The New Sudoku Players' Forum

[docjohn]

xchain.jpg (109.11 KiB) Viewed 1379 times

There is a three link X-chain here that resembles a Skyscraper except that the weak link is on the opposite end (weak link is in box 3 instead of column 3).

Does anyone know if this have a name?

[eleven]

7 in r2c4 is a single in box 2, which gives you a pointing pair in r13c3 to eliminate 7r78c3.

More generally: If you have the 2 strong links, 7 must be restricted to row 2 of box 2, and can be eliminated by box/line reduction from row 2 in box 1 and 3.
So the weak link in box 3 is irrelevant.

[SpAce]

Hi docjohn,

eleven already gave you the relevant answer. I'll try to answer your actual question anyway.

There is a three link X-chain here that resembles a Skyscraper except that the weak link is on the opposite end (weak link is in box 3 instead of column 3).

Does anyone know if this have a name?

First of all, note that the X-Chain is actually a loop, so you get eliminations along every weak link sector (b3,c3,b1):

X-Loop: (7)r1c3 = r1c7 - r3c9 = (7)r3c3 - loop => -7 r2c79,r78c3,r2c2

It's a perfectly valid X-Loop of length four, but it doesn't have or deserve a more specific name because no one would ever use it like that. When an X-Chain/Loop is fully contained in a single chute like here, there's always a simpler alternative (single, pointing, claiming) available. For the same reason we don't use things like these even though they're valid alternatives for the hidden single 7r2c4:

Siamese Franken/Alien Cyclopsfish: (7)B2\[r2|c4|2n4] => -7 r2c279,r5c4, -25 r2c4

or:

Franken X-Wing: (7)R13\b13 => -7 r2c279

[docjohn]

Thanks SpAce (and Eleven)!

I agree with your answer. I'm writing a solver which shows everything available in a given situation. So even though the X-loop isn't needed, it could help the user who doesn't see the hidden 7 in box 2.

Plus you answered my question: X LOOP! Thanks!

[StrmCkr]

N x M fish is my preferred method.

formally N x (N+K)
as M = N +K, where k is additional sectors used to balance the equation
(their is limitations to what can be used as superfluous covers for increasing k size with out affecting M total value)
edit:

http://forum.enjoysudoku.com/about-the-arithmetic-of-ultimate-fish-t5256.html

Franken X-Wing: 7 r13 c3b3 => r2c3789,r456789c3<>7

Franken X-Wing: 7 r13 b13 => r2c123789<>7 (edit renamed after discussion)

edited typos

cover-sets:
C3 and B1 can be exchanged which accounts for R2C123 eliminations.


notes:
theoretical elimination i was working on that accounted for the extra eliminations: {theoretical because its the bases for the no-fish eliminations i posted as plausible solution to using fish. }
superfluous cover set:
is any sector that can be directly exchanged for an identical relation ship of (base x single cover )
in the above case C3 x base = R13C3
and B1 x base = R13C3
where by R13C3 is counted by 2 sectors thus is locked
eliminate in (cover+S cover) - base

[SpAce]

N x n+K fish is my perfered method.

Makes no difference here as fins aren't needed. It's the same fish in UFG. (Btw, why not simply call it NxM fish? Much easier on the eyes.)

Mutant X - wing
Base R13
Cover C3, B3
Eliminations = r78c3, r2c79 <> 2

It's actually Franken, not Mutant (and the digit is 7 not 2). Expressed a bit more compactly:

Franken X-Wing: (7)R13\c3b3 => -7 r2c79,r78c3

Making It a finned mutant adds b2 to covers and eliminates, R2c2 <>2

I'm guessing you meant b1 and not b2. I don't know why you'd want to make the fish finned, as fins only reduce eliminations. In fact, if you simply add b1 as an additional cover, you lose all eliminations:

(7)R13\c3b13 => (no eliminations)

To get more eliminations you should use more than one fish or use alternate covers that don't increase the Rank, i.e. make it Siamese:

Siamese Franken X-Wing: (7)R13\b3[c3|b1] => -7 r2c279,r78c3

That's still a Rank 0 fish even though it seemingly has three covers (but only two are used at a time; i.e. it's really a shorthand for two different fishes -- yours and the other Franken I presented earlier).

(pretty sure the mutant already eliminates R2c2, but can't check)

No, it does not. How could it, if your covers are c3 and b3 (r2c2 is in neither)?

[StrmCkr]

fn power outage sucked, couldn't fix my post.... now its fixed.

cause the extra cover isn't increasing rank...

