## exocet pattern in hardest puzzles

Advanced methods and approaches for solving Sudoku puzzles

### Re: bi bi pattern in hardest puzzles

champagne wrote:
ronk wrote:Sometime soon, maybe even before doing all of the above, would you please look at "G1, G2, ... multi-fish" detection.
...
If you need more examples, I have several.

first of all, the next step in my "to do" list is to work on the multi fish detection.

I'm glad to hear that. From the present "03 NN nothing special" file, here are three puzzles which have all-row (and all-column) fish.

2926;elev;L294 - an 03 NN: Show
Code: Select all
`000400700400080006009002000000030008300800400018000350090000010700600003002005000Has a 0-rank 5-dig 4-row fish     18 Truths = {34678R3 467R6 34678R7 34678R9}     18 Links = {3c4 4c59 6c157 7c459 8c17 39n2 7n3 67n6 39n8}and a complementary 0-rank 4-dig 5-row fish     20 Truths = {1R12458 2R12458 5R12458 9R12458}     20 Links = {1c36 2c28 5c23 9c68 14n1 24n4 158n5 248n7 15n9}`

3173;elev;1405 - an 03 NN: Show
Code: Select all
`100050000057009006098300000006700008080000000500040020000030100030900007000002040Has a 0-rank 4-dig 5-row fish     19 Truths = {1R23458 2R23458 4R23458 5R3458}     19 Links = {1c568 2c157 4c167 5c678 2n4 3n9 4n2 5n349 8n3}and a complementary 0-rank 4-dig 4-col fish      15 Truths = {1C2349 2C2349 4C2349 5C349}     15 Links = {24r1 1r6 245r7 15r9 2n4 3n9 4n2 5n349 8n3}`

1582;elev;567 - an 03 NN: Show
Code: Select all
`100006000000080200009700005030900004005000090900020100004000007090300040800000600Has a 0-rank 5-dig 4-row fish     19 Truths = {34579R1 34579R2 3457R6 34579R9}     19 Links = {3c389 4c24 5c248 7c238 9c9 2n1 19n5 269n6 1n7}and a complementary 0-rank 5-dig 4-col fish     19 Truths = {3457C1 34579C5 34579C6 34579C7}     19 Links = {3r357 4r35 5r478 7r458 9r7 2n1 19n5 269n6 1n7}`

champagne wrote:but I have difficulties to understand what is your point.

Not so difficult to understand. The smaller the "03 NN nothing special" file, the higher the probability I can find something new. Remember I'm searching manually with an assist from XSUDO, which sometimes helps a lot but often doesn't find a suitable base set (truths) on these hardest puzzles.
ronk
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### Re: bi bi pattern in hardest puzzles

champagne wrote:After I released the constraint to have all digits in the target, I have many more exocets, but still one or two bases, except for 3 new oddities

Code: Select all
`..3..6...4.67...3..7....5...6...597..3...7.4.9............2......8.....1.4...3.5.;6519;elev;3594;..3..6...4.67...3..7....5...6...5.7..3.9.7.4.9............2......8.....1.4...3.5.;6527;elev;3595..3.5.......7...2.7...31..5....4..9..6.........51....2.....8.....73....18.25....7;6530;elev;3613`

these 3 puzzles seem to have (unchecked) interleaved exocets from different bases.

Here's the only productive Exocet that I found in your 2nd puzzle.

Code: Select all
`Puzzle #2:   6527;elev;3595   Double-J Exocet with secondary placements..3..6...4.67...3..7....5...6...5.7..3.9.7.4.9............2......8.....1.4...3.5. after Naked Quad(s) +--------------------------------------------------------------------------------+ |  1258    12589   3       |  12458   14589   6       |  124789  1289    24789   | |  4       12589   6       |  7       1589    1289    |  1289    3       289     | |  128     7       129     |  12348   13489   12489   |  5       12689   24689   | |--------------------------+--------------------------+--------------------------| |  128     6       4       |  1238    138     5       |  12389   7       2389    | |  1258    3       125     |  9       168     7       |  1268    4       2568    | |  9       1258    7       |  123468  13468   1248    |  12368   1268    23568   | |--------------------------+--------------------------+--------------------------| |  367     159     159     |  14568   2       1489    |  346789  689     346789  | |  367     259     8       |  456     45679   49      |  234679  269     1       | |  67      4       129     |  168     16789   3       |  26789   5       26789   | +--------------------------------------------------------------------------------+ # 179 eliminations remain ### <1289> JExocet:   Base = r2c79   Target = r1c2,r3c6==r1c1 ### <1289> JExocet:   Base = r3c13   Target = r1c8==r2c5,r2c6`
daj95376
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### Re: bi bi pattern in hardest puzzles

An Exocet in a chute that doesn't meet (my understanding of) the JExocet definition -- see value <4>.

