## Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

### Re: Exotic patterns a resume

champagne wrote:
ronk wrote:
champagne wrote:They are in the files "multifish" because a "multifish" has been identified by the solver ...
Posting the multifish "identified by the solver" (for one of the three puzzles) would be helpful.
All three are in the answer to pjb (who clearly has seen them) but in hidden mode, ... May be this is not the right way

So we've come full circle. I saw those sk-loops in your post to pjb, which is why I asked here ... "Are you counting sk-loops as multi-fish too?" You gave no answer then, but your answer now indicates that you do consider sk-loops to be multifish.

But earlier you wrote here ... "I have only one puzzle tagged as having an SK loop and no multi fish; it is number 7765" ... implying that you don't consider sk-loops to be multifish. I find such contradictions confusing, and suspect others would too.
ronk
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### Re: Exotic patterns a resume

ronk wrote:So we've come full circle. I saw those sk-loops in your post to pjb, which is why I asked here ... "Are you counting sk-loops as multi-fish too?" You gave no answer then, but your answer now indicates that you do consider sk-loops to be multifish.

Now I am completely lost
I did not make any reference to any SK loop in my post.

A rank 0 logic is a rank 0 logic : same number of truths and links, that's it.

It can be that the same puzzle has a SK loop, and this was precisely the puzzles analysed by pjb, but this does not change the fact that a rank 0 logic is a rank 0 logic.
champagne
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### Re: Exotic patterns a resume

champagne wrote:I did not make any reference to any SK loop in my post.

Since the logic sets you described to pjb are actually those of sk-loops, I don't see how your omission of the term is relevant.
ronk
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### Re: Exotic patterns a resume

RonK,

I'm as lost about your point as champagne. It appears to me that you are confusing the multi-fish with the sk-loop that's also present. Consider champagne's first puzzle reply above:

Code: Select all
`..9.....6.1...8.3.2.....7.........1.....73..5.4.8.5.....6.....9.5.3...4.7.....2..;9698;TkP;395216 Truths = {2679R28 2679C28 }16 Links  = {2b37 6b19 7b19 9b37 + 2n45 4n2 5n28 6n8 8n56 }elims 45r2c4 45r2c5 38r4c2 8r5c2 8r5c8 18r8c5 1r8c6      11 elims done`

The cover sets (29b37 67b19) contain eight truths. The cover cells (2n45 45n2 56n8 8n56) contain the remaining eight truths. This is a (mutant) multi-fish pattern as I understand it from previous examples. The only distinction is that the truth sets are a mix of rows and columns, and boxes are present as cover sets.

There isn't any pairing of candidate values as in an sk-loop. Specifically, there isn't any reference to the 4s and 8s in [b3] used by the sk-loop.

If I understand champagne correctly, he says that he can't currently handle cover sets with boxes when the base sets are only rows or only columns. That's not the case here.
daj95376
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### Re: Exotic patterns a resume

In earlier posts, perhaps in this thread or perhaps in others, champagne has described two type of 'multi-fish' pattern his programme looks for:
a) with parallel truth sets either in the rows or the columns
b) with truth sets in 2 rows, & 2 columns that intersect in 4 boxes.
I therefore have no problem understanding him, although I would prefer it if two different terms were used. I should hasten to add that not all elimination patterns picked up by b) are recognisable SK loops.

As I see it, these patterns are rank 0 and essentially identify Multi-Sector Locked Sets.
In this row/column multi-fish the MSLS is the 20 cells marked # which contain 20 candidates confined to different houses
....56.8...71.....6.....4.......85...3......29...4..6..1.7.......2.....38...9..5.;55;elev;30;G1
Code: Select all
`     v                            v       v          v      v  *----------------------*-----------------------*-----------------------*  |  123-4 249    1349   | 2349   5       6      |  1237-9  8      179   |  >| #2345  4589-2 7      | 1     #238    #2349   | #2369   #239    569   |< 23  |  6     2589   13589  | 2389   237-8   237-9  |  4       123-9  159   |   *----------------------*-----------------------*-----------------------*  |  127-4 2467   146    | 2369   1237-6  8      |  5       137-49 1479  |  >| #1457  3      4568-1 | 569   #167    #1579   | #1789   #1479   2     |< 17  |  9     2578   158    | 235    4       1237-5 |  137-8   6      178   |   *----------------------*-----------------------*-----------------------* >| #345   1      4569-3 | 7     #2368   #2345   | #2689   #249    4689  |< 23 >| #457   4569-7 2      | 4568  #168    #145    | #16789  #1479   3     |< 17  |  8     467    346    | 2346   9       123-4  |  127-6   5      1467  |   *----------------------*-----------------------*-----------------------*     ^                            ^        ^         ^     ^     45                           68       459      689    49`

