The New Sudoku Players' Forum

[Yogi]

4..5.769....3....2.681...3.65.2.4..9...73.4.....9.......68........6.3..738947....
I'm told this can be solved with a Sashimi XWing, but I can't spot it.
Have identified conjugate pairs 5c3, 7r3, 8r1 but nothing else to go with them.
Any ideas?
Thanx.

[SpAce]

It's in 8s. Full answer hidden, in case you want to try to look for it yourself first. Hint: it has a double fin, i.e. you need to look for group links as well if you see it as a chain (Grouped Skyscraper).

Hidden Text: Show

Code: Select all

.--------------------.-----------------.--------------------------.
| 4     123    123   | 5  b28*   7    |  6         9      a1(8)*  |
| 1579  179    157   | 3   4689  689  |  1578      14578   2      |
| 2579  6      8     | 1   249   29   |  57        3       45     |
:--------------------+----------------+---------------------------:
| 6     5      137   | 2  c18*    4   | d137(#8)  d17(#8)  9*     |
| 1289  129    12    | 7   3     1568 |  4         12568   156-8  |
| 1278  12347  12347 | 9   1568  1568 |  123578    125678  1356-8 |
:--------------------+----------------+---------------------------:
| 1257  1247   6     | 8   1259  1259 |  12359     1245    1345   |
| 125   124    1245  | 6   1259  3    |  12589     12458   7      |
| 3     8      9     | 4   7     125  |  125       1256    156    |
'--------------------'----------------'---------------------------'

Sashimi X-Wing (8)r14\c59 f:r4c78

aka Grouped Skyscraper: (8)r1c9 = r1c5 - r4c5 = (8)r4c78

=> -8 r56c9; stte

Here's how you can spot it if you're not using candidates:

Hidden Text: Show

sxw.png (37.1 KiB) Viewed 2187 times

[tarek]

Returning to the UFG:

Sashimi would refer to the ability to reduce the fish to simpler fish in the absence of fins. In these specific terms, you don't need to have fins to have a sashimi fish. Unfortunately the common use of these terms to describe Finned Sashimi fish proved more popular than the definition.

[SpAce]

Sashimi would refer to the ability to reduce the fish to simpler fish in the absence of fins. In these specific terms, you don't need to have fins to have a sashimi fish. Unfortunately the common use of these terms to describe Finned Sashimi fish proved more popular than the definition.

Hi tarek! Since you say "unfortunately" I guess you would rather advocate using the original definition. Can you give an example of when it would provide practical benefits? If we have a finless Sashimi fish, then by definition we have a smaller fish available (in the case of a Sashimi X-Wing that would be a 1-fish, i.e. a hidden single). Why would we need to talk about the larger Sashimi fish in those cases at all, except from a theoretical point of view?

In other words, it seems to me that any useful instance of Sashimi implies Finned as well, but am I wrong? Given that the names of complex fishes are quite long anyway, it seems understandable to drop apparent redundancies.

[tarek]

I wouldn’t say that a finless sashimi fish is useful however definitions don’t care about usefulness. It is all about avoiding confusion. Unfinned and non-sashimi can be looked at as redundant. Finned, however is not. So I will always keep saying finned sashimi. A trained fisherman will obviously have very little interest in definitions and proper use. My target has always been newcomers!!!

I’m not here to debate popular use v proper use as I’ve done that so many times. Your point however is well taken.

Tarek

[SpAce]

Thanks for explaining, tarek! I think I understand your POV, so no argument there. I hope you don't mind too much if I still keep using Sashimi a bit improperly myself

Btw, has the term "Headless" been dropped altogether as I've only run into it in very old posts? Are those cases seen as Franken Fishes nowadays?

