## exocet pattern in hardest puzzles

Advanced methods and approaches for solving Sudoku puzzles

### Re: bi bi pattern in hardest puzzles

champagne, once again thanks for your helpful response. I nearly got the (2789) multi-fish on my own but unfortunately went off in another direction too quickly.

I like the way your example satisfies my desire to keep the all the strong links in rows and all the weak links in columns. This makes it easier to describe in words and nicely excludes non-member digits one direction and member digits in the other.

[Added] As the pattern directly produces exclusions, I suppose that there must be Almost Multi Fish swimming about waiting to be caught.

I haven't had time today to look for the other examples you mention, but will get back to them when I can.

DPB
David P Bird
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Location: Middle England

### Re: bi bi pattern in hardest puzzles

David P Bird wrote:champagne, once again thanks for your helpful response. I nearly got the (2789) multi-fish on my own but unfortunately went off in another direction too quickly.

I like the way your example satisfies my desire to keep the all the strong links in rows and all the weak links in columns. This makes it easier to describe in words and nicely excludes non-member digits one direction and member digits in the other.

[Added] As the pattern directly produces exclusions, I suppose that there must be Almost Multi Fish swimming about waiting to be caught.

I haven't had time today to look for the other examples you mention, but will get back to them when I can.

DPB

that one, by chance, was exactly in your mood.

Sometimes, you have to add as "set" a cell containing only the multi fish digit outside of the row;column base.

Anyway, if you take in my data base of potential hardest the file "03 G multi fish seen", you have at the end of each puzzle a clue to find it.

each puzzle ends with Gxxx

'1' means the solver found a row based SLG
'2' means the solver found a column based SLG
'3' means the solver found a "rectangle based" SLG. ( 2 rows + 2 columns)

I could for sure give more clues, but for a player, too many clues kill the pleasure.

As far a I remember, all "row" or "column" based SLG are pure rank 0 logic.

The third group is pure rank 0 logic when the four intersections are empty
and "nearly rank 0 logic" if some are not empty.

for the other pattern found by ronk, I have to dig in the "hardest new thread"

One more indication: for the type '3', the main link sets are in the four boxes where are intersections.

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

As a quickie, here is a prototype procedure for finding multi-fish of that type based on balancing the truth counts:

1) Select a set of digits, (suggest looking to combine those that don't appear as givens in two parallel bands).
2) Count the rows and columns that don't contain any member digits as givens
3) If these line counts add up to 9: count their intersection cells that can contain member digits and subtract the total number of givens for the digit set.
4) The result gives the number of non-member digits these intersection cells can hold.
If this is zero then exclude any non-member digits from these cells and any member digits that see member givens in both the same row and the same column.

To be continued as I must stop now.
David P Bird
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Location: Middle England

### Re: bi bi pattern in hardest puzzles

David Bird wrote:

As a quickie, here is a prototype procedure for finding multi-fish of that type based on balancing the truth counts:

Well done. I put this into code a tried it out and it works beautifully. I'd love to know how you worked it out! Can it be extended to a wider range of senarios eg base sets of 3 or 5 or higher rank?

Regards,
pjb
pjb
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### Re: bi bi pattern in hardest puzzles

Regarding David P Bird's 'quickie' method I commented on in the previous post, I stumbled upon a puzzle with a 16 truth 16 link rank 0 pattern that is not picked up by this shortcut. It was posted by Ronk here. In this case the rows and columns that don't contain any member digits as givens add up to 10 (5 each). Can the shortcut be adapted to accommodate such cases?

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

pjb wrote:Regarding David P Bird's 'quickie' method I commented on in the previous post, I stumbled upon a puzzle with a 16 truth 16 link rank 0 pattern that is not picked up by this shortcut. It was posted by Ronk here. In this case the rows and columns that don't contain any member digits as givens add up to 10 (5 each). Can the shortcut be adapted to accommodate such cases?

pjb

I think there are more different patterns for multi-fish than for Exocet.