Multi-sector Locked Set:(23)r2,(17)r5,(23)r7,(17)r8,(45)c1,(68)c5,(459)c6,(689)c7,(49)c8
17 Eliminations in 16 cells

In pjb's three examples the MSLSs are the 16 cells, r28c1379,c28r1379 which contain 16 candidates confined to different houses.
For the 3rd example: Multi-sector Locked Set:(59)r2,(27)r8,(47)c2,(25)c8,(18)b1,(36)b3,(36)b7,(18)b9

Of course, truth and link sets aren't the only way to find MSLSs

I assume that with Xsudo, setting these cells as cell truth sets, would then automatically produce the link sets to accompany them – although the notations would be longer than using the MSLSs. The question then arises what rank zero patterns should be classed as multi-fish? Having only a casual acquaintance with truth and link sets I can't say.

pjb you may find that in addition to allowing an 'occasional' box link set, if you also allowed an 'occasional' box truth set, your problem might be solved.
David P Bird
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### Re: Exotic patterns a resume

daj95376 wrote:I'm as lost about your point as champagne. It appears to me that you are confusing the multi-fish with the sk-loop that's also present. Consider champagne's first puzzle reply above:

Code: Select all
`..9.....6.1...8.3.2.....7.........1.....73..5.4.8.5.....6.....9.5.3...4.7.....2..;9698;TkP;395216 Truths = {2679R28 2679C28 }16 Links  = {2b37 6b19 7b19 9b37 + 2n45 4n2 5n28 6n8 8n56 }`

The Xsudo images for this (on left) and for Easter Monster (on right), with the hidden-pair-loop as first identified by Steve Kurzhals, are shown below. After a bit of morphing, these could be made to look very similar. Even as they are, I don't see how anyone could validly claim the logic on the left to be structurally different than that for Easter Monster.

___ _ (Clickable images)

logic sets: Show
Code: Select all
`9698;TkP;3952 009000006010008030200000700000000010000073005040805000006000009050300040700000200     16 Truths = {2679R28 2679C28}     16 Links = {45n2 2n4 28n5 8n6 56n8 29b37 67b19}     11 Eliminations --> r2c45<>4, r2c45<>5, r5c28<>8, r8c56<>1, r4c2<>38, r8c5<>8  Easter Monster100000002090400050006000700050903000000070000000850040700000600030009080002000001     16 Truths = {1267R28 1267C28}     16 Links = {56n2 8n4 28n5 2n6 45n8 16b37 27b19}     13 Eliminations --> r2c56<>8, r5c2<>48, r5c8<>39, r1c3<>7, r2c5<>3, r3c1<>2, r7c3<>1,      r8c5<>4, r8c4<>5, r9c1<>6 `

[edit: Change to clickable thumbnails and add hidden logic sets]
Last edited by ronk on Mon Sep 03, 2012 2:04 am, edited 1 time in total.
ronk
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### Re: Exotic patterns a resume

I think that the fact that nearly almost puzzles having a SK loop have also some multi fish patterns is confusing.

The SK loop logic has a corresponding rank 0 logic. I took the puzzle 7765 where my solver finds no multi fish to show it.

The rank 0 logic is based on 16 cells made of the SK loop itself.
The links are the row/column/box sest corresponding to the common digits