[Yogi]

OK thanx. Let’s work it through with my kind of picture logic. We know how X Wings work when two parallel conjugate pairs, the base set, exclude the candidate in the cover set, except for the remaining pair that make up the X Wing.
Then we come to the Sashimi situation here, where we have 3 corners of a degenerate X Wing and the 4th corner is solved as a 9. In this case all the action (as in eliminations) can only take place in this 4th corner’s box, which is Box6.
The reasoning approach regarding the 8-candidate fins in Box6 could be summed up as ‘Either or Neither.’ This highlights the fact that we have a simple two-case scenario: In Case1, if Either of the fins is an 8, then r56c9<>8. In Case2, if Neither of the ins is an 8, then r4c5,r1c9=8 => r56c9<>8. So 8 is eliminated from r56c9 anyway. Great!
But it’s not quite so simple! The same logic can be applied from a different start-point: If Either r56c9 is 8, then r4c78<>8. And if Neither r56c9 is 8, then r1c9,r4c5=8, and again r4c78<>8. How do we decide which are the fin cells and which are the elimination cells? Or are both approaches valid, eliminating 8 from all of r4c78 and r56c9?
Another question, about spotting this as a type of degenerate X Wing. At this stage r6c5 is also candidate 8, meaning that r14c5 is not a conjugate pair in 8s.
Why do we ignore r6c5 in spotting this as a Sashimi X Wing in candidate 8?

[tarek]

Hi Yogi,

The X-Wing is made from Bases (in this example they are Rows 1 & 4) that intersect with Covers (Here they are Columns 5 & 9) to form the Finned Sashimi X-wing.

The candidates in the Bases that are not in Covers are called fins (Here r4c78) and the candidates in Covers but not in bases are Potential eliminations (r56c9 & your r26c5)

Only potential eliminations that can see all fins are eventual eliminations (r56c9) and not r26c5.


This is a Finned Sashimi X wing because without the fins, r4c5 becomes true eliminating r1c5 (the fish degenerates)

tarek

[tarek]

Btw, has the term "Headless" been dropped altogether as I've only run into it in very old posts? Are those cases seen as Franken Fishes nowadays?

The UFG was evolving and the terms came & went. Some were used then got subsumed or modified by other terms. When the sashimi term was going through an expansion, it became apparant that a box as a cover sector can be used & therfore the Franken fish term came to be!!!

tarek

[SpAce]

But it’s not quite so simple! The same logic can be applied from a different start-point: If Either r56c9 is 8, then r4c78<>8.

True so far.

And if Neither r56c9 is 8, then r1c9,r4c5=8, and again r4c78<>8.

False. Why do you think r4c5=8 in that scenario? It's not, and thus the conclusion is wrong too.

Another question, about spotting this as a type of degenerate X Wing. At this stage r6c5 is also candidate 8, meaning that r14c5 is not a conjugate pair in 8s.
Why do we ignore r6c5 in spotting this as a Sashimi X Wing in candidate 8?

For the same reason we ignore 8r2c5. Just like in normal X-Wings, we only need strong links in the bases, and the bases here are rows 1 and 4 (like tarek explained). We have our strong links in those rows: 8r1c5=8r1c9 and 8r4c5=8r4c56. We don't need (or want *) strong links in the cover sectors, i.e. columns 5 and 9. 8r6c5 is a cover candidate and thus a potential elimination, just like 8r2c5. They just don't get eliminated because they don't see the fin cells in r4c78. (* If we have strong links in the cover sectors of a normal X-Wing, there's nothing to eliminate.)

Note that, if r26c5<>8 (which is not true, but if it were), then we'd have a column-based Sashimi X-Wing as well: (8)c59\r14 f:r56c9. In that case we could eliminate 8r4c78. (That could also be seen as a 5-link grouped oddagon with guardians in b6p578, which would eliminate 8r4c78,r56c9 in one move.)

Added: One more thing. I personally think any variant of X-Wing is much easier to see as a chain instead of a fish. For example, this Finned Sashimi X-Wing is a Grouped Skyscraper (or simply a grouped X-Chain) which proves that either r1c9=8 or r4c78=8 (or both); thus we can eliminate 8 from any cells both end nodes see, i.e. r56c9. In fact, I don't think I've ever spotted a Finned (Sashimi) X-Wing as such -- I always see them as either simple or grouped X-Chains because I naturally look for chains anyway. Thinking in terms of fishes, i.e. bases and covers and fins, is a different process and much more complicated and totally unnecessary with X-Wing variants. It makes more sense with larger fishes that can't be seen as linear chains.