The "rectangle pattern" (2rows and 2 columns as sets) is quite different

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

When we partition the rows and columns into two sets we create 4 cell sets which can be coloured. The colours I use are yellow and blue for the selected rows and columns, green for their intersection cells, and white for cells that are in neither set. If we wanted we could then rearrange the rows and columns to give four colour blocks:
White Blue
Yellow Green
We can then
a) grey out any cells that can't contain any of the N digits in the focus set
b) add a # symbol to any cell that must contain one of them

We can now calculate the maximum and minimum truth holding capacity of the colour sets working first by rows and then by columns
The rows must all hold N truths but the number the blue cells can hold is reduced by any # cells in the white cells. If there are sufficient blue cells (that haven't been greyed) in the row to hold this number there is no constraint but otherwise a minimum number of truths that must be held in the white cells will be imposed. This can then be repeated in reverse to see if there is a minimum number of truths the blue cells must hold.

When this is done for every row and column and the minimum numbers for each colour added the larger of the (minimum by rows) and (minimum by columns) will apply to each colour set. Where this equals the number of coloured cells available, we know that all non-member candidates in that set must be false.

This may then establish that member candidates must be false in some complementary cells in the same row or column but this needs to be checked.

The calculations here are over-kill but will work for any way the rows and columns are split and any number of selected digits. Most splits will yield nothing, and the trick seems to be organising the divisions to concentrate the grey and # cells in 'diagonal' colour sets. This is what I'm currently trying to explore in the limited time I have available.

The method I described earlier is just a simplification that applies in a special case.

This is the puzzle you referenced with the selected rows and columns marked:
98.7..6....5.4.......9...8.7.....8.336......9..2....1..3.6....8....2.........1.40;11.60;11.60;10.00
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`   v      v             v                   v            v      *--------------------*--------------------*-------------------*>| x      x     14    | x      15    25    | x     25    1245# | <  1 | 12     12    5 #   | 12     4 #   2     | 12    2     12    | >| 124    124   14    | x      15    25    | 1245  x     1245  | <  4 *--------------------*--------------------*-------------------*>| x      145   14    | 1245 # 15    245   | x     25    x     | <  2>| x      x     14    | 1245   15    245   | 245   25    x     | <  2 | 45     45    2 #   | 45     5     45    | 45    1 #   45    |  *--------------------*--------------------*-------------------*>| 1245 # x     14    | x      5     45    | 125   25    x     | <  2 | 145    145   14    | 45     2 #   45    | 15    5     15    |  | 25     25    x     | 5      5     1 #   | 25    4 #   25    |  *--------------------*--------------------*-------------------*   ^      ^             ^                    ^           ^`

As you say there are a total of 10 rows & columns selected and to rectify the count one of them should be taken out for the simple calculation to apply. The figures on the right hand side show the number of the intersection cells in the selected rows that can hold a member digit and row 3 has the most. Deselecting this row therefore reduces the count of the eligible intersection cells down to 7 which matches the number of givens and so produces the same exclusions as ronk's diagram.

It's an approach I haven't considered before so I don't know how general it would be.

champagne's approach is effectively the same as a truth-and-link-sets one which I believe can refine the method further by considering if any of the member digits are confined to one colour set because they form locked sets with non-member digits. I'm not sure if that means that the rank then goes up to 1.

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

pjb wrote:Regarding David P Bird's 'quickie' method I commented on in the previous post, I stumbled upon a puzzle with a 16 truth 16 link rank 0 pattern that is not picked up by this shortcut. It was posted by Ronk here. In this case the rows and columns that don't contain any member digits as givens add up to 10 (5 each). Can the shortcut be adapted to accommodate such cases?

pjb

Hi pjb and david

I just launched a run on the entire file of "multi fish seen" to give you some examples of such puzzles;

For exocets, we have so many puzzles that I'll work differently, but I have to add some code to my program.

I'll extract the first pattern identified by david,
then the second one he suggests

and we'll have an idea of the frequency of each of these patterns and the list of puzzles having another one.

Hope this will help in your work.

