

StrmCkr wrote:http://sudopedia.enjoysudoku.com/Almost_Locked_Candidates.html
looks like people started using this old technique and appreciating it with some advancement
Nice.

this is really cool to see documentation where this has been thought of before! especially that very first post on the chinese forum, is basically identical :D

yzfwsf wrote:I have implemented the first five of the six firework techniques introduced by shye in my solver,
but firework MSLS has not been implemented. Then I used the batch generated puzzle module to test
the frequency of these techniques. I found that the frequency of these techniques in random puzzles is
very low, 1/1700 ~ 1000, of which 18% are dual w-wing and the rest are Firework Triple. Only one Fire Exocet
is not standard and is an extended type.Of course, my test results are for really effective steps.I put its priority
behind SDC. I searched more than a million puzzles to get the above statistics.

I think these puzzle examples must be specially designed.

these are kind of results i was more expecting before seeing andrews. lots of the advanced uses, DFALP or FExocet especially, are one-off kinda setups (but the point of making them is to show that you can be creative with how fireworks are implemented :))
is sharing more novel deductions around here frowned upon? quite a few people commenting in the thread it seems primarily want to know the frequency of the pattern, and i do understand that yes it would be nice if it was a very common thing, but if it isnt then does that make it not worth talking about?

thank you for taking the time to code them up and search though! i think that implementation of FMSHS will return a lot more results and hopefully show a stronger case for it. that is, any general hidden set consisting of fireworks and positional truths (bilocals for example) im no good at this technical stuff tho so i have no idea how hard that would be to get working

while i'm here, i have a few more uses of the pattern to share, made by others

Code: Select all
+-------+-------+-------+
| . . 9 | 4 . . | 6 . . |
| 6 . . | . 7 . | . . 3 |
| 7 . . | 8 . 6 | . . 4 |
+-------+-------+-------+
| . . . | . 9 . | . . . |
| . 2 3 | 7 6 . | 9 8 . |
| . . 1 | . . . | 7 . . |
+-------+-------+-------+
| . 9 . | . . . | . 3 . |
| . 8 7 | . . . | 1 2 . |
| . . . | . 5 . | . . . |
+-------+-------+-------+
Fused Cake - Fryer
skfr 7.2
..94..6..6...7...37..8.6..4....9.....2376.98...1...7...9.....3..87...12.....5....

.-------------------.----------------------.-----------------.
|x123-58 135   9    |  4      123    1235    | 6    157  y78-15|
| 6      145   2458 |  1259   7      1259    | 258  15    3    |
| 7      13    25   |  8      13     6       | 25   9     4    |
:-------------------+----------------------+-----------------:
| 458    7     4568 |  125    9      1245    | 3    1456  1256 |
| 45     2     3    |  7      6      145     | 9    8     15   |
| 9      456   1    |  235    2348   23458   | 7    456   256  |
:-------------------+----------------------+-----------------:
| 1245   9     2456 |  126    1248   12478   | 458  3     5678 |
| 345    8     7    |  369    34     349     | 1    2     569  |
|x123-4  1346  246  |xy1239-6 5    xy123789-4| 48   67   y789-6|
'-------------------'----------------------'-----------------'

FMSHS (or Firework Sextuple, but at this size giving each a name becomes kinda pointless)
six cells for six candidates, fireworks on 123 in r9c1b7 and on 789 in r9c9b9, all others removed
stte

not a hugely secure puzzle, many other chains do the job, but i find this solution very pretty

here is another very nice and simple FMSHS

Code: Select all
+-------+-------+-------+
| 7 8 . | . . 4 | . . . |
| . . 4 | 5 1 . | . . . |
| . . 5 | . . 2 | 4 . . |
+-------+-------+-------+
| . . 6 | . . 5 | 2 . 7 |
| . . 7 | . . . | . 1 . |
| 8 9 . | . . . | . 4 . |
+-------+-------+-------+
| . . . | . 8 7 | 6 5 . |
| . . . | 4 . . | . . 9 |
| 3 . . | 6 . . | . . 4 |
+-------+-------+-------+
Locking in the Groove - jovi_al
skfr 8.3
78...4.....451......5..24....6..52.7..7....1.89.....4.....8765....4....93..6....4

