Looking for a rule: finned x wing

Advanced methods and approaches for solving Sudoku puzzles
Havard wrote:I guess the thing about this that differs most from "public opinion" is the definiton I use for a "fin". My definition is: After you have covered a fish with N sectors with N other sectors, you are left with some candidates, these are concidered "fins" The rule that will always apply to fins are then that: any candidates that are part of any of the covering sectors, but not part of the basis sectors, that can see all the fins, can be eliminated This POV will then be completly in line with what was concidered "fins" in the early fishes, but will IMO be more flexible to deal with the more complex sea-creatures that we are facing.

Intersting, this should provide some thoughts for discussion, but just to make things clearer to me, could you show The N sectors & the N covering sectors for this fish....
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`*-----------------------------------------------------------------* | 5      9      68    | 1     *48     7     | 346   *348    2     | | 3      2      68    | 568    9      456   | 46     1      7     | | 4      1      7     | 268    3      26    | 5      9      68    | |---------------------+---------------------+---------------------| | 2      367    19    | 35689  58     13569 | 367    3578   4     | | 16    #346    5     | 2368   7      12346 | 9      38     68    | | 8     *3467  -49    | 3569  *45     34569 | 2      357    1     | |---------------------+---------------------+---------------------| | 69    *46     2     | 379    1      39    | 8     *47     5     | | 19     8      14    | 579    6      59    | 47     2      3     | | 7      5      3     | 4      2      8     | 1      6      9     | *-----------------------------------------------------------------* Eliminating 4 From r6c3 (Finned Swordfish in Columns 258 with 1 fin in Box 4)`

tarek

tarek

Posts: 2650
Joined: 05 January 2006

Michael Mephem's 4th extreme puzzle has an interesting big fish...
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` *-----------* |..5|3..|6..| |.2.|.7.|.4.| |...|.1.|..8| |---+---+---| |3..|4..|..1| |.6.|251|.8.| |2..|..8|..4| |---+---+---| |4..|.2.|...| |.7.|.4.|.9.| |..1|..3|4..| *-----------*`

Basic methods will take you here...
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` *-----------------------------------------------------------------------------* | 179     489     5       | 3       89      24      | 6       127     279     | | 1689    2       3       | 5689    7       569     | 159     4       59      | | 679     49      679     | 569     1       24      | 2579    3       8       | |-------------------------+-------------------------+-------------------------| | 3       5       8       | 4       69      679     | 279     267     1       | | 79      6       4       | 2       5       1       | 379     8       379     | | 2       1       79      | 679     3       8       | 579     567     4       | |-------------------------+-------------------------+-------------------------| | 4       3       69      | 156789  2       5679    | 1578    157     567     | | 568     7       2       | 1568    4       56      | 1358    9       356     | | 569     89      1       | 5679    689     3       | 4       257     2567    | *-----------------------------------------------------------------------------*`

Filtering on the sevens we have a swordfish with two distinct fins...
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` +-----------+-----------+-----------+ |*7   .   . | .   .   . | .  *7  *7 | | .   .   . | .   7   . | .   .   . | | 7   .   7 | .   .   . | 7   .   . | +-----------+-----------+-----------+ | .   .   . | .   .  A7 | 7  -7   . | |*7   .   . | .   .   . |#7  *.  *7 | | .   .   7 |a7   .   . | 7   7   . | +-----------+-----------+-----------+ | .   .   . | 7   .  a7 | 7   7   7 | | .   7   . | .   .   . | .   .   . | |*.   .   . |#7   .   . | .  *7  *7 | +-----------+-----------+-----------+`

Either the r159c189 swordfish is true, or the fin in r5c7 is true, or the fin in r9c4 is true, which with a little weak then strong link extension would imply A (r4c6) contains a 7. In all three possible cases, seven can be removed from r4c8. The resulting 26-cell was key to my eventual solution path.
Myth Jellies

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Joined: 19 September 2005

tarek wrote:
Havard wrote:I guess the thing about this that differs most from "public opinion" is the definiton I use for a "fin". My definition is: After you have covered a fish with N sectors with N other sectors, you are left with some candidates, these are concidered "fins" The rule that will always apply to fins are then that: any candidates that are part of any of the covering sectors, but not part of the basis sectors, that can see all the fins, can be eliminated This POV will then be completly in line with what was concidered "fins" in the early fishes, but will IMO be more flexible to deal with the more complex sea-creatures that we are facing.