I should post examples of various multi_fish patterns to-day

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

here some examples of the maain patterns

row based multi fish

12.3.....4.5...6...7.....2.6..1..3....453.........8..9...45.1.........8......2..7;5;elev;1
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`X     X     89+   |X     789+  79+   |789+  79+   8+    X     89+   X     |2789  2789+ 79+   |X     79+   8+    89+   X     89+   |89+   89+   9+    |89+   X     8+    X     89+   2789  |X     279+  79+   |X     7+    28+   2789  89+   X     |X     X     79+   |278   7+    28+   27+   X     27+   |27+   27+   X     |27+   7+    X     2789+ 89+   2789+ |X     X     79+   |X     9+    2+    279+  9+    279+  |79+   79+   79+   |29+   X     2+    9+    9+    9+    |89+   89+   X     |9+    9+    X     `

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`sets2789R2 2789R4 2789R5 2789R7 linksets89C2 79C6 79C8 28C9 r2c4 r2c5 r4c3 r4c5 r5c1 r5c7 r7c1 r7c3 `

===============================================================
second example, two possibilities to build a multi fish

2.......6.5..8..1...4...9...7.3.1......82.......7.5.3...9...4...8..1..5.6.......2;10;tax;tarek-ultra-0203

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`X     9+    X     |49+   49+   49+   |X     4+    X     9+    X     6+    |2469  X     2469+ |2+    X     4+    X     6+    X     |26+   6+    26+   |X     2+    X     49+   X     26+   |X     469   X     |26+   2469+ 49+   49+   469+  6+    |X     X     469   |6+    469+  49+   49+   2469+ 26+   |X     469   X     |26+   X     49+  X     2+    X     |26+   6+    26+   |X     6+    X     4+    X     2+    |2469  X     2469+ |6+    X     9+    X     4+    X     |49+   49+   49+   |X     9+    X      `

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`sets2469R2 2469R4 2469R6 2469R8 linksets49C1 26C3 26C7 49C9 r2c4 r2c6 r4c5 r4c8 r6c2 r6c5 r8c4 r8c6 `

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`2469R2 2469R8 2469C2 2469C8 linksets69B1 24B3 24B7 69B9 r2c4 r2c6 r4c8 r5c2 r5c8 r6c2 r8c4 r8c6 `

===============================================================
third example, tree possibilities to build a multi fish

1.......2..94...5..6....7.....89..4....3.6.....8.4.....2....1..7.......6..5.8..3.;12;tax;gsf-2007-05-24-003 64879;G123
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`X     7+    7+    |67+   67+   7+    |6+    6+    X     2+    7+    X     |X     1267+ 127+  |6+    X     1+    2+    X     2+    |12+   12+   12+   |X     1+    1+    26+   17+   1267+ |X     X     127+  |26+   X     17+   2+    17+   127+  |X     127+  X     |2+    127+  17+   26+   17+   X     |127+  X     127+  |26+   1267+ 17+   6+    X     6+    |67+   67+   7+    |X     7+    7+    X     1+    1+    |12+   12+   12+   |2+    2+    X     6+    1+    X     |1267+ X     127+  |2+    X     7+    `

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`sets1267R2 1267R4 1267R6 1267R9 linksets26C1 17C2 127C6 26C7 17C9 r2c5 r4c3 r6c4 r6c8 r9c4 `

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`sets1267C3 1267C4 1267C5 1267C8 linksets67R1 12R3 67R7 12R8 r2c5 r4c3 r5c3 r5c5 r5c8 r6c4 r6c8 r9c4 `

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`sets1267R2 1267R9 1267C3 1267C8 linksets27B1 16B3 16B7 27B9 r2c5 r2c6 r4c3 r5c3 r5c8 r6c8 r9c4 r9c6 `

====================================
fourth example
three possibilities to build a rank 0 logic
but here we need cell sets

..1...5...2.4...6.3....7....6.28........9..2.......4.65.....1...9.8...4...7.....3;54;col;H2;G13
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`7+    7+    X     |3+    3+    3+    |X     37+   7+    7+    X     5+    |X     135   135+  |37+   X     17+   X     5+    5+    |15+   15+   X     |X     1+    1+    17+   X     35+   |X     X     135+  |37+   1357+ 157+  17+   1357+ 35+   |1357+ X     135+  |37+   X     157+  17+   1357+ 35+   |1357  1357  135   |X     1357+ X     X     3+    3+    |37+   37+   3+    |X     7+    7+    1+    X     3+    |X     1357+ 135+  |7+    X     57+   1+    1+    X     |15+   15+   15+   |X     5+    X     `