.------------------.-------------------.--------------------.
| 7     8    x123-9| 39    369    4    | 1359  2369   x12-35|
| 269   236   4    | 5     1      3689 | 3789  236789  238  |
| 169   136   5    | 3789  3679   2    | 4     3689    138  |
:------------------+-------------------+--------------------:
| 14    134   6    | 1389  349    5    | 2     389     7    |
| 245   2345  7    | 2389  23469  3689 | 389   1       368  |
| 8     9    y123  |y12-37 2367   136  | 35    4       356  |
:------------------+-------------------+--------------------:
| 1249  124   129  |y123-9 8      7    | 6     5      x123  |
| 56    567   128  | 4     235    13   | 1378  2378    9    |
| 3     57    1289 | 6     259    19   | 178   278     4    |
'------------------'-------------------'--------------------'

FMSHS
six cells for six candidates, fireworks on 12 in r1c9b3, more on 12 in r6c4b5, 3c3 & 3r7, all others removed
stte

this next one is very creative i thought

Code: Select all
+-------+-------+-------+
| . 7 6 | 5 . . | 4 8 . |
| 4 . . | . 6 . | . 1 5 |
| 5 . . | . . . | . . 7 |
+-------+-------+-------+
| . . 2 | 4 . 3 | . . . |
| 8 . . | . . . | . 7 . |
| . 1 3 | . . 5 | . . 4 |
+-------+-------+-------+
| . . . | 3 . 1 | . . 9 |
| . . . | 2 . . | . . 6 |
| . . . | . 9 . | 7 5 . |
+-------+-------+-------+
LED Madness - Qinlux
skfr 8.4
.765..48.4...6..155.......7..24.3...8......7..13..5..4...3.1..9...2....6....9.75.

.------------------.------------------.-------------------.
|A123  7     6     | 5    C123    9   | 4       8    B3+2 |
| 4    2389  89    | 78    6      278 | 239     1     5   |
| 5    2389  189   | 18    12348  248 | 2369    2369  7   |
:------------------+------------------+-------------------:
| 679  569   2     | 4     17     3   | 1569    69    8   |
| 8    4569  459   | 169  B1+2    26  | 123569  7    A123 |
| 679  1     3     | 6789  278    5   | 269     269   4   |
:------------------+------------------+-------------------:
| 26   4568  4578  | 3     4578   1   | 28      24    9   |
| 139  4589  45789 | 2     4578   478 | 138     34    6   |
|B13+2  2348  148   | 68    9      468 | 7       5    C123 |
'------------------'------------------'-------------------'

this is the state of the grid after lc's, a firework triple (123 in r9c1b7) and resulting singles

since r1c1, r9c1 & r9c9 are known to be a triple, they can be labelled ABC, and then cells limited to 123 must also be ABC and we can determine what some are
AC look at r1c9 making it B
A has to be placed in col 9
C has to be placed in row 1
AC look at r5c5 making it B

then the only common digit left for B is 2
+2r1c9, +2r5c5, +2r9c1
stte
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Re: Fireworks

Postby yzfwsf » Wed Dec 29, 2021 1:19 pm

shye wrote: quite a few people commenting in the thread it seems primarily want to know the frequency of the pattern, and i do understand that yes it would be nice if it was a very common thing, but if it isnt then does that make it not worth talking about?

Your work is excellent, please continue to share such delightful puzzles.
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Re: Fireworks

Postby StrmCkr » Thu Dec 30, 2021 5:02 am

http://forum.enjoysudoku.com/strong-links-within-fish-patterns-t30392.htmlhere's another thread I hinted at years back that seems to be another practical application of this.
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Re: Fireworks

Postby denis_berthier » Thu Dec 30, 2021 5:10 am

I have,'t followed all the details of the discussion.
Is this the right conclusion: "the most frequent use if the FW Triple"?
If yes, where is the definition of this pattern, so that I can try it in SudoRules (I've already implemented the or3 part)?
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Re: Fireworks

Postby StrmCkr » Sat Jan 08, 2022 3:06 am

finally found some free time to digest this post a bit further and post some markups.

for me these are found using my initial post comment : the alc - Almost locked Candidates , which is the inverse OF Almost locked Sets {n digits in n+1 cells}
the
Almost Hidden set. {n cells with N+1 digits}
aahs etc

not a well defined subject and even less used, thanks to a lot of it found and explained much easier as the larger ALS

should it take away from the fun: defiantly not
use it how you like for me its not really new. Ive liked using the weak set to solve stuff for a long while now :)

Code: Select all
    +-------+-------+-------+
    | . 4 5 | . . . | . . . |
    | . . . | 1 . . | . 7 . |
    | 8 . . | . 2 3 | . . . |
    +-------+-------+-------+
    | . . . | 9 . 7 | 1 . . |
    | . . . | . . . | 3 . . |
    | . 8 . | 4 . 6 | . 2 . |
    +-------+-------+-------+
    | . . 3 | . . . | . . 5 |
    | . 7 . | 8 . . | . . 6 |
    | . . . | . . . | 9 . . |
    +-------+-------+-------+
    Triple Laser - Qinlux
    skfr 8.3
    .45.........1...7.8...23......9.71........3...8.4.6.2...3.....5.7.8....6......9..