Intersting, this should provide some thoughts for discussion, but just to make things clearer to me, could you show The N sectors & the N covering sectors for this fish....
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`*-----------------------------------------------------------------* | 5      9      68    | 1     *48     7     | 346   *348    2     | | 3      2      68    | 568    9      456   | 46     1      7     | | 4      1      7     | 268    3      26    | 5      9      68    | |---------------------+---------------------+---------------------| | 2      367    19    | 35689  58     13569 | 367    3578   4     | | 16    #346    5     | 2368   7      12346 | 9      38     68    | | 8     *3467  -49    | 3569  *45     34569 | 2      357    1     | |---------------------+---------------------+---------------------| | 69    *46     2     | 379    1      39    | 8     *47     5     | | 19     8      14    | 579    6      59    | 47     2      3     | | 7      5      3     | 4      2      8     | 1      6      9     | *-----------------------------------------------------------------* Eliminating 4 From r6c3 (Finned Swordfish in Columns 258 with 1 fin in Box 4)`

tarek

sure thing! The basis sectors are columns 2, 5 and 8, and the covering sectors are rows 1, 6 and 7. That leaves one candidate("the fin") in r5c2, that can see a candidate(r6c3) in one of our covering sectors (row 6) and hence that candidate can be eliminated.

Note that you could also make the argument that the covering sectors are row 1, row 7 and BOX 4. That would make the fin in r6c5, and you would use that argument that the fin can see some of the candidates in Box 4 (r6c3) and that can then be eliminated.

So as you can see, what candidates that are concidered "fins" also holds true with this POV, but it is IMO better suited to deal with big complex fishes. (like frankenfish only having one fin)

Myth: Your example is a perfect one for the almost/kraken fish discussion, linking one "extra" candidates of the fish to one of the fishes potential eliminations.

Havard
Havard

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ronk,
I guess you can do, but in the Filet-O-Fish thread we have always referred to each fin cell as a fin, so we can have up to 4 fins in a skinny Finned fish

Havard,

Thanx & very interesting indeed.....

The N sector * N sector fish would be a nice catch..........

Now for the sake of simplicty & providing an link between what we have already been doing & the more difficult fish....A step-wise difficulty categorization should be applied....... something along these lines for example....
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`1. Classic fish (N rows * N columns or vv.) - no fins(Smallest Counterpart)2. Finned  fish (true N rows * N columns or vv.) - with fins in 1 sector (Smallest Counterpart) No simpler Classic fish is present3. Sashimi fish (virtual N rows * N columns or vv.) - with fins in 1 sector (Smallest Counterpart) No simpler alternative out of 1-2 is present4. Headless fish (virtual N rows * N columns or vv.) - with fins in 1 sector  & a cover sector has no true vertices) (Smallest Counterpart) No simpler alternative out of 1-3 is present5. ? Franken fish (Finned/Sashimi/headless) - with fins in >1 sector (Smallest Counterpart) No simpler alternative out of 1-4 is present6. ? Kraken fish (true/virtual N Sector * N Sector or vv.) - (Smallest Counterpart) No simpler alternative out of 1-5 is presentFin(s) have to be in the base Sectors, Elimination cells have to be in the Cover Sectors`

so along those preliminary lines the following fish posted by Myth is a franken fish
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`*-----------------------------------------------------------------------------* |*179     489     5       | 3       89      24      | 6      *127    *279     | | 1689    2       3       | 5689    7       569     | 159     4       59      | | 679     49      679     | 569     1       24      | 2579    3       8       | |-------------------------+-------------------------+-------------------------| | 3       5       8       | 4       69      679     | 279    -267     1       | |*79      6       4       | 2       5       1       |#379    *8      *379     | | 2       1       79      | 679     3       8       | 579     567     4       | |-------------------------+-------------------------+-------------------------| | 4       3       69      | 156789  2       5679    | 1578    157     567     | | 568     7       2       | 1568    4       56      | 1358    9       356     | |*569     89      1       |#5679    689     3       | 4      *257    *2567    | *-----------------------------------------------------------------------------*Eliminating 7 from r4c8 (franken swordfish in r159 & c189 with fins r5c7,r9c4)`