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`sets1357R2 1357R4 1357R5 1357R8 r6c6 linksets17C1 35C3 135C6 37C7 157C9 r2c5 r4c8 r5c2 r5c4 r8c5 `

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`sets1357C2 1357C4 1357C5 1357C8 r6c6 linksets37R1 15R3 1357R6 37R7 15R9 r2c5 r4c8 r5c2 r5c4 r8c5 `

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`sets1357R2 1357R8 1357C2 1357C8 r6c4 r6c5 r6c6 linksets1357R6 57B1 137B3 13B7 57B9 r2c5 r2c6 r4c8 r5c2 r8c5 r8c6 `

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

I have still to find an example of "nearly rank 0" logic
something my solver recognise in the "rectangle pattern" when intersections are not empty

but may-be i have first to extract puzzles complying with the above patterns which seem to the majority

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

pjb, champagne my description of why the case when the selected rows and columns add up to 9 works was woefully incomplete as I was rushed for time.

Say we have 6 selected rows and 3 selected columns to give the required total of 9. If we were to reorder the rows and columns to form colour blocks we'd get this:
Code: Select all
`*--------*-----*| Yellow |Green|   |   6x6  | 6x3 |   |        |     |   *--------*-----*| White  |Blue |   |   3x6  | 3x3 |   *--------*-----*`

Now assume there are 4 digits in the focus set and a minimum of 7 truths must be true in the white block.
If there were no more truths in the white block:
In columns 1 to 6 the yellow block must contain (6x4) â€“ 7 truths.
In rows 1 to 6 the green block must now contain (6x4) â€“ ((6x4) â€“7) truths, which equals 7 again.
Hence the white and green cells must hold the same number of truths.
Now if the green block only has 7 eligible cells there can't be any further truths in the white block.
This then eliminates all member digits form the remaining free cells in the white block and all non-member digits from the eligible cells in the green block.

Note also that if there was one more eligible cell in the green block, there would be a weak links a) between all member digits in the free white cells, and b) between the non-member digits in the eligible green cells.

I've avoided using algebra to keep this description biref, but it works regardless of the numbers.

The selection system for the simple system forces all the givens into the white block.
Using the freedom available to minimise the eligible cells in the green block then got pjb's example to balance.

When the selected rows and columns are restricted to 9 in total the truth balacing technique is therefore most powerful, but there are still things to be tested when they don't naturally fall that way.

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

David P Bird wrote:champagne, does your database of puzzles contain any instances of this twist on the classic one-band Exocet?

Code: Select all
`*------------*-----------*----------*| abc abc .  | .   .  .  | .   .  . || .   .   .  | /   .  .  | /   .  . |  / = (abc) excluded | .   .   .  | T1  .  .  | T2  .  . |  T1, T2 = target cells*------------*-----------*----------*| .   .   a  | a   .  .  | .   .  . |  | .   .   bc | b   .  .  | bc  .  . || .   .   .  | .   .  .  | .   .  . |*------------*-----------*----------*| .   .   ab | ab  .  .  | a   .  . || .   .   .  | .   .  .  | .   .  . || .   .   c  | c   .  .  | c   .  . |*------------*-----------*----------*`

Perhaps this form is trivial for your solver, but unless I've missed something, it would extend the scope of the pattern for manual solvers.

DPB

I still don't have the answer to your point, but i started codification of the search of your pattern.
In my first test, I had that pattern

Code: Select all
`*------------*-----------*----------*| abc abc .  | .   .  .  | .   .  . || .   .   .  | /   .  .  | T2   .  . |  / = (abc) excluded | .   .   .  | T1  .  .  | /   .  . |  T1, T2 = target cells*------------*-----------*----------*| .   .   a  | a   .  .  | .   .  . |  | .   .   bc | b   .  .  | b   .  . || .   .   .  | .   .  .  | .   .  . |*------------*-----------*----------*| .   .   ab | a   .  .  | a   .  . || .   .   .  | .   .  .  | .   .  . || .   .   c  | c   .  .  | c   .  . |*------------*-----------*----------*`

so I changed slightly the rule to

. not more than 2 occurrences of any digit in one of the 2 "columns" attached to the target
. keeping the rule for the "column" attached to the third cell in the mini row .