    .---------------------.-------------------.--------------------.
    |x123-679 4     5     | 67   6789   89    | 268   189   x123-89|
    | 2369    2369  269   | 1    45689  4589  | 2568  7      2389  |
    | 8       169   1679  | 567  2      3     | 456   1459   149   |
    :---------------------+-------------------+--------------------:
    | 23456   2356  246   | 9    358    7     | 1     4568   48    |
    | 145679  1569  14679 | 25   158    1258  | 3     45689  4789  |
    | 13579   8     179   | 4    135    6     | 57    2      79    |
    :---------------------+-------------------+--------------------:
    | 12469   1269  3     | 267  14679  1249  | 2478  148    5     |
    | 12459   7     1249  | 8    1459   12459 | 24    3      6     |
    | 12456   1256  8     | 3    14567  1245  | 9     14    x12-47 |
    '---------------------'-------------------'--------------------'


firework triple

123 in r1 and c9 limited to r1c1, r9c9, and box 3, and therefore limited to r1c1, r9c9 and r1c9
three cells for three candidates, all others removed
stte


previous comments of: ALC aka Almost hidden locked sets

account for the triples

Code: Select all
+----------------------+---------------------+------------------------+
| 123-679  4     5     | (67)  (6789)  (89)  | (268)  (189)  (123-89) |
| 2369     2369  269   | 1     45689   4589  | 568-2  7      (2389)   |
| 8        169   1679  | 56-7  2       3     | 456    459-1  (149)    |
+----------------------+---------------------+------------------------+
| 23456    2356  246   | 9     358     7     | 1      4568   (48)     |
| 145679   1569  14679 | 25    158     1258  | 3      45689  (4789)   |
| 13579    8     179   | 4     135     6     | 5-7    2      (79)     |
+----------------------+---------------------+------------------------+
| 12469    1269  3     | 267   14679   1249  | 2478   148    5        |
| 12459    7     1249  | 8     1459    12459 | 24     3      6        |
| 12456    1256  8     | 3     14567   1245  | 9      14     12-47    |
+----------------------+---------------------+------------------------+


is the opposite of this:
Almost Locked Set XZ-Rule: A=r1c45678 {126789},B=r123456c9 {1234789}, X=12, Z=/ => r3c8<>1 r2c7<>2 r9c9<>4 r1c1<>6 r1c1<>7 r3c4<>7 r6c7<>7 r9c9<>7 r1c9<>8 r1c9<>9 r1c1<>9

The aHS- is this one:
Code: Select all
+------------------------+-------------------+------------------------+
| -679(123)  4     5     | 67   6789   89    | 68(2)  89(1)  -89(123) |
| 2369       2369  269   | 1    45689  4589  | 568-2  7       2389    |
| 8          169   1679  | 567  2      3     | 456    459-1  49(1)    |
+------------------------+-------------------+------------------------+
| 23456      2356  246   | 9    358    7     | 1      4568   48       |
| 145679     1569  14679 | 25   158    1258  | 3      45689  4789     |
| 13579      8     179   | 4    135    6     | 57     2      79       |
+------------------------+-------------------+------------------------+
| 12469      1269  3     | 267  14679  1249  | 2478   148    5        |
| 12459      7     1249  | 8    1459   12459 | 24     3      6        |
| 12456      1256  8     | 3    14567  1245  | 9      14     -47(12)  |
+------------------------+-------------------+------------------------+

{the missing eliminations are found post clean up}


Code: Select all
    Cobra Roll - jovi_al
    skfr 8.5
    ..23..5...1..4..9....5....6.76......8...2..4.9.....8.3.....5..2.....6.1....87....