[SpAce]

Btw, has the term "Headless" been dropped altogether as I've only run into it in very old posts? Are those cases seen as Franken Fishes nowadays?

The UFG was evolving and the terms came & went. Some were used then got subsumed or modified by other terms. When the sashimi term was going through an expansion, it became apparant that a box as a cover sector can be used & therfore the Franken fish term came to be!!!

Thanks. Have I understood correctly that a Headless fish is still a valid concept, a kind of an extreme Sashimi, even if it's no longer mentioned anywhere? Even if the same eliminations can be achieved with a corresponding Franken fish, I'm wondering if a headless r\c fish -- being more basic -- might actually be easier to understand and catch for many manual solvers. What do you think? Should it be revived as an optional POV?

[tarek]

Have I understood correctly that a Headless fish is still a valid concept, a kind of an extreme Sashimi, even if it's no longer mentioned anywhere? Even if the same eliminations can be achieved with a corresponding Franken fish, I'm wondering if a headless r\c fish -- being more basic -- might actually be easier to understand and catch for many manual solvers. What do you think? Should it be revived as an optional POV?

I would say that it will be confusing because it may cause a conflict with the definitions of the UFG

If I had my druthers, we would rename "franken" to "finned franken" and "headless" to "franken" ... and then add "sashimi franken." And if I really had my druthers, we'd drop the "sashimi" name and just consider it part of the "finned" pattern

You can see that as the terms evolved and were modified, some terms that were used were not necessarily suitable.


tarek

[Yogi]

A footnote to SpAce's comment: you are correct. The key issue in my mistake was that there WAS a CP in 8s in Row1, but r14c5 was not a true conjugate pair. So the forcing chain goes around the loop one way to exclude 8r56c9, but it would not go around the other way as I had thought. 8r1c9 does not drive 8r4c5 because r26c5 could also be 8.
..729.81.......9.7...8.75.6..6...1.5......4.97.5...2....96537.156.17239.371984652
Just to nail that issue down, here we find a case of a Sashimi X Wing in candidate 4 which points to Box1 and solves the puzzle quite easily: Fin cells r1c12 => r23c3<>4. That is enough to solve the puzzle anyway, but in this case both r8c39 AND r18c9 are true conjugate pairs, so regarding r23c3 as a double fin the forcing chain would go around the other way to show => r1c12<>4 with the same result. All good fun but the real lesson is that Sashimi X Wings don’t HAVE to be made up entirely of CPs to work.

[SpAce]

..729.81.......9.7...8.75.6..6...1.5......4.97.5...2....96537.156.17239.371984652
Just to nail that issue down, here we find a case of a Sashimi X Wing in candidate 4 which points to Box1 and solves the puzzle quite easily: Fin cells r1c12 => r23c3<>4. That is enough to solve the puzzle anyway, but in this case both r8c39 AND r18c9 are true conjugate pairs, so regarding r23c3 as a double fin the forcing chain would go around the other way to show => r1c12<>4 with the same result.

Glad you found an example of such a situation, so we can see the 5-link Grouped Oddagon I mentioned earlier. Yes, you have two different Sashimi X-Wings (or Grouped Skyscrapers) there:

(4)r1c9 = r8c9 - r8c3 = (4)r23c3 => -4 r1c12
(4)r8c3 = r8c9 - r1c9 = (4)r1c23 => -4 r23c3

You can choose one but not both, because using one kills the other (but of course you get both eliminations via basics afterwards). To get both eliminations in one move, you could use the Oddagon:

Code: Select all

.------------------------.-----------------.-------------.
|*6-4     *35-4      7   | 2    9     56   | 8  1    *34 |
|#12468  #123458  *238-4 | 345  1346  156  | 9  234   7  |
|#1249   #12349   *23-4  | 8    134   7    | 5  234   6  |
:------------------------+-----------------+-------------:
| 2489    23489    6     | 347  234   89   | 1  378   5  |
| 128     1238     238   | 357  1236  1568 | 4  3678  9  |
| 7       13489    5     | 34   1346  1689 | 2  368   38 |
:------------------------+-----------------+-------------:
| 248     248      9     | 6    5     3    | 7  48    1  |
| 5       6       *48    | 1    7     2    | 3  9    *48 |
| 3       7        1     | 9    8     4    | 6  5     2  |
'------------------------'-----------------'-------------'

5-link Grouped Oddagon [(4)r1c12=r1c9=r8c9=r8c3=(4)r23c3], 4 guardians: (4)b1p4578

(4)b1p4578 => -4 r1c23,r23c3; stte

In other words: if you remove all guardians in box 1, you end up with an impossible pattern of 4s (assuming the puzzle has at least one solution). Thus one of them must be true, and any non-guardian 4s in the same box must be false.