I opened the door for patterns with missing digits.

A first look let's hope that

. we catch nearly all previously known exocets
. many of the "nothing special" seem to have an exocet with missing digits.

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

David P Bird wrote:
Code: Select all
`*------------*-----------*----------*| abc abc .  | .   .  .  | .   .  . || .   .   .  | /   .  .  | /   .  . |  / = (abc) excluded | .   .   .  | T1  .  .  | T2  .  . |  T1, T2 = target cells*------------*-----------*----------*| .   .   a  | a   .  .  | .   .  . |  | .   .   bc | b   .  .  | bc  .  . || .   .   .  | .   .  .  | .   .  . |*------------*-----------*----------*| .   .   ab | ab  .  .  | a   .  . || .   .   .  | .   .  .  | .   .  . || .   .   c  | c   .  .  | c   .  . |*------------*-----------*----------*`

In c3, it appears only the strong inference for 'a' is required. Also, an explanation that 'ab' in a cell, e.g., means that cell is void of candidate 'c' would have been helpful. IOW it's not obvious that you are illustrating hidden sets.
ronk
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### Re: bi bi pattern in hardest puzzles

To remove all ambiguity, here is the prospective search pattern that would give the widest scope and that lay behind my query.
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`*-------*-------*-------*| B B . | . . . | . . . |  B = Base Cells restricted to candidates from [abc] or [abcd] | . . . | Q . . | R . . |   | . . . | Q . . | R . . |  Q = 1st Target Pair *-------*-------*-------*  R = 2nd Target Pair | . . S | S . . | S . . |      One cell incapable of holding a base digit candidate | . . S | S . . | S . . |      The other holding at least one base digit candidate| . . S | S . . | S . . |    *-------*-------*-------*  S = Swordfish Completion Cells| . . S | S . . | S . . |      Each base digit restricted to 2 rows in these cells| . . S | S . . | S . . |      | . . S | S . . | S . . |  . = Any combination of candidates *-------*-------*-------*`

I have doubts if the empty cells in the target pairs can occupy the same row in a valid puzzle in practice. This is why I asked the question.

If all three cells in the base mini-row are restricted to the Exocet digit set, there will be options about which two to use.

champagne I'm pleased that you're making time to explore this and look forward to hearing your results.

DPB
David P Bird
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### exocet more and more exotic!!!

David P Bird wrote:To remove all ambiguity, here is the prospective search pattern that would give the widest scope and that lay behind my query.
Code: Select all
`*-------*-------*-------*| B B . | . . . | . . . |  B = Base Cells restricted to candidates from [abc] or [abcd] | . . . | Q . . | R . . |   | . . . | Q . . | R . . |  Q = 1st Target Pair *-------*-------*-------*  R = 2nd Target Pair | . . S | S . . | S . . |      One cell incapable of holding a base digit candidate | . . S | S . . | S . . |      The other holding at least one base digit candidate| . . S | S . . | S . . |    *-------*-------*-------*  S = Swordfish Completion Cells| . . S | S . . | S . . |      Each base digit restricted to 2 rows in these cells| . . S | S . . | S . . |      | . . S | S . . | S . . |  . = Any combination of candidates *-------*-------*-------*`

I have doubts if the empty cells in the target pairs can occupy the same row in a valid puzzle in practice. This is why I asked the question.

If all three cells in the base mini-row are restricted to the Exocet digit set, there will be options about which two to use.

champagne I'm pleased that you're making time to explore this and look forward to hearing your results.