Just as interesting, it came from Champagne's latest set of "03 NN" puzzles.

Code: Select all
`Puzzle:   35;GP;H4;11.70;11.70;11.30;85298.7.....6.....9....5....7..4..3..2...85..4.......4..1..69..5......2...3.....1.4. +--------------------------------------------------------------------------------+ |  9       8       1234    | /7       1456    2356    | T1236    1356    2456    | |  6       1237    12347   | T12348   1458    2358    | /9       1358    2458    | | B1234   B123     5       |  123468  14689   23689   |  12368   7       2468    | |--------------------------+--------------------------+--------------------------| |  157     4       179     |  168     3       6789    |  678     2       56789   | |  1237    123679  8       |  5       1679    2679    |  4       369     679     | |  2357    235679  2379    |  268     6789    4       |  3678    35689   1       | |--------------------------+--------------------------+--------------------------| |  123478  1237    6       |  9       478     378     |  5       18      278     | |  14578   1579    1479    |  468     2       5678    |  1678    1689    3       | |  23578   23579   2379    |  368     5678    1       |  2678    4       26789   | +--------------------------------------------------------------------------------+ # 181 eliminations remain ### <1234> Exocet:   Base = r3c12   Target = r1c7,r2c4`
daj95376
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### Re: bi bi pattern in hardest puzzles

Ditto!

Code: Select all
`Puzzle:   12120;GP;kz0;11.70;11.70;11.30;63798.7.....7...6......5..87..5....69....43...6.....2...1.5...48.....6....3....1..2. +--------------------------------------------------------------------------------+ |  9       8       1236    |  7       345     1235    |  123456  1345    2456    | |  7       1234    123     |  12459   6       12359   |  12345   134589  24589   | |  12346   12346   5       |  1249    349     8       |  7       1349    2469    | |--------------------------+--------------------------+--------------------------| |  5       1237    12378   |  148     478     6       |  9       3478    2478    | |  128     1279    4       |  3       5789    1579    |  25      6       2578    | |  368     3679    36789   |  4589    2       579     |  345     34578   1       | |--------------------------+--------------------------+--------------------------| |  1236    5       123679  |  29      379     4       |  8       179     679     | |  1248    12479   12789   |  6       5789    2579    |  145     14579   3       | |  3468    34679   36789   |  589     1       3579    |  456     2       45679   | +--------------------------------------------------------------------------------+ # 176 eliminations remain ### <1236> Exocet:   Base = r12c3   Target = r4c2,r7c1`

Code: Select all
`Puzzle:   14596;GP;kz1a;11.40;11.40;11.30;52598.7.....7...6......5..97..5....69....43...6.....2...1.5...48.....6...3.....1...2 +--------------------------------------------------------------------------------+ |  9       8       1236    |  7       345     1235    |  123456  1245    3456    | |  7       1234    123     |  12458   6       12358   |  12345   124589  34589   | |  12346   12346   5       |  1248    348     9       |  7       1248    3468    | |--------------------------+--------------------------+--------------------------| |  5       1237    12378   |  148     478     6       |  9       2478    3478    | |  128     1279    4       |  3       5789    1578    |  25      6       578     | |  368     3679    36789   |  4589    2       578     |  345     4578    1       | |--------------------------+--------------------------+--------------------------| |  1236    5       123679  |  29      379     4       |  8       179     679     | |  1248    12479   12789   |  6       5789    2578    |  145     3       4579    | |  3468    34679   36789   |  589     1       3578    |  456     4579    2       | +--------------------------------------------------------------------------------+ # 172 eliminations remain ### <1236> Exocet:   Base = r12c3   Target = r4c2,r7c1`

[Edit: removed erroneous reference to puzzle "2051".]
Last edited by daj95376 on Sat Apr 21, 2012 12:48 am, edited 1 time in total.
daj95376
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### Re: bi bi pattern in hardest puzzles

daj95376 wrote:
Code: Select all
`Puzzle:    2051;elev;1452;11.20;11.20;9.90;542... ### <1346> Exocet:   Base = r5c46   Target = r4c9,r6c3`

Because of the lack of a clue in r1c3, I don't believe this one is an exocet. However, the other three (of the last four) contain a degenerate case we've not addressed before. Degenerate because, for one of the exocet digits:

If (x)B1B2, then (x)T1 ... rather than (x)T1 = (x)T2 where B1, B2, T1, and T2 are the base and target cells.

Good find!
ronk
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### Re: bi bi pattern in hardest puzzles

ronk wrote:
daj95376 wrote:
Code: Select all
`Puzzle:    2051;elev;1452;11.20;11.20;9.90;542... ### <1346> Exocet:   Base = r5c46   Target = r4c9,r6c3`

Because of the lack of a clue in r1c3, I don't believe this one is an exocet.!