[SpAce]

I would say that it will be confusing because it may cause a conflict with the definitions of the UFG

How? Is there a different definition for "headless" then? Otherwise I don't see how it would cause a conflict. [Edit: As an afterthought, I think I've seen somewhere a definition that says something about all cover sectors coinciding with at least one base candidate, or something like that. Is it in the UFG? That would of course cause a conflict with headless fishes.]

Perhaps all headless fishes can be replaced by franken fishes, but as far as I understand, they're two very different things and as such could both be valid points of view to the same eliminations. In my experience, the more ways to see the same thing, the more likely to find something. Then again, my understanding of this topic is very limited. Let's take your own example from here, though:

Code: Select all

.------------------.----------------.--------------------.
| 567    2456  247 |*1   8     467  | 456-7  *9    *3    |
| 1678   468   3   | 5   2479  4679 | 1468   #267  #478  |
| 15678  9     147 | 3   247   467  | 14568  #267  #4578 |
:------------------+----------------+--------------------:
| 138    238   12  | 6   47    38   | 47      5     9    |
| 4      7     5   | 89  39    2    | 68      36    1    |
| 368    368   9   |*47  1     5    | 2      *37   *48   |
:------------------+----------------+--------------------:
| 39     34    8   | 2   4579  479  | 57      1     6    |
| 2      1     6   |*78  35    38   | 9      *4    *57   |
| 579    45    47  | 49  6     1    | 3       8     2    |
'------------------'----------------'--------------------'

Finned Headless Swordfish c489\r168 f:r23c8,r23c9 => -7 r1c7

I'd say that's pretty easy to understand, if the player is familiar with basic finned/sashimi fishes. The shape of the pattern is the familiar 3x3 Swordfish, and no boxes are needed. The only weird thing is the lack of true vertices in the top row, but one must imagine vertices for sashimi fishes anyway.

Btw, another POV might be to see a deadly pattern of 7s with the fins as guardians:

DP(7)r68c489 + (7)r23c8,r23c9 => -7 r1c7

Here's the same elimination with a Franken Swordfish:

Code: Select all

.------------------.------------------.------------------.
| 567    2456  247 | 1    8     *467  | 456-7  9    3    |
| 1678   468   3   | 5   *2479  *4679 | 1468   267  478  |
| 15678  9     147 | 3   *247   *467  | 14568  267  4578 |
:------------------+------------------+------------------:
| 138    238   12  | 6   *47     38   |*47     5    9    |
| 4      7     5   | 89   39     2    | 68     36   1    |
| 368    368   9   | 47   1      5    | 2      37   48   |
:------------------+------------------+------------------:
| 39     34    8   | 2   *4579  *479  |*57     1    6    |
| 2      1     6   | 78   35     38   | 9      4    57   |
| 579    45    47  | 49   6      1    | 3      8    2    |
'------------------'------------------'------------------'

Franken Swordfish r47b2\c567 => -7 r1c7

That's a very different beast. Sure, it's conceptually simpler, but not necessarily easier to spot and understand (for a typical basic fisherman).

Or, we could see it as another deadly pattern with different guardians:

DP(7)r2347c56 + (7)r1c6,r47c7 => -7 r1c7

So... multiple points of view are available anyway. Is there a reason why the headless POV is not officially among them? Like I said, it doesn't seem to be the same thing as franken or any other fish type I know.

Personally I doubt I'd spot any of the above, so I'd be more likely to use the chain POV (which, of course, is not always available):

(7)r23c9 = r8c9 - r8c4 = r6c4 - r6c8 = (7)r23c8 => -7 r1c7

Edit: fixed the link.