## The Sudoku-X FISH appendix

Advanced methods and approaches for solving Sudoku puzzles
Each set of weak link squares is a constraint

2 diagonals * 2 groups of weakly linked squares that is a mutant 2-fish ......

there is no intersection in the cover sectors (which is fine)
there is an intersection in the base sectors at r5c5 (the endofin)

So it you can name it a skewed x-wing (skewed being a special case of mutant as described above) or as I would like it (just drop the term completely) & keep it as a mutant x-wing

On the Sudopedia pages .... are you planning to post the permutaions allowed for the 3 groups of weakly linked boxes ?

Example:
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tarek

tarek

Posts: 2807
Joined: 05 January 2006

Pyrrhon wrote:A further overview about Fishs in Sudoku-X is the Skewed Fish article and in the articles linked there.

Based on just the candidates in the diagonals and constraint set (aka fish) theory, I've "replicated" your Finned Double Crossover figures below.
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*  *  X |  *  *  * |  X ** **        *  *  X |  *  *  * |  X ** **
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Fig 1: dd\rr + 2 fin (cells)         Fig 2: dd\rr + 1 fin

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*  *  X |  *  *  * |  / ** **        *  *  X |  *  *  * |  X  *  *
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Fig 3: dd\rr + 1 fin (sashimi)       Fig 4: dd\rr with no fin

Relative to a constraint set POV, elimination discrepancies are:
• your (unnumbered) Figures 2 & 3 do not show r2c9<>X
• your Fig 4 does not show all the eliminations in r2 and r7
Naming discrepancies are:
• Fig 4 is an unfinned fish, not your sashimi
• Fig 3 is the only sashimi, not your Figs 2, 3, and 4
• only in Fig 3 do our fin cell designations match exactly
Disclaimer: I've only ever tried to solve a Sudoku-X puzzle once, so I may be way off base.
ronk
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@tarek
No I didn't plan this. From my point of view it should be next clarified whether for example this pictures

shows a Skewed X-Wing or not. This is a question of definition and an example that is different with the both definitions I thing Ruud and Unkx80 use. It is important for questions like is Skewed Turbot Fish the same as Triangular Connection or not ...

BTW: I have added some skewed xy-Wing now.
Last edited by Pyrrhon on Mon Jan 14, 2008 12:06 pm, edited 1 time in total.
Pyrrhon

Posts: 240
Joined: 26 April 2006

@ronk

Only the yellow cells allow deletion by the shown (Finned/Sashimi) Double Crossover. In the green cells in the pictures you can delete by other techniques. In case of R2C9 by pointing pairs on the Diagonal D\, in the last picture in R27 by the Skewed X-Wing with both diagonals.

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Fig. 0

But remember Double Crossover are Turbot Fishs and this is not a kind of fish (but a fishy cycle). So far I know there is no Finned Turbot Fish in vanilla sudoku.

The fish diagrams of the fishs we consider would be:

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Fig. 1

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Fig. 2

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Fig. 3

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Fig. 4

In fish diagrams the is no mean to differentiate between C8C8 and C7C7 (Fig. 3)/C9C9 (Fig. 4) in the last two figures.

In all the cases the name is considered what we have in the first figure. If you take not R8C8 as the fourth cell and R7C7/R9C9 as the possible fins you get other names. So all the sashimi examples could also be considered as Finned Skewed X-Wing (the example with two fins with R7C7 or R9C9 as fourth cell) or as Double Crossover (the examples with one fin and the fin considered as the fourth cell).
Pyrrhon

Posts: 240
Joined: 26 April 2006

Pyrrhon, you're using the fishy terms "finned" and "sashimi." Fish are based on constraint sets, so IMO there should be a solid connection between your illustrations and constraint set theory.

Let's consider only your first illustration:
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Fig 1A: dd\?? + fin ??

AFAIK the following are the only two interpretations that are consistent with constraint set theory:
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*  *  X |  *  *  * |  X ** **        .  .  F |  .  .  . |  X ** **
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/  .  . |  .  .  . |  .  .  F        /  .  . |  .  .  . |  *  *  X
Fig 1B: d1d2\r2r7 + fin b9           Fig 1C: d1d2\r2b9 + fin r7

In Fig 1B, e.g., all candidates in the base set (units d1 and d2) are "covered" by the cover set (units r2 and r7) and fin unit b9. Valid eliminations are those that are covered twice, in this case r7c89.