& this Bizarre fish as you described Havard although lit looks like a kraken swordfish, it has the simpler Finned Swordfish counterpart & therefore should be left as a Finned swordfish
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`*-----------------------------------------------------------------* | 5     *9      68    | 1     *48     7     | 346   *348    2     | | 3      2      68    | 568    9      456   | 46     1      7     | | 4      1      7     | 268    3      26    | 5      9      68    | |---------------------+---------------------+---------------------| | 2     *367    19    | 35689  58     13569 | 367    3578   4     | | 16    *346    5     | 2368   7      12346 | 9      38     68    | | 8     *3467  -49    | 3569  #45     34569 | 2      357    1     | |---------------------+---------------------+---------------------| | 69    *46     2     | 379   *1      39    | 8     *47     5     | | 19     8      14    | 579    6      59    | 47     2      3     | | 7      5      3     | 4      2      8     | 1      6      9     | *-----------------------------------------------------------------* Eliminating 4 From r6c3 (Kraken Swordfish in c258 & r17,b4 with fin r6c5)`

I hope this is sounds logical, but I would really like to see these terms unified here so that we can Reproduce the same terms for the same creature.

How does that sound everybody ????

tarek

tarek

Posts: 2650
Joined: 05 January 2006

A frankenfish is capable of it's own eliminations. The fish Myth posted is an ALMOST fish in my eyes. It can't have any eliminations on its own, but need help from something external. (in this case the strong link in box 5: [r6c4]=7=[r4c6]). In this case it is an ALMOST finned Swordfish, using the argument that if it had not been for the "other" fin in r9c4 it would have been a finned swordfish.

I really think that there should be made a separation about fish that creates their own elimination, and almost-fish that needs a bit of help. I think Mike Barker gave the "kraken" name to such "almost-fish", and should then only be used when the fish is not capable of eating it's food without a bit of help.

Now the frankenfish definition is a fish that needs at least two boxes as covering sectors, and have a fin, and the Myth Fish does not need any boxes as covering sectors, so even if it had not been an almost-fish, I still would not call it a frankenfish, rather just a finned swordfish.

The "bizarre" fish I described was just showing another POV that arises from my way of thinking about fish. I absolutly agree that it should be kept as a Finned Swordfish, and my general inclination is to use lines (row/columns) as covering sectors before using boxes. I was merly showing that you CAN use a box, and still have the general approach hold true(even though then what becomes the "fin" is not in line with the general idea of one).

So summed up I would say:

If you can cover your 3-column-fish with 3 rows you have a classic swordfish.

If you can cover your 3-column-fish with 3 rows and are left with one or more candidates that all can see another candidate(s) in one of the 3 rows (not part of the fish), you have a classic finned-swordfish.

If you can cover your 3-column fish with 2 rows and one box, you have a headless swordfish. (not a neccessary term IMO)

If you can cover your 3-column-fish with 1 row and two boxes, and are left with one or more candidates that all can see another candidate(s) in one of the 1 row or two boxes (not part of the fish), you have a classic frankenswordfish.

Now if I could have it my way , I would want that using boxes as covering sectors becomes a "natural" procedure, and then you would only ever have finned and non-finned fish. Maybe the "franken" term could be used to describe that boxes has been used as covering sectors, but what I would much prefer would be to be told (with any fish) what sectors went into making it, and what sectors was used to cover it, and then the description of any additional fins. I know ronk and Mike already use descriptions like this.
So you would have (for your fish before)

Swordfish (c258)
cover: (r167)
fins: [r23c2]

or the bizarro option:
Swordfish (c258)
cover: (r17b4)
fin: [r6c5]

My 2c anyway!

Havard
Havard

Posts: 377
Joined: 25 December 2005

tarek wrote:... in the Filet-O-Fish thread we have always referred to each fin cell as a fin, so we can have up to 4 fins in a skinny Finned fish

That was my viewpoint also until someone pointed out that ...
Myth Jellies wrote:Filet-O-Fish Rule

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.

Note that "cells" is plural and "fin" is singular. Myth Jellies, is a revision or clarification of the rule in order?

tarek wrote:so along those preliminary lines the following fish posted by Myth is a franken fish
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`*--------------------------------------------------------------------* |*179    489    5      | 3      89     24     | 6     *127   *279    | | 1689   2      3      | 5689   7      569    | 159    4      59     | | 679    49     679    | 569    1      24     | 2579   3      8      | |----------------------+----------------------+----------------------| | 3      5      8      | 4      69     679    | 279   -267    1      | |*79     6      4      | 2      5      1      |#379   *8     *379    | | 2      1      79     | 679    3      8      | 579    567    4      | |----------------------+----------------------+----------------------| | 4      3      69     | 156789 2      5679   | 1578   157    567    | | 568    7      2      | 1568   4      56     | 1358   9      356    | |*569    89     1      |#5679   689    3      | 4     *257   *2567   | *--------------------------------------------------------------------* Eliminating 7 from r4c8 (franken swordfish in r159 & c189 with fins r5c7,r9c4)`

On the "Big Fish" thread, MJ called that an "almost finned swordfish" ... a name with which I agree. I don't think "franken swordfish" is correct ... because of the indirect exclusion using a chain, even though a short one. A "Kraken fish" maybe, but not a "franken fish." [edit: I see Havard already posted the same POV.]