X-Wing, Franken r13/c3b13 => r2456789c3<>7, r2c12789<>7

Code: Select all

+-------------+---------+--------------+
| .   .   (7) | .  .  . | (7)  .   .   |
| -7  -7  -7  | 7  7  7 | -7   -7  -7  |
| .   .   (7) | .  .  . | .    .   (7) |
+-------------+---------+--------------+
| .   .   -7  | .  .  . | .    .   .   |
| .   .   -7  | .  .  . | .    .   .   |
| .   .   -7  | .  .  . | .    .   .   |
+-------------+---------+--------------+
| .   .   -7  | .  .  . | .    .   .   |
| .   .   -7  | .  .  . | .    .   .   |
| .   .   -7  | .  .  . | .    .   .   |
+-------------+---------+--------------+

[SpAce]

fn power outage sucked, couldn't fix my post.... now its fixed.

Yet you introduced a new mistake:

Mutant X-Wing: 7 r13 b13 => r2c123789<>7

It's Franken, just like I originally wrote. It would be a Mutant if it had both rows and columns as either bases or covers (or both).

cause the extra cover isn't increasing rank...

Of course it is, unless you clearly mark it as an alternate -- which you didn't:

X-Wing, Franken r13/c3b13 => r2456789c3<>7, r2c12789<>7

That's incorrect. As written, the fish is Rank 1 (3-2) so it can only eliminate where two covers overlap (i.e. nothing here). To get the eliminations you listed, c3 and b1 need to be marked as alternate covers (which makes the fish Siamese). I already showed one way to do it, but of course you can't acknowledge that, because once again you're so busy pushing your own half-baked ideas. Why don't you first read what's already been said and think it through? It might make sense if you gave it a chance.

cover-sets:
C3 and B1 can be exchanged which accounts for R2C123 eliminations.

Indeed, but your fish notation does not depict that at all. You can't just assume that the reader knows which covers are alternate possibilities unless they're marked as such.

That being said, feel free to write whatever pleases you. I'm not willing to enter another exhausting debate with you over nothing. I'm only saying this much because I don't want to leave your ideas as the only things newcomers see. Then it's up to them to decide what makes sense and what doesn't.

[StrmCkr]

Yet you introduced a new mistake:

Mutant X-Wing: 7 r13 b13 => r2c123789<>7

Strange, that's a direct copy paste from hodoku.
Name and all.

so ill look back at the ufg and

n sectors x n sectors as their isn't a box used in the base & cover for it to be a franken.

2. Franken: N (rows+Nonet) sectors x N (columns+Nonet) sectors or vv.

which puts its as a mutant.
3. Mutant: N sectors x N sectors (That is not Basic nor Franken)

X-Wing, frankenr13/c3b13 => r2456789c3<>7, r2c12789<>7

Is from xsudoku and its a rank 0 as
As written and displayed above.

Rank only increases when the balancing equations do not balance
Same with K values in N X M fish. {name adjusted as per suggested}
as M = N +K, where k is additional sectors used to balance the equation
(their is limitations to what can be used as superfluous covers for increasing k size with out affecting M total value)

in full following obi's math directly {instead of the noted shortcuts i use in my set based version of obis math which cannot reuse sectors}
would be R1133 / c3b133 => r2456789c3<>7, r2c12789<>7 { rank zero }

and reduces to R13/C3B13 => r2456789c3<>7, r2c12789<>7 and still holds the rank zero as displayed in xsudoku

However you are correct they won't work in ufg terms and would instead have to be listed as alternatives.
where by and nicely displayed by you

Siamese Franken X-Wing: (7)R13\b3[c3|b1] => -7 r2c279,r78c3
is another great way of doing it

That being said, feel free to write whatever pleases you. I'm not willing to enter another exhausting debate with you over nothing

replay how ever you wish or don't. nxm vs nxn is completely different subjects but both have similar analysis of n digits in n cells more over both operate under different contexts.

because once again you're so busy pushing your own half-baked ideas

defiantly not a half baked idea, as its been used and implemented by others that is not just me.

[SpAce]

Yet you introduced a new mistake:

Mutant X-Wing: 7 r13 b13 => r2c123789<>7

Strange, that's a direct copy paste from hodoku. Name and all.

That doesn't mean much. Hodoku is perfectly capable of making mistakes or using obsolete ideas, even though its fish stuff is generally really good. However, your UFG findings are a bit more serious concern, considering that it's supposed to be the definitive documentation:

so ill look back at the ufg and

2. Franken: N (rows+Nonet) sectors x N (columns+Nonet) sectors or vv.
3. Mutant: N sectors x N sectors (That is not Basic nor Franken)

I must apologize. You're right that the UFG definitions are unclear enough to allow your and Hodoku's interpretation, so I shouldn't have called it a mistake (well, not yours anyway). It just doesn't make much sense, which is probably why I've unconsciously ignored such a possibility. More importantly, there's this:

Code: Select all

 .  .  . |  X  *  X |  .  .  .        .  .  . |  X  /  X |  .  .  .
 .  .  . |  X  *  X |  .  .  .        .  .  . |  X  /  X |  .  .  .
 .  .  . |  X  *  X |  .  .  .        .  .  . |  X  /  X |  .  .  .
---------+----------+----------      ---------+----------+----------
 .  .  . |  /  .  / |  .  .  .        .  .  . |  *  .  * |  .  .  .
 .  .  . |  /  .  / |  .  .  .        .  .  . |  *  .  * |  .  .  .
 .  .  . |  /  .  / |  .  .  .        .  .  . |  *  .  * |  .  .  .
---------+----------+----------      ---------+----------+----------
 .  .  . |  X  *  X |  .  .  .        .  .  . |  X  /  X |  .  .  .
 .  .  . |  X  *  X |  .  .  .        .  .  . |  X  /  X |  .  .  .
 .  .  . |  X  *  X |  .  .  .        .  .  . |  X  /  X |  .  .  .
 Fig 2B: cc\bb                        Fig 2B inverse: bb\cc
 rr\bb transpose                      bb\rr transpose
 franken x-wing
 Note Fig 2B is equivalent to Fig 1A.

So... what should we believe? An imprecisely worded definition or a clear example, both from the same source? The former may or may not support your POV, but the latter definitely supports mine (our fish being of type rr\bb and listed as a franken x-wing).

Either way, to me it doesn't make any sense if the fish in question is considered Mutant (in which case the UFG Franken X-Wing example is wrong too). If it really is, then I'll simply drop using the Franken vs. Mutant distinction and call them all just Complex fishes.

To me the defining characteristic of a Mutant is that it has a mix of rows and columns in one or both of its sets, because it's what makes it more complex than a Franken (both having at least one box in one or both sets). On the other hand, a Franken only has either rows or columns in each set, but possibly neither if one set has only boxes like in our fish.

I don't think my interpretation is in conflict with the UFG definitions either, but I do admit that it's not the only one allowed by them (which means that the definitions should be made more precise). The actual Franken X-Wing example leaves no doubt, however.

I think we need tarek's judgment here. I'm glad this was brought up, because someone (possibly I) has a wrong idea about the Franken/Mutant distinction.

(Btw, the basic/franken/mutant distinctions seem to lose most of their relevance with NxM fishes anyway, because the fish body isn't clearly defined when M>N. Is there any naming convention for them?)

I'll reply to the rank stuff separately.

[tarek]

Hopefully this clarifies it,

If base/cover are made up of lines only & type of lines in base are different to those in cover ====> Basic (rr/cc or cc/rr)
Not Basic ==>
if base OR cover have box(es) & type of lines in base are different to those in cover ===> Franken (rr/bb cc/bb rr/cb rrb/ccb …)
Not Basic Not Franken ===> Mutant

The turbot fish for instance with 2 strong links (one in box and the other in a line) would be a Finned Franken Sashimi X-Wing

Code: Select all

.....75...1..4..8.6..9.....3...7.8...7.4.8.2...8.3...9.....4..5.3..1..4...56.....
+----------------------+----------------------+----------------------+
| 2489   2489   2349   | 1238   268    7      | 5      1369   12346  |
| 2*579  1      2379   | 235    4      2356   | 23679  8      2367   |
| 6      24*58  2347   | 9      2-58   1235   | 12347  137    12347  |
+----------------------+----------------------+----------------------+
| 3      24569  12469  | 125    7      12569  | 8      156    146    |
| 1%59   7      169    | 4      %569   8      | 136    2      136    |
| 1245   2456   8      | 125    3      1256   | 1467   1567   9      |
+----------------------+----------------------+----------------------+
| 12789  2689   12679  | 2378   289    4      | 123679 13679  5      |
| 2789   3      2679   | 2578   1      259    | 2679   4      2678   |
| 124789 2489   5      | 6      289    239    | 12379  1379   12378  |
+----------------------+----------------------+----------------------+
Turbot Fish 5:r5c15 r2c1 r3c2 ==> r3c5<>5
Finned Franken Sashimi X-Wing  b1r5/c1c5 fr3c2 ==> r3c5<>5

Skyscraper ==> Basic, 2-String Kite ==> Mutant, Turbot fish ==> Franken

row + box / column + box means: any number of rows + any number of boxes / any number of columns + any number of boxes

[SpAce]

Hopefully this clarifies it

Yes, it does. Thanks a lot, tarek!