    .------------------------.--------------------.--------------------.
    | 467     4689    2      | 3     1689   1789  | 5      78    14    |
    | 3567    1       3578   | 267   4      278   | 23     9     78    |
    | 347     3489    34789  | 5     189    12789 | 14     23    6     |
    :------------------------+--------------------+--------------------:
    |x1234-5  7       6      | 149   13589 x34-189| 129    25    159   |
    | 8       35      135    | 1679  2      1379  | 1679   4     1579  |
    | 9       245     145    | 1467  156    147   | 8      2567  3     |
    :------------------------+--------------------+--------------------:
    | 13467   34689   134789 | 149   139    5     | 34679  3678  2     |
    | 23457   234589  345789 | 249   39     6     | 3479   1     45789 |
    |x12-3456 234569  13459  | 8     7     x1234-9| 3469   356   459   |
    '------------------------'--------------------'--------------------'


firework quadruple
original post

12 in r9 and c1 limited to r4c1, r9c6 or b7 and therefore r4c1, r9c6, r9c1
34 in r4 and c6 limited to r4c1, r9c6 or b5 and therefore r4c1, r9c6, r4c6
four cells for four candidates, all others removed
stte (after naked pairs at the start)


Code: Select all
 AHS - chain/ring
+------------------------------+--------------------------+--------------------+
| 467        4689      2       | 3      1689     1789     | 5      78    14    |
| 3567       1         3578    | 267    4        278      | 23     9     78    |
| 347        3489      34789   | 5      189      12789    | 14     23    6     |
+------------------------------+--------------------------+--------------------+
| -5(1234)   7         6       | 19(4)  1589(3)  -189(34) | 129    25    159   |
| 8          35        135     | 1679   2        179(3)   | 1679   4     1579  |
| 9          245       145     | 167-4  156      17(4)    | 8      2567  3     |
+------------------------------+--------------------------+--------------------+
| 3467(1)    34689     34789-1 | 149    139      5        | 34679  3678  2     |
| 3457(2)    34589-2   345789  | 249    39       6        | 3479   1     45789 |
| -3456(12)  34569(2)  3459(1) | 8      7        -9(1234) | 3469   356   459   |
+------------------------------+--------------------------+--------------------+



Code: Select all
    |x149  8       5      | 7    #19    23   | 6      2349  2-9  |
    | 3    67      679    | 2569  4     8    | 579    1     259  |
    | 2    1467    1679   | 3569  1569  356  | 34579  3479  8    |
    :---------------------+------------------+-------------------:
    | 5    1237    4      | 8     679   36   | 179    2679  1269 |
    | 6    137     1378   | 349   2     34   | 14789  5    #19   |
    | 78   9       278    | 456   567   1    | 478    2467  3    |
    :---------------------+------------------+-------------------:
    | 178  123567  123678 | 256   568   9    | 135    36    4    |
    | 489  23456   23689  | 1     568   2456 | 359    369   7    |
    |x149  1456    169    | 456   3     7    | 2      8    x1569 |
    '---------------------'------------------'-------------------'

dual firework w-wing (tentative name)

fireworks on 1&9 r9c1b7
either a naked 19 pair in r1c15 or r59c9 exists
=> -9r1c9 stte



this is covered Under the W-wing extensions... not really new but still fun. very unconventional to use overlapping weak-links to form any chains.{box 7} pretty sure no one really has this programed.. }
Code: Select all
 +-----------------------+------------------+---------------------+
| 4(19)  8       5      | 7     (19)  23   | 6      2349  2-9    |
| 3      67      679    | 2569  4     8    | 579    1     259    |
| 2      1467    1679   | 3569  1569  356  | 34579  3479  8      |
+-----------------------+------------------+---------------------+
| 5      1237    4      | 8     679   36   | 179    2679  1269   |
| 6      137     1378   | 349   2     34   | 14789  5     (19)   |
| 78     9       278    | 456   567   1    | 478    2467  3      |
+-----------------------+------------------+---------------------+
| 78(1)  123567  123678 | 256   568   9    | 135    36    4      |
| 48(9)  23456   23689  | 1     568   2456 | 359    369   7      |
| 4(19)  456(1)  6(19)  | 456   3     7    | 2      8     56(19) |
+-----------------------+------------------+---------------------+