here is the XSUDO corresponding result
Code: Select all
`+---------------------+----------------------+-------------------------+| 9       8      7    | 1256-4  1345   2346  | 1256     135     236    || 6       5      123  | 9       1378   2378  | 4        1378    2378   || 123     123    4    | 1256-8  13578  23678 | 1256-79  135789  236789 |+---------------------+----------------------+-------------------------+| 125-7   4      1256 | 3       (579)  (279) | 8        (179)   (679)  || 13578   1379   1358 | (458)   6      4789  | (179)    2       34     || 2378    23679  2368 | (248)   4789   1     | (679)    34      5      |+---------------------+----------------------+-------------------------+| 125-48  126    9    | 7       (148)  (468) | 3        (458)   (248)  || 134578  137    1358 | (148)   2      39    | (579)    6       4789   || 23478   2367   2368 | (468)   39     5     | (279)    4789    1      |+---------------------+----------------------+-------------------------+     16 Truths = {5689N4 47N5 47N6 5689N7 47N8 47N9}     16 Links = {79r4 48r7 48c4 79c7 1b68 2b59 5b59 6b68}     7 Eliminations --> r3c7<>79, r7c1<>48, r1c4<>4, r3c4<>8, r4c1<>7,      `

This is the diagram that we are sure to find in any puzzle having the SK loop
Following daj95376 remark, is uses (and must use) all the digits contained in the SK loop

And to answer to David, I surely would not call it a multi fish. I have no clear definition of the multi fish rank 0 logic, but the constraint to start the search of the rank 0 logic in my solver is that the corresponding multi floors sub grid must have a solving potential.

As we can see here and as ronk already showed it, many other kinds of rank 0 logic can be found.
champagne
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### Re: Exotic patterns a resume

Some statistics out of the last update of my file of "potential hardest"

in that file

2013 puzzles have an SK loop
2012 with one or more multi fish patterns
1695 with a row based multi fish
1693 with a column based multi fish
1931 with a mix 2 rows 2 columns multi fish

The mix (2 rows 2 columns) multi fish pattern has been found in 3681 puzzles.
I guess but this should be analysed that most of these puzzles not having the SK loop have a "quasi" SK loop.

Just for history, it is for sure one of the diagram proposed by Allan Barker to explain eliminations in the SK loop that pushed me to study the Mix mode
champagne
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### Re: Exotic patterns a resume

champagne, it seems to me that the essence of a multi-fish pattern is that the 9 digits are partitioned into two sets which are maintained throughout a search for a MSLS. The search method is of secondary importance, and whether it uses hidden pair loops, strong & weak inference sets, templates, or truth balances shouldn't matter. I therefore feel that to tie the definition of a multi-fish pattern to a search method is wrong – but we've been here before.

Using this concept it then follows that SK loops are simply a subset the general multi-fish category that are much easier to find (at least for a manual solver). Looking for them first, before resorting to a more complex algorithm to find the others is therefore quite a sensible thing to do. From your posts it appears your program runs the more extensive algorithm first that finds some SK loops but not others (whereas truth balancing will find all of them). Those it finds you report as multi-fish and those it doesn't you report as SK loops which leads to confusion.

If this general approach is acceptable, on my side the idea of a shark pattern can be dropped and what I have described would simply be a truth balancing method for finding multi-fish.
David P Bird
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### Re: Exotic patterns a resume

David,

I can not answer step by step to your post, just some key points.

SK loop

This is in my head a very very precise definition (see first post). My solver finds all SK loops using a specific process, so I have difficulties to follow you when you state that my solver does not find some of them.

MSLS

Unhappily, I never worked on that concept, so I can not follow your explanations. Have you a link to a thread giving the basic knowledge of that logic.

Pre processing looking for the potential of some floors :

this is not exactly a research process, but an accelerator. What is for sure is that if a multi floors set has no potential, nobody will find an active rank 0 logic using that set of floors. My search on patterns uses again the results of the potential analysis to stop as soon as possible hopeless "truths" assumptions
champagne
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### Re: Exotic patterns a resume

Up until now, I can understand that multi-fishes are studied only from a theoretical POV. As a manual solver, except in the simplest cases, I only look for loops of cells giving identical or equivalent eliminations.

1. They have a simpler structure : Naked Tuples, N-Fish of cells and their generalizations to "ALS-XZ Rule, N Link + cells".
2. The cover is simpler : lines+box is simpler than line+box+cell, IMHO.
3. They are "easier" to find : for N=2, this is evident; otherwise, the basic starting point is the analysis of the structure of a set of NxN cells at the intersection of N rows and N columns and, eventually, at the intersection of 2 rows and 2 columns with 4 boxes.
4. And, last but not least, the eliminations are easy to understand : it is almost straightforward to show that the set of cells covered in the same "row, column or box" contains the same naked tuple in each of its solution.
JC Van Hay

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### Re: Exotic patterns a resume

champagne wrote:SK loop

This is in my head a very very precise definition (see first post). My solver finds all SK loops using a specific process, so I have difficulties to follow you when you state that my solver does not find some of them.