What are the cover units and fin unit(s) that explain your Fig 1A? (Note: By definition, the fin cells are the candidates of the base set not covered by the cover set.)

P.S. I see your post expanded significantly while I was preparing mine.
ronk
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I've moved in the Sudopedia the Finned Skewed Double Crossover article to Finned Skewed X-Wing and I've changed something. I hope this meets the results of our discussion.

Pyrrhon
Pyrrhon

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Joined: 26 April 2006

Pyrrhon wrote:I've moved in the Sudopedia the Finned Skewed Double Crossover article to Finned Skewed X-Wing and I've changed something. I hope this meets the results of our discussion.

Much much better, except I think you're still missing an elimination at r2c9 in Example 2. [edit: link added]
Last edited by ronk on Tue Jan 15, 2008 9:07 am, edited 1 time in total.
ronk
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The deletion at R2C9 follows from another Finned X-Wing (with the same defining and secondary constraints, but with the fin constraint C9, and not B9). I have added this Finned Skewed X-Wing.

In general in a finned fish we can delete in the cells that

(1) are in the secondary constraints
(2) are in the fin constraint and
(3) are not in the defining constraints.

Pyrrhon
Pyrrhon

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Pyrrhon wrote:(1) are in the secondary constraints
(2) are in the fin constraint and
(3) are not in the defining constraints.

Thre are some elements about intersection within the Base set or within the Cover set that need to be taken into account too.

tarek

tarek

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Joined: 05 January 2006

Of couse. I didn't wrote what a base set, a cover set and a fin set is. I only wrote how to find the cells where you can delete, given these sets.

Pyrrhon
Pyrrhon

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Pyrrhon wrote:The deletion at R2C9 follows from another Finned X-Wing (with the same defining and secondary constraints, but with the fin constraint C9, and not B9).

A valid elimination of a finned fish is a valid elimination of the unfinned fish which also "sees" all the fin cells. Therefore valid eliminations of a finned fish with a single fin cell are all valid eliminations of the unfinned fish which the single fin cell can see.

IOW in this case of a single fin cell, your interpretation of "[edit: fin] constraint" is too strict.
Last edited by ronk on Tue Jan 15, 2008 11:13 am, edited 1 time in total.
ronk
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I don't see what you mean with my strict view of secondary constraints. Secondary constaints are R2 and R7.

In case of vanilla sudoku we are on the same line because we can conclude from the fins, defining and secondary constraints to a single house. But as the example shows in variants like Sudoku-X there may be different houses for the same defining and secondary constraints and the same fins. If we follow your proposal we would have to change the definition in the sudopedia (fish article)

A fin is a candidate or group of candidates in the defining set, which does not belong to the secondary set. It is a surplus to the underlying fish pattern. The fin must lie within a single house which is neither part of the defining set nor the secondary set. There must be at least one surplus candidate from the secondary set inside this house. For each finned version of a fish pattern, we can only eliminate the surplus candidates in the house that hosts the fin.

As said in our example we have the choice between two houses B9 or C9.

Contrary to the definition in the sudopedia the original Filet-O-Fish Rule by Myth Jellies is on your side:

If you can form a swordfish/x-wing pattern by not considering candidates in cells (1..n), then you can keep any eliminations from that swordfish/x-wing pattern that share a group with all cells (1..n). The cells (1..n) have been called the fin.

So what is not different in vanilla sudoku between these definitions is different here. And the rest is a question of which of both definition is taken.

BTW: Your definition would be different from Myth Jellies one in other sudoku variants.
Pyrrhon

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Pyrrhon wrote:I don't see what you mean with my strict view of secondary constraints. Secondary constaints are R2 and R7.

Sorry, I meant to write "fin constraint."

Do what you want with the r2c9 elimination. Because of the domino effect, I don't want to get involved in other sudopedia definitions.
ronk
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the UFG provides very straightforward rules that blankets everything:

1. Fin cells: Base set - Cover Set
2. Target Elimination Cells: Cover Set - Base set
3. if Target elimination cells = 0 then forget about the whole thing
4. if Fin cells = 0 then valid elimination cells = Target elimination cells
5. otherwise valid elimination cells: Target elimination cells that ALL fin cells SEE

tarek

tarek

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