Code: Select all
    .---------------------.------------------.--------------------.
    | 4579   345    3457  | 6   x24789  1    | 3589   235  x28-39 |
    | 4569   145    2     | 458  3      89   | 7      156   689   |
    | 5679   8      13567 | 25   79-2   279  | 13569  4     2369  |
    :---------------------+------------------+--------------------:
    | 1      9      68    | 238  7-28   4    | 368    2367  5     |
    |x24568  7      456-8 | 1   #28     35-28| 346-8  9    x23468 |
    | 3      245    458   | 9    6      2578 | 48     27    1     |
    :---------------------+------------------+--------------------:
    | 2457   6      13457 | 234  149-2  239  | 13459  8     3479  |
    | 478    134    9     | 348  5      38   | 2      136   3467  |
    |x28-45  12345  13458 | 7   x12489  6    | 13459  135   349   |
    '---------------------'------------------'--------------------'
dual firework ALP
original post

like the above this uses the (x|y)cell1 = (x|y)cell2 idea, but for something a bit fancier

fireworks on 2s and 8s in both r1c9b3 & r9c1b7
(2|8)r1c5 = (2|8)r5c9
(2|8)r5c1 = (2|8)r9c5
combined with r5c5 limited to only [28], at most one of 2 or 8 can be in r5c19 and at most one in r19c5. almost locked pairs in r5 and c5
stte


AHS + als looping 2 chains together ... not new either but fun :)
Code: Select all
+---------------------------+---------------------+------------------------+
| 4579     345      3457    | 6    479(28)  1     | 359(8)  35(2)  -39(28) |
| 4569     145      2       | 458  3        89    | 7       156    69(8)   |
| 5679     8        13567   | 25   79-2     279   | 13569   4      369(2)  |
+---------------------------+---------------------+------------------------+
| 1        9        68      | 238  7-28     4     | 368     2367   5       |
| 456(28)  7        456-8   | 1    (28)     35-28 | 346-8   9      346(28) |
| 3        245      458     | 9    6        2578  | 48      27     1       |
+---------------------------+---------------------+------------------------+
| 457(2)   6        13457   | 234  149-2    239   | 13459   8      3479    |
| 47(8)    134      9       | 348  5        38    | 2       136    3467    |
| -45(28)  1345(2)  1345(8) | 7    149(28)  6     | 13459   135    349     |
+---------------------------+---------------------+------------------------+
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 1283
Joined: 05 September 2006

Re: Fireworks

Postby yzfwsf » Sat Jan 08, 2022 10:27 pm

After modifying the code to allow individual FW missing corners, the Dual ALP/FW Quadruple appears.

Dual ALP
Code: Select all
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610000000000008059000470030800210000007806400000043005050024000130600000000000082
600400800040050002000001060006190050700000008050023600030600000100030020008002003
050070600009140500600002000100800000307000209000007004000900002008015700003020010


Firework Quadruple
Hidden Text: Show
Code: Select all
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Re: Fireworks

Postby StrmCkr » Mon Jan 10, 2022 1:29 am

to point this out---
still works not using "triples"
Code: Select all
+-----------------------+-------------------+-----------------------+
| 2679(13)  4     5     | 67   6789   89    | 268   89(1)  -89(123) |
| 2369      2369  269   | 1    45689  4589  | 2568  7      89(23)   |
| 8         169   1679  | 567  2      3     | 456   1459   49(1)    |
+-----------------------+-------------------+-----------------------+
| 23456     2356  246   | 9    358    7     | 1     4568   48       |
| 145679    1569  14679 | 25   158    1258  | 3     45689  4789     |
| 13579     8     179   | 4    135    6     | 57    2      79       |
+-----------------------+-------------------+-----------------------+
| 12469     1269  3     | 267  14679  1249  | 2478  148    5        |
| 12459     7     1249  | 8    1459   12459 | 24    3      6        |
| 12456     1256  8     | 3    14567  1245  | 9     14     47(12)   |
+-----------------------+-------------------+-----------------------+

this also works as well.
Code: Select all
+------------------------+-------------------+------------------------+
| -679(123)  4     5     | 67   6789   89    | 68(2)  89(1)  -89(123) |
| 2369       2369  269   | 1    45689  4589  | 568-2  7      389(2)   |
| 8          169   1679  | 567  2      3     | 456    459-1  49(1)    |
+------------------------+-------------------+------------------------+
| 23456      2356  246   | 9    358    7     | 1      4568   48       |
| 145679     1569  14679 | 25   158    1258  | 3      45689  4789     |
| 13579      8     179   | 4    135    6     | 57     2      79       |
+------------------------+-------------------+------------------------+
| 12469      1269  3     | 267  14679  1249  | 2478   148    5        |
| 12459      7     1249  | 8    1459   12459 | 24     3      6        |
| 12456      1256  8     | 3    14567  1245  | 9      14     -47(12)  |
+------------------------+-------------------+------------------------+
Some do, some teach, the rest look it up.
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Re: Fireworks