DPB

I can give you the results of my test "subject to final validation"

42 puzzles in a file (not the last one) of 11454 puzzles having the exocet pattern have not been recognised in the search

2973 puzzles out of 5297 in the file of "nothing identified" have shown the searched pattern.

here the 42 puzzles

Hidden Text: Show
98.7..6..5..........4.3....3....5.8..7.9....6..2.4.....9.1...6......29.7......1..;;220;GP;H28;2BN H8H9
..3.5...94..1......8...7....1.......7.48.......5.6..2......4.52.......93..2.3.6..;;732;elev;H30;2BN G7G8
...4....94....923..8..2...4..6..3...8..59...2.......7.3..9....5..8..21...1...5...;;1952;elev;1806;2BN F1F3
.....6....5.78...2..9.1..4..7...8.....1.3.2..6..5.......2.4...18.....49.......3..;;4868;elev;1931;2BN I8I9
98.7..6..5...4......3..2...4...3..9..9.8....6..2.......7.1...6......57.8........1;;5302;GP;H978;2BN H8H9
..3.....9.5....12...91..5...............4..6..4.5....1.3.9....2.1.3.4..58...7....;;6392;elev;3546;2BN A2C2
1.3.....9.5.....2...91..5...............4..6..4.5....1.3.9....2.1.3.4..58...7....;;6619;elev;4077;2BN A2C2
98.7..6..7..6..5......4..3.6.85..9...2.........1......1...........1...96....571..;;9554;GP;cy4;2BN E8F8
..6..9....4..8....9.1.....8....3..7..1...4..92.....5...6...87.4...7...2.....5.3..;;9737;TkP;4534;2BN A2C2
98.7..6..5...4......3..9...4......5..2.1..7....9.3.....6......2...8...76.....18..;;10475;GP;22ky5;2BN H9I9
98.7..6..5...4......3..9...4...5.....7.6..2....9....3..1......2...1...68....7.1..;;10477;GP;22ky5;2BN H9I9
98.7..6..5...9......4..3...3...4.....6.2..8....8..5.9..1.....68..7...1.....1....2;;10526;GP;22ky5;2BN H8I8
98.7..6..7......8...6.5....4....3.....95...7.........2..89..26...72...5.........1;;10630;GP;22ky5;2BN E1F1
98.7..6....5.9..4......3...8....79...4......2..1....5.6...7.3...2.3........6.8..1;;12546;GP;kz0;2BN r8c5
98.7..6..5...4......3..8...4...5.....9.8...2...1..3....7.2....6.....127.......89.;;12678;GP;kz0;2BN r8c9
98.7..6..5...4......3..9...4....3....9.8...7...2.5.....6.1....8.....276.......91.;;12692;GP;kz0;2BN r8c9
98.7..6..5...9......4....5.3.........7.8..2....9..3..4.1...2..6...1...2.....871..;;12854;GP;kz0;2BN r9c8
98.7..6..7...6..9...6.5.....4......3..73...8............95...7...86..35......2..1;;13207;GP;kz0;2BN r1c5
98.7..6..7..9..5....4.3....5..8..2....8....1..........2....7..6.7.6...52.....97..;;13252;GP;kz0;2BN r8c5
98.7..6..7..9..5....4.3....5..8..2....8....1..........2....9..6.9.6...52.....79..;;13253;GP;kz0;2BN r8c5
98.7..6..7.5....4.....5....67.8....4....3..7.......86.45.9...8...2.....9.....1...;;13257;GP;kz0;2BN r8c8
98.7..6..5..........4.8..5.3.9.....4.6.8..2......3.....1...6......1...26....781..;;14808;GP;kz1a;2BN r8c5
98.7..6..7......9...6.5.....4....3....73...8.....2......98...6...85...73....71...;;15057;GP;kz1a;2BN r1c5
98.7..6..7......9...6.5.....4..9...3..73...8............95...7...86..35......2..1;;15058;GP;kz1a;2BN r1c5
98.7..6..7..5..84.....3....8..4..7...2......4.....1...6....5....798....6..8...9..;;15118;GP;kz1a;2BN r8c5
98.7..6..7..65.4.......3.2.6.84..9...5...........6....1...........1...96....741..;;15122;GP;kz1a;2BN r8c5
98.7..6..7..9..5....4.3....5..8..2....8..2.1..........2.......6.9.6...52.....79..;;15126;GP;kz1a;2BN r8c5
98.7..6..7..9..5....4.3....5..8..2....8.9..1..........2.......6.9.6...52.....79..;;15127;GP;kz1a;2BN r8c5
98.7..6....5.9.........4...4...5..3..6.2..8....9..3..6.1......8...1...62.....71..;;16624;GP;Kz1 b;2BN r9c8
98.7..6..5...4......3..9...4....3....7.8..2....8.5..9..6.....27...1...68......1..;;16792;GP;Kz1 b;2BN r9c8
98.7..6..5...4......4..9.5..7.8..3....9.....2.....2....1..3...6...1...38.....71..;;16806;GP;Kz1 b;2BN r9c8
98.7..6..5...9......4..3...3.7.5.....6.2..7....9....4..1......8...1...67.....21..;;16979;GP;Kz1 b;2BN r9c8
98.7..6..5...9......4..3.9.3....5....652..8......4.....1......6...1...87....2.1..;;16980;GP;Kz1 b;2BN r9c8
98.7..6..5...9..4...4..5....6.3..8....9.2............2.1...7.3...7.6.1.....1...8.;;17067;GP;Kz1 b;2BN r8c8
98.7..6..5...9..4...4..5....7.6..8....9.....3....3.....2...1..6...2...81....7.2..;;17068;GP;Kz1 b;2BN r9c8
98.7..6..5...9..4...4..5....7.8..3....9.....2....2.....1...3..6...1...38....7.1..;;17069;GP;Kz1 b;2BN r9c8
98.7..6..7......9...6.5.....4......3..78..26.......5....96...52..85...7......1...;;17207;GP;Kz1 b;2BN r1c5
98.7..6..7......9...6.5.....9........4......3..73...8...96..35...85...7......2..1;;17210;GP;Kz1 b;2BN r1c5
98.7..6..7......9...6.5...7.4......3..75...8......2.....96...5...83...7.....1.3..;;17217;GP;Kz1 b;2BN r1c5
98.7..6..7..85.9....4......5..9..3...2............5.1.3....8.96.7....8.....6....3;;17345;GP;Kz1 b;2BN r7c2
98.7..6..7..85.9....4......6....8.93.7....8.....3....65..9..3...2............5.1.;;17346;GP;Kz1 b;2BN r4c2
98.7..6..7..9..5....4.3....5..8..2....8..2.1..........2.......6.7.6...52.....97..;;17349;GP;Kz1 b;2BN r8c5