Sorry, I don't have specific suggestions for your definitions.

[edits: minor rephrasing]
Last edited by ronk on Sun Oct 22, 2006 11:22 am, edited 2 times in total.
ronk
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Location: Southeastern USA

Wow, you guys are making my head spin! Too bad confuseder is not a word because that's what I'm getting.

I'd like to go back to Myth Jelly's original reply to the question. The Scanraid solver sez this pattern constitutes a "finned x wing."

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` | 6     19    2     | 3     19    5     | 4     8     7     |  | 578   19    4     | 28    67    1679  | 3     159   1259  |  | 578   3     57    | 28    4     179   | 19    6     1259  |  |-------------------+-------------------+-------------------|  | 3    *678   568   |*17    2     179   | 1679  159   4     |  | 57    4     1     | 6     379   8     | 2     3579  359   |  | 9     2     67    | 4     5     137   | 167   137   8     |  |-------------------+-------------------+-------------------|  | 2    *5   -367    |*17    8     1367  | 179   4     139   |  | 4    #67   9      | 5     1367  2     | 8     137   13    |  | 1    #78   378    | 9     37    4     | 5     2     6     |  *-----------------------------------------------------------*`

Myth wrote:
The starred cells represent a potential x-wing which would eliminate all the sevens in the non-starred cells in rows 4 and 7. Just like the bigger seafood (swordfish, jellyfish) you can ignore the fact that not every vertex of the potential x-wing contains a 7.

The only thing preventing the potential x-wing from being a real x-wing are the sevens marked with the hash marks, known as the fin.

So here's what I'm getting.

If there were sevens in all the starred squares you'd have a classic, rectangular x-wing. The fact that one of the vertices (r7c2) is already solved to the value of 5 is immaterial (!?!). Preventing this hypothetical x wing (that doesn't and could never exist) are the other two 7's in column 2 in rows 8 and 9. They constitute the "fin."

Now I assume the reason the 7 in r7c3 becomes the victim is that it sees both the fin squares and the other lower vertex at r7c4. If so, I'd have the little "rule" I'm looking for.

Luke in Ca

Luke
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Luke451 wrote:Now I assume the reason the 7 in r7c3 becomes the victim is that it sees both the fin squares and the other lower vertex at r7c4. If so, I'd have the little "rule" I'm looking for.

You're there Luke451. One small restriction is that in this type you have to restrict all your eliminations to THE BOX WHERE THE FIN(S) is LOCATED.......

Hvard,
I agree that the generalised rule works PERFECTLY. one problem is that we inhereted pattern identification techniques that are widely used in Latin squares & other sudoku variants...so we can't start from scratch on this......

We can use the general rules as an ubmbrella & as pattern identification in advanced finned fish but we have to build up on what we are already using.........

Now, terms like Classic, Finned & Sashimi.... there seems to be no one objecting on using them (Fish #1,2,3)

Headless fish (Fish #4) ... it is a special case of Sashimi fish & a special case of 2 lines 1 box cover sectors.....it also provides a link-up between the N rows*N columns to the general rule....... so I will keep it as a step higher than sashimi......

I didn't know that kraken was used for fish that needed life-support so IMO as ronk seems to object to franken fish to describe Myths example....

we sum it up in that we need a consensus in naming the following creatures.......

(FISH #5) virtulal fish that have N rows * N columns configration - fins > 1 box (Myth's example)----how about Extended? Super-Finned? or should we as Havard said merge it with 2,3 & 4 above(I'm inclined to keep it as a seperate entity)?

(FISH #6) virtual/true fish but with N sectors* N Sectors configuration (No simpler counterpart)--------This sounds like Franken?

(FISH #7) ANY fish that needs life support (Mike Barker has been using these and referring to them as kraken fish)

tarek

tarek

Posts: 2650
Joined: 05 January 2006

ronk wrote:
tarek wrote:... in the Filet-O-Fish thread we have always referred to each fin cell as a fin, so we can have up to 4 fins in a skinny Finned fish

That was my viewpoint also until someone pointed out that ...
Myth Jellies wrote:Filet-O-Fish Rule

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.