Yes, I missed the presence of the <3> candidate in r1c3 while examining this puzzle. Thanks for catching it !!!
daj95376
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### Re: bi bi pattern in hardest puzzles

champagne wrote:After I released the constraint to have all digits in the target, I have many more exocets, but still one or two bases, except for 3 new oddities

Code: Select all
`..3..6...4.67...3..7....5...6...597..3...7.4.9............2......8.....1.4...3.5.;6519;elev;3594; ..3..6...4.67...3..7....5...6...5.7..3.9.7.4.9............2......8.....1.4...3.5.;6527;elev;3595 ..3.5.......7...2.7...31..5....4..9..6.........51....2.....8.....73....18.25....7;6530;elev;3613 `

these 3 puzzles seem to have (unchecked) interleaved exocets from different bases.

On my side, I have to add a filter in the program to clean naked quads

Just one more remark, the current code still works in a band/stack. I did not yet restart a code looking for a target outside the band/stack containing the base.

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

ronk wrote: From the present "03 NN nothing special" file, here are three puzzles which have all-row (and all-column) fish.
...
Not so difficult to understand. The smaller the "03 NN nothing special" file, the higher the probability I can find something new. Remember I'm searching manually with an assist from XSUDO, which sometimes helps a lot but often doesn't find a suitable base set (truths) on these hardest puzzles.

Now I see clearly your point.

Unhappily, picking up the old code and opening the search to catch all these patterns not seen so far by my solver requires time.

I have heavy duties till mid may, but I hope to have covered the point by end of may.

A sample file of all new cases would help in building the new design.

If you have one available, posting it can save some time

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

ronk wrote:
daj95376 wrote:
Code: Select all
`Puzzle:    2051;elev;1452;11.20;11.20;9.90;542... ### <1346> Exocet:   Base = r5c46   Target = r4c9,r6c3`

Because of the lack of a clue in r1c3, I don't believe this one is an exocet. However, the other three (of the last four) contain a degenerate case we've not addressed before. Degenerate because, for one of the exocet digits:

If (x)B1B2, then (x)T1 ... rather than (x)T1 = (x)T2 where B1, B2, T1, and T2 are the base and target cells.

Good find!

An interplanetary interpreter is needed for me to make sense of that explanation .

I don't know if it is an Exocet, but it certainly isn't a JExocet.

The difference is an Exocet requires an in-depth investigation to prove the target cells must hold the base digits whereas a JExocet just requires a pattern check.

Puzzle: 2051;elev;1452;11.20;11.20;9.90;542
....5...94..1...3..6.7..1....59......8..7.......5.2..73......6...8.9...2.1....4..
Code: Select all
` *-------------------------*-------------------------*-------------------------* | 1278    237     1237 %  | 23468   5       3468    | 2678    2478    9       | 13..  | 4       2579    279     | 1       268     689     | 25678   3       568     | ...6 | 2589    6       239  %  | 7       2348 %  3489    | 1       2458    458     | .34. *-------------------------*-------------------------*-------------------------* | 1267    2347    5       | 9       13468   13468   | 2368    1248    13468 # |  | 1269    8       123469  | 346 #   7       1346 #  | 23569   12459   13456   |  | 169     349     13469 # | 5       13468   2       | 3689    1489    7       |  *-------------------------*-------------------------*-------------------------* | 3       24579   2479    | 248     1248    14578   | 5789    6       158     | 1.4. | 567     457     8       | 346     9       134567  | 357     157     2       | .... | 25679   1       2679    | 2368    2368 %  35678   | 4       5789    358 %   | .3.6 *-------------------------*-------------------------*-------------------------*                    ^ 3               ^ 3                               ^ 3`

(1346)JExocet:r5c46,r6c3,r4c9 isn't valid because three instances of digit (3) can be held in columns 3, 5,& 9 in tiers 1 & 3 in the cells marked %.
Consequently unlike the other digits, if (3) is in one of the base cells it isn't forced to be in either target cell.
That's the reason for imposing the additional JExocet condition.

The JExocet would be valid if (3) was missing from one of r1c3, r3c5, or r9c9, as then the % cells could be covered by two lines.
David P Bird
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### Re: bi bi pattern in hardest puzzles

David P Bird wrote:Puzzle: 2051;elev;1452;11.20;11.20;9.90;542
Exocet: Base = r5c46 Target = r4c9,r6c3

I don't know if it is an Exocet, but it certainly isn't a JExocet.

The difference is an Exocet requires an in-depth investigation to prove the target cells must hold the base digits whereas a JExocet just requires a pattern check.

It seems that more exocets are not Jexocets with the degenerated form.

There is a simple reason to that;
In degenerated forms, we often have a direct elimination linked to the digit(s) alone in the base.