If base/cover are made up of lines only & type of lines in base are different to those in cover ====> Basic (rr/cc or cc/rr)
Not Basic ==>
if base OR cover have box(es) & type of lines in base are different to those in cover ===> Franken (rr/bb cc/bb rr/cb rrb/ccb …)
Not Basic Not Franken ===> Mutant
...
row + box / column + box means: any number of rows + any number of boxes / any number of columns + any number of boxes

That's exactly how I've always interpreted it, because it makes the most sense and it matches with almost all of the examples I've seen -- in fact, this Hodoku blunder was probably the first counter-example. However, the UFG definition alone doesn't necessarily make it crystal-clear:

2. Franken: N (rows+Nonet) sectors x N (columns+Nonet) sectors or vv.

It seems to me that StrmCkr (and possibly hobiwan) have understood it so that both bases and covers of a Franken must have rows OR cols AND boxes. With that interpretation rr\bb wouldn't qualify, because the base side doesn't have any boxes and the cover side doesn't have any columns. To avoid such confusion, it might be a good idea to update the definition a bit.

I guess some smart person could write regular expressions to define each type without ambiguity. I can't, and they would probably be pretty complex expressions anyway (that few would understand), but I think some simple pseudo-regexes could help catch the essential differences. For example:

Code: Select all

Basic:   r+\c+
         c+\r+

Franken: r*b*\c*b*
         c*b*\r*b*

         (also: at least one b)

Mutant:  r*c*b*\r*c*b*

         (also: at least one b, at least one side has both r and c)

+ : at least one of the preceding letter
* : any number (including zero) of the preceding letter

Invariant constraint (for NxN fishes): both sides of '\' must have an equal number of letters

--

PS. Why are you using '/' above? That's not standard UFG notation! Have you changed your mind about using '\' as the base\cover separator? I wouldn't like that, because I think the '\' makes it easy to recognize fishes since it's not used for anything else in sudoku notations. Besides, I think there was originally a mathematical reason for that symbol.

Personally I've also chosen to capitalize the base letters to make fish nodes even more easily recognizable within chains and to comply with Allan Barker's general set logic expressions (since fishes are just a special case of them), but obviously that's not standard UFG.

[tarek]

The “/“ is a typo. Still struggling to use windows on Mac keyboard! I will fix that.

When the definition “Franken” came about there was a problem in using that term when the base sectors had boxes. It was agreed at the end that as long as there is no line type mixing in the base or cover sectors then it would be allowed

Although every attempt has been made to make things clear and in ambiguous in the UFG, I can see how the Franken definition can lead to some confusion and therefore should be revised to make it clearer.

[SpAce]

The “/“ is a typo. Still struggling to use windows on Mac keyboard! I will fix that.

Great, thanks for the clarification!

When the definition “Franken” came about there was a problem in using that term when the base sectors had boxes. It was agreed at the end that as long as there is no line type mixing in the base or cover sectors then it would be allowed

I think it was a good decision because it makes the boundaries of the types really easy to grasp, and it also makes the most sense from the complexity point of view: Mutant (boxes+line type mixing) > Franken (boxes, no line type mixing) > Basic (no boxes, no line type mixing).

Btw, one more thing about this:

Skyscraper ==> Basic, 2-String Kite ==> Mutant, Turbot fish ==> Franken

That's a nice example of the three types, but unfortunately I don't think it's quite that simple. Since they're all finned fishes the exact type depends on which base candidates are chosen as fins (because what's left is the fish body that determines the type). It's related to what I said earlier about the impossibility to name NxM fishes accurately, because they have no clearly defined N-fish bodies at all (no dedicated fin sectors).

As 2x3 fishes the Turbot Fish variants can be seen as:

Code: Select all

Skyscraper:

  RR\ccb
  CC\rrb

2-String Kite:

  RC\rcb

Turbot Crane:

  RB\rcc
  CB\rrc

Of those, only the Kite is clearly a mutant because the base side is a constant and has line type mixing. Both Skyscrapers and Cranes have ambiguous types, because the covering sets have multiple grouping options which imply different types when viewed as finned 2-fishes:

Code: Select all

Skyscraper (RR\ccb):

  RR\cc + b (basic)
  RR\cb + c (franken)

2-String Kite (RC\rcb):

  RC\rc + b (mutant)
  RC\rb + c (mutant)
  RC\cb + r (mutant)

Turbot Crane (RB\rcc):

  RB\rc + c (mutant)
  RB\cc + r (franken)

So, a Skyscraper can be seen as either basic or franken (but not mutant). A Kite is always a mutant. A Crane is either franken or mutant (but not basic).

Would you agree with that? How would you resolve the related NxM naming problem? Would it make the most sense to use the minimum possible complexity for a given configuration? That way a 2x3 Skyscraper would be Basic, a 2x3 Kite would be Mutant, and a 2x3 Crane would be Franken -- just like you said.

[tarek]

Good point. The reference to nxn fish has to be explicit. I will do that in the Hint explanation text in Sukaku explainer too when describing these strong-linked fishy techniques