Note that "cells" is plural and "fin" is singular. Myth Jellies, is a revision or clarification of the rule in order?

Since MJ used the phrase two distinct fins just seven messages back in this thread, a singluar vs. plural definition for fin seems necessary.

Too bad Almost is locked into the terminology. Astronomers reference planets outside our Solar System as exo-planets. We could have exo-finned fish for those where the fin(s) is/are outside the box referenced in the finned fish definition.
daj95376
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The way I've tried to use it is that a fin can consist of multiple cells, but all of those cells have to be part of the same group (box). I indicated two fins in my prior post because the two cells were not in the same box. I like this distinction because then the two-finned label will indicate a significant difference in the deduction (the concept is the same but the execution is more difficult) as compared to a single-finned fish with a two-cell fin like the opening example.

It's just my opinion, and if enough others think that some other interpretation is more clear or consistent, then I can modify the post accordingly.
Myth Jellies

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Last edited by ronk on Sun Oct 22, 2006 4:08 pm, edited 1 time in total.
ronk
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Great (Although the fin definition according to generalization rule should be according to the cover sector but it shouldn't be a major thing really, SO all fin cells in a box should be called A fin),

That makes naming things easier ??

Fish #4 becomes (Multi-finned) fish: true/virtual fish - N rows * N columns >1 fin (or fin cells not restricted to 1 box) - no simpler counterpart [Although if pedantic, 2 fins shouldn't be multi, but for unification purposes as there will be >2 finned fish out there, this name sounds OK]

so the suggestd list now stands at:
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`Fish#1 Classic fishFish#2 Finned fishFish#3 Sashimi fishFish#4 Headless fishFish#5 Multi-finned fishFish#6 Franken FishFish#7 Kraken Fish (Fish requiring life support)`

When everybody is in agreement, we should put these in a new thread along with the Generalization rule & Fish types with examples IMO

tarek

tarek

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Joined: 05 January 2006

Myth Jellies wrote:The way I've tried to use it is that a fin can consist of multiple cells, but all of those cells have to be part of the same group (box). I indicated two fins in my prior post because the two cells were not in the same box. I like this distinction because then the two-finned label will indicate a significant difference in the deduction (the concept is the same but the execution is more difficult) as compared to a single-finned fish with a two-cell fin like the opening example.

It's just my opinion, and if enough others think that some other interpretation is more clear or consistent, then I can modify the post accordingly.

Seems reasonable. I was concerned that eliminations from non-box fin cells might be questioned because they only indirectly cause an overlay with the (parent) fish eliminations. What about the case where the exo-fin cells cause a contradiction and force the fish to be true? See following message for an example.
Last edited by daj95376 on Sun Oct 22, 2006 8:59 pm, edited 1 time in total.
daj95376
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Six eliminations on <9>, Locked Candidate (2), and six eliminations on <1>. (sans Singles)

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` *-----------* |.23|..8|..6| |.5.|3..|..9| |..9|...|4..| |---+---+---| |.4.|..6|8..| |..7|.3.|5..| |..2|7..|.6.| |---+---+---| |..4|...|3..| |2..|..3|.1.| |9..|1..|62.| *-----------*# after Singles, six Template eliminations on <9> exist *-----------------------------------------------------------------------------* | 147     2       3       |*459    *14579   8       | 17      57      6       | | 14678   5       168     | 3       1467    147     | 2       78      9       | | 1678    1678    9       | 256     12567   1257    | 4       3578    13578   | |-------------------------+-------------------------+-------------------------| | 135     4       15      |-259    -1259    6       | 8       379     1237    | | 168    *1689    7       |*289     3      *129     | 5       4       12      | | 1358   *189     2       | 7      *14589  *1459    |#19      6       13      | |-------------------------+-------------------------+-------------------------| | 15678   1678    4       |*25689  *256789 *2579    | 3      #5789    578     | | 2       678     568     |-45689  -456789  3       | 79      1       4578    | | 9       3       58      | 1       4578    457     | 6       2       4578    | *-----------------------------------------------------------------------------*`

I see a finned Jellyfish in [r1567c2456] with exo-cells [r6c7] and [r7c8].

If [r6c7]=9 or [r7c8]=9, they would force X-Wing [r48c45] and cause a contradiction in [b2] for <9>.
Therefore, the Jellyfish is correct, the X-Wing is eliminated, and [r6c7]<>9 & [r7c8]<>9 result.