Postby yzfwsf » Wed Jan 19, 2022 8:36 am

Code: Select all
.-------------------.------------------.--------------------.
| 15689  *189 14679 | 367  35678  2478 | #129   #2469 #12469|
| 156    2    1467  | 9    567    47   | 3      8     #146  |
| 689    3    469   | 1    68     248  | 7      5     #2469 |
:-------------------+------------------+--------------------:
| 139    4    8     | 37   2      179  | 59     369   35679 |
| 139    5    1239  | 4    13789  6    | 289    239   23789 |
| 7      6    239   | 5    389    89   | 4      1     2389  |
:-------------------+------------------+--------------------:
| 4      189  6-19  | 67   1679   3    | 12589  29    12589 |
| 2      *19  139   | 8    4      5    | 6      7    *139   |
| 368-19 7    5     | 2    169    19   | 189    349   13489 |
'-------------------'------------------'--------------------'
 Dual Firework ER: 19r8c2b7 is firework => r7c3<>19,r9c1<>19
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Re: Fireworks

Postby jco » Sun Feb 13, 2022 2:00 pm

yzfwsf wrote:
Code: Select all
.-------------------.------------------.--------------------.
| 15689  *189 14679 | 367  35678  2478 | #129   #2469 #12469|
| 156    2    1467  | 9    567    47   | 3      8     #146  |
| 689    3    469   | 1    68     248  | 7      5     #2469 |
:-------------------+------------------+--------------------:
| 139    4    8     | 37   2      179  | 59     369   35679 |
| 139    5    1239  | 4    13789  6    | 289    239   23789 |
| 7      6    239   | 5    389    89   | 4      1     2389  |
:-------------------+------------------+--------------------:
| 4      189  6-19  | 67   1679   3    | 12589  29    12589 |
| 2      *19  139   | 8    4      5    | 6      7    *139   |
| 368-19 7    5     | 2    169    19   | 189    349   13489 |
'-------------------'------------------'--------------------'
 Dual Firework ER: 19r8c2b7 is firework => r7c3<>19,r9c1<>19

For this example, it seems that using the Firework interpretation, cells r7c2, r8c3 need to receive stars as well, due to
Grouped X-Chain: (1)r8c23 = r8c9 - r12c9 = r1c7 - r1c2 = (1)r78c2 => -1 r7c3, r9c1
Grouped X-Chain: (9)r8c23 = r8c9 - r13c9 = r1c78 - r1c2 = (9)r78c2 => -9 r7c3, r9c1
Hidden Text: Show
To distinguish from the view:
Grouped X-Chain: (1)r8c23 = r8c9 - r2c9 = r2c13 - r1c2 = (1)r78c2 => -1 r7c3, r9c1
Grouped X-Chain: (9)r8c23 = r8c9 - r3c9 = r3c13 - r1c2 = (9)r78c2 => -9 r7c3, r9c1

For this reason, I have doubts if this is a Firework (probably my understanding of it is too restrictive).
EDIT: corrected small typo.
@yzfwsf: thanks for your reply (in the next post).
Last edited by jco on Sun Feb 13, 2022 8:00 pm, edited 1 time in total.
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Re: Fireworks

Postby yzfwsf » Sun Feb 13, 2022 2:32 pm

jco wrote:For this reason, I have doubts if this is a Firework (probably my understanding of it is too restrictive).

This is indeed Fireworks, xsudo style:
6 Trueth=19r8,19c2(Dual Fireworks)+19b3(Dual ERI)
6 Links =19r1,19c9,19b7
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Re: Fireworks

Postby StrmCkr » Sun Feb 13, 2022 6:40 pm

i see it it as a muti-fish
digits 1/9 using the same swordfish

Code: Select all
+----------------------+------------------+------------------------+
| 15689   8(19)  14679 | 367  35678  2478 | 2(19)  246(9)  246(19) |
| 156     2      1467  | 9    567    47   | 3      8       46(1)   |
| 689     3      469   | 1    68     248  | 7      5       246(9)  |
+----------------------+------------------+------------------------+
| 139     4      8     | 37   2      179  | 59     369     35679   |
| 139     5      1239  | 4    13789  6    | 289    239     23789   |
| 7       6      239   | 5    389    89   | 4      1       2389    |
+----------------------+------------------+------------------------+
| 4       8(19)  6-19  | 67   1679   3    | 12589  29      12589   |
| 2       (19)   3(19) | 8    4      5    | 6      7       3(19)   |
| 368-19  7      5     | 2    169    19   | 189    349     13489   |
+----------------------+------------------+------------------------+
Some do, some teach, the rest look it up.
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