Here, it's not the situation for digit 3, but if you look at the PM of the digit, it's never to hard to verify the validity of the target.

but I agree, it's nicer when it appears to be a Jexocet.

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

champagne, thanks for the help, and I'm willing to believe that there can be a simple proof that the base digits must occupy the target cells when the JExocet conditions aren't satisfied. In this case I just don't see it though!

But I did find one derived inference that may be of help to others:
Here digits (146) satisfy the JExocet requirements and just (3) doesn't.
If the base cells hold (3x) we know that (x) must be true in one of the target cells. So, if (3) is assumed true in one, it must therefore be false in the other. (I'm not sure how well XSUDO can handle derived inferences like this.)

Even using that inference I wasn't successful however.

I should also repeat that I don't believe in exploring multiple cases when I'm solving, only when I'm looking for new patterns.

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

David P Bird wrote:I'm not sure how well XSUDO can handle derived inferences like this.

If one spells out precisely the logic required to derive an inference, it handles such an inference very well.
ronk
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### Re: bi bi pattern in hardest puzzles

I am afraid daj95376 pushed us in a bad trap with puzzle 2051

I intended to show to David how easy it was to prove the exocet.

Unhappily

My solver does not see an exocet in puzzle 2051

working by hand the 3PM I come to that point

Code: Select all
`+--------------------------+ |  x 3 3 |  3 x 3 |  x x x | |  x x x |  x x x |  x g x | |  x x 3 |  x 3 3 |  x x x | |--------+--------+--------| |  x 3 x |  x 3 3 |  3 x 3t| |  x x 3 | b3 x 3b|  3 x 3 | |  x 3 3t|  x 3 x |  3 x x | |--------+--------+--------| |  g x x |  x x x |  x x x | |  x x x |  3 x 3 |  3 x x | |  x x x |  3 3 3 |  x x 3 | +--------------------------+`

where
g is a given 3
3b is the base proposed
3t is the target proposed

To show the exocet, I put the target to nothing and I expand the base
I come here

Code: Select all
` +--------------------------+ |  x x 3 |  x x x |  x x x | |  x x x |  x x x |  x g x | |  x x x |  x 3 x |  x x x | |--------+--------+--------| |  x 3 x |  x x x |  3 x x | |  x x x | b3 x 3b|  x x x | |  x 3 x |  x x x |  3 x x | |--------+--------+--------| |  g x x |  x x x |  x x x | |  x x x |  3 x 3 |  x x x | |  x x x |  x x x |  x x 3 | +--------------------------+`

it's clear that we have solutions for the '3' PM without the targets

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

champagne wrote:On my side, I have to add a filter in the program to clean naked quads

I'll assume you're referring to the hidden quads I mentioned and illustrated earlier. Are you planning to claim the exclusions of such hidden quads as exclusions of the "exocet double"? IMO this would overstate the case for this pattern.

champagne wrote:I am afraid daj95376 pushed us in a bad trap with puzzle 2051
I intended to show to David how easy it was to prove the exocet.

He withdrew his claim several hours ago, so he wasn't pushing very hard.
ronk
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### Re: bi bi pattern in hardest puzzles

ronk wrote:
champagne wrote:On my side, I have to add a filter in the program to clean naked quads

I'll assume you're referring to the hidden quads I mentioned and illustrated earlier. Are you planning to claim the exclusions of such hidden quads as exclusions of the "exocet double"? IMO this would overstate the case for this pattern.

I was in fact speaking of naked quads covering the full region

..3..6...4.67...3..7....5...6...597..3...7.4.9............2......8.....1.4...3.5.;6519;elev;3594;
r2c7 r2c9 r1c1 r1c2;
r2c7 r2c9 r1c2 r3c6;
r3c1 r3c3 r1c8 r2c6;
r3c1 r3c3 r2c5 r2c6;
r1c1 r3c1 r5c3 r6c2;
r7c2 r8c2 r3c3 r5c3

in that puzzle, the last code sees 7 "exocets" six are shown just above

Code: Select all
`A     B     C   |D      E     F     |G      H     I      1258  12589 3   |12458  14589 6     |124789 1289  24789  4     12589 6   |7      1589  1289  |1289   3     289    128   7     129 |12348  13489 12489 |5      12689 24689  --------------------------------------------------------128   6     4   |1238   138   5     |12389  7     2389   1258  3     125 |9      168   7     |1268   4     2568   9     1258  7   |123468 13468 1248  |12368  1268  23568  --------------------------------------------------------367   159   159 |14568  2     1489  |346789 689   346789 367   259   8   |456    45679 49    |234679 269   1      67    4     129 |168    16789 3     |26789  5     26789 `

box 4 and column 3 are reduced to a quad generating the most degenerated form of exocet;

This brings nothing and should be eliminated from the list

champagne
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