Is there another fishy scenario for these eliminations?

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`# after eliminations on <9>, Singles, and Locked Candidate (2)# six Template eliminations on <1> exist *--------------------------------------------------------------------* | 14     2      3      | 49     149    8      | 7      5      6      | | 1467   5     -16     | 3      1467  -147    | 2      8      9      | | 678    68     9      | 256    2567   257    | 4      3      1      | |----------------------+----------------------+----------------------| | 3      4      15     | 25    -125    6      | 8      9      7      | |-168   -1689   7      | 89     3      19     | 5      4      2      | | 58     89     2      | 7      4589   459    | 1      6      3      | |----------------------+----------------------+----------------------| |-156    16     4      | 25689  25689  259    | 3      7      58     | | 2      7      568    | 4568   4568   3      | 9      1      458    | | 9      3      58     | 1      4578   457    | 6      2      458    | *--------------------------------------------------------------------*`

Colors will perform the eliminations in [r24], and the other eliminations follow as Hidden Singles.

Singles complete the puzzle.

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

In this example, the critical pattern is:

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`*-----------------------------*| .  .  . | 9  9  . | .  .  . || .  .  . | .  .  . | .  .  . || .  .  . | .  .  . | .  .  . ||---------+---------+---------|| .  .  . | 9  9  . | .  9  . || .  .  . | .  .  . | .  .  . || .  .  . | .  .  . | .  .  . ||---------+---------+---------|| .  .  . | .  .  . | .  .  . || .  .  . | 9  9  . | 9  .  . || .  .  . | .  .  . | .  .  . |*-----------------------------*`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

As I understand Myth's fish it is the same thing as a Kraken fish so I don't think we need both types. If we are cataloguing all types then there is still the almost fish and ARCs which are first cousin to the Kraken. The biggest difference is Kraken start with the fish and uses extra links to reduce the covering set to n-1 and can have more than two nice chains connected to the fish. Almost fish and ARCs are part of nice loops. Kraken fish are described in Ruud's ARC thread ( http://forum.enjoysudoku.com/viewtopic.php?t=4731&start=0 ) where I subsequently changed the name from almost fish to Kraken to distinguish them from Jeff's almost fish.

I made an attempt to summarize big fin, headless, skinny, and Franken fish as well as Siamese fish at http://forum.enjoysudoku.com/viewtopic.php?p=23576#p23576. This includes my interpretation of the corresponding covering sets.

My understanding of a fin is that it is up to two extra cells in a line in a box. "Big fin" has been used to identify multiple fins in a box. So the following fish can be thought of as having two regular fins or one big fin. A big fin fish includes basic big fin, headless and skinny fish.
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`. . . | . . . | # # . . . . | . X . | X X * . . . | . | . | # # . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . X . | X X . . . . | . | . | | | . ------+---|---+-|-|-- . . . | . | . | | | . . . . | . | . | | | . . . . | . X . | X X . `

Luke, you may want to check out DAJ's puzzle, there is a finned X-wing that eliminates 9 in r4c45 (that is row 4 and columns 4 and 5). The eliminations in r6c7, r7c8, and r8c45 follow directly. A finned X-wing (in rows this time in DAJ's final puzzle configuration) which eliminates 1 in r5c1 and r2c3 will solve the puzzle.
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`+-------------------+----------------------+------------------+|   147     2    3  |   459   14579     8  | 17    57      6  || 14678     5  168  |     3    1467   147  |  2    78      9  ||  1678  1678    9  |   256   12567  1257  |  4  3578  13578  |+-------------------+----------------------+------------------+|   135     4   15  |  25-9   125-9     6  |  8   379*  1237  ||   168  1689    7  |   289       3   129* |  5     4     12  ||  1358   189    2  |     7   14589  1459* | 19     6     13  |+-------------------+----------------------+------------------+| 15678  1678    4  | 25689  256789  2579* |  3  5789*   578  ||     2   678  568  | 45689  456789     3  | 79     1   4578  ||     9     3   58  |     1    4578   457  |  6     2   4578  |+-------------------+----------------------+------------------+`

[Edit: in both cases the "finned fish" are sashimi versions. In the second case the fish can be thought of as a Siamese fish (two X-wings in one) as well.]
Last edited by Mike Barker on Mon Oct 23, 2006 9:29 am, edited 1 time in total.
Mike Barker

Posts: 458
Joined: 22 January 2006

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