these puzzles should require a different XSUSO SLG

I did not work exactly on your specifications, so here are the constraints included in the search

a) base an target in the same band
b) base in a mini row/column 3 or 4 digits
c) target in a pattern
assigned/empty
empty/assigned
d) target has all digits of the base
e) each cell of the target has at least one of the digits of the base

and the constraints on the other direction for regions attached to

xa last cell in the mini row
xb;xc the target

f) for each digit xb|xc has at maximum 2 locations (Xwing authorised)
g) xa is "covered" by xb|xc

This is not exactly your set of constraints, but the final condition "no solution in xa" is satisfied.

The generic condition in that simplified pattern is anyway "no solution in xa"

I think we have now passed 75%

champagne

PS: last but not least, a 10 000 puzzles file is searched is less than 5 seconds
champagne
2017 Supporter

Posts: 6541
Joined: 02 August 2007
Location: France Brittany

### Re: bi bi pattern in hardest puzzles

Puzzle No1 in your list of 42 should have been recognised with (2345)Exocet:r78c8,r1c9,r5c7 => r1c9 <> 1
It has empty cells in different columns as usual at r1c7 & r5c9, so it should have been found.

Your conditions d) and e) are confusing
If call the target cells as the ones where the eliminations will be made, they need only contain one of the base digits (ronk has already found a case when the target doesn't have every base candidate)
Then the companion cells must have no base digits in them.

I find it better to think of the Swordfish (or 3Fish) cells as holding two of the rows or columns and the third one will be discovered when a target cell is solved. I think this is what you describe with f) and g) but am not completely sure.

Congratulations on the speed of the algortihm!

DPB
David P Bird
2010 Supporter

Posts: 1040
Joined: 16 September 2008
Location: Middle England

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