The problem is that your definition has only one of the three equivalent forms of the sk-loop. Note the obvious loop in all three illustrations below.

That the exclusions for the three are identical is not coincidence, it's because they are equivalent. And why is this? Hidden sets in two rows and two columns have complementary naked sets in those rows and columns. (Here "hidden sets" is shorthand for "hidden sets", "almost hidden sets", "almost almost hidden sets", etc. Ditto for naked sets.) For the sk-loop, naked sets in two rows and two columns can be regrouped into naked sets in four boxes, which have complementary hidden sets in those four boxes. It makes no sense to me that one of these forms should be called an sk-loop, but not the other two. Besides, excluding the hidden-pair-loop form first posted by Steven Kurzhals, the SK of the SK-loop term, is an affront to him IMO.

___ ___ ___ (Clickable images)

Logic sets for the three forms: Show
Code: Select all
`..9.....6.1...8.3.2.....7.........1.....73..5.4.8.5.....6.....9.5.3...4.7.....2..;9698;TkP;3952Hidden sets in 2 rows & 2 boxes (hidden-pair-loop)     16 Truths = {2679R28 2679C28}     16 Links = {45n2 2n4 28n5 8n6 56n8 29b37 67b19}Cell sets in 2 rows & 2 boxes (or cell sets in 4 boxes)     16 Truths = {28N1 1379N2 28N3 28N7 1379N8 28N9}     16 Links = {45r2 18r8 3c2 5c8 8c28 2b37 6b19 7b19 9b37}Hidden sets in 4 boxes     16 Truths = {1B379 3B179 4B137 5B139 8B1379}     16 Links = {45r2 18r8 3c2 5c8 8c28 17n1 39n3 17n7 39n9}Exclusions for each of the three above:     11 Eliminations --> r2c45<>4, r2c45<>5, r5c28<>8, r8c56<>1, r4c2<>38, r8c5<>8`
ronk
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### Re: Exotic patterns a resume

ronk wrote:The problem is that your definition has only one of the three equivalent forms of the sk-loop. Note the obvious loop in all three illustrations below.

I would be highly interested to see the same diagrams applied to puzzle 7765, it could be one way to get out of sterile discussions

BTW, I think I never betrayed Steven Kurzhals. He first used more cells, but all where aahs and the kind of loop he showed is exactly in line with the shortest presentation I make. Unhappily, I could not find the post where he first posted that loop to put it in the references

EDIT I looked at the first set of diagrams, at least 2 of them would not have been studied by my solver (to many floors), But let's see how they are in the puzzle 7765
Last edited by champagne on Sun Sep 02, 2012 2:03 pm, edited 1 time in total.
champagne
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### Re: Exotic patterns a resume

champagne wrote:I would be highly interested to see the same diagrams applied to puzzle 7765

As I have recorded them in my files, here they are :

Loops in 7765 giving the same eliminations ...

Base : 16 Truths = {1256R4 1256R7 1256C4 1256C7}
OR
Base : 16 Truths = {5689N4 47N5 47N6 5689N7 47N8 47N9}
OR
Base : 12 Truths = {4789B5 79B6 48B8 4789B9}
JC Van Hay

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### Re: Exotic patterns a resume

JC Van Hay wrote:
champagne wrote:I would be highly interested to see the same diagrams applied to puzzle 7765

As I have recorded them in my files, here they are :

Loops in 7765 giving the same eliminations ...

Base : 16 Truths = {1256R4 1256R7 1256C4 1256C7}
OR
Base : 16 Truths = {5689N4 47N5 47N6 5689N7 47N8 47N9}
OR
Base : 12 Truths = {4789B5 79B6 48B8 4789B9}

thank you very much

do you have the cover for the first one. I want to see why my solver did not detect it. As I said int the former edit, my solver does not look for the 2 other forms

EDIT I think I have the cover, which means there is a bug in my code for that pattern.
It means also that probably, in the statistics, all puzzles having a sk loop should have the mix (2 rows 2 columns) pattern which is not true by far to-day
Last edited by champagne on Sun Sep 02, 2012 2:30 pm, edited 1 time in total.
champagne
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