The New Sudoku Players' Forum

[StrmCkr]

Code: Select all

+---------------+---------------+---------------+
| 1    1    1   | 1    1    1   | .    (1)  .   |
| .    (1)  .   | .    .    .   | (1)  (1)  (1) |
| 1    1    1   | 1    1    1   | .    (1)  .   |
+---------------+---------------+---------------+
| .    (1)  .   | 1    1    1   | 1    .    1   |
| (1)  (1)  (1) | 1    1    1   | 1    .    1   |
| .    (1)  .   | 1    1    1   | 1    .    1   |
+---------------+---------------+---------------+
| 1    1    1   | .    (1)  .   | 1    .    1   |
| 1    1    1   | (1)  (1)  (1) | 1    (1)  1   |
| 1    1    1   | .    (1)  .   | 1    .    1   |
+---------------+---------------+---------------+

yes, the examples where the ERI cell is relative is complicated sorta {making one from scratch is harder}
most of the complication arise when an ERI over lays a "2-string kyte" style elimination like box 3 in this case when the R2C8 is removed we have eliminations seen below.

Code: Select all

+---------------+---------------+---------------+
| 1    1    1   | 1    1    1   | .    (1)  .   |
| .    (1)  .   | .    .    .   | (1)  .    (1) |
| 1    1    1   | 1    1    1   | .    (1)  .   |
+---------------+---------------+---------------+
| .    (1)  .   | 1    1    1   | 1    .    1   |
| (1)  (1)  (1) | 1    -1   1   | 1    .    1   |
| .    (1)  .   | 1    1    1   | 1    .    1   |
+---------------+---------------+---------------+
| 1    1    1   | .    (1)  .   | 1    .    1   |
| 1    -1   1   | (1)  (1)  (1) | 1    (1)  1   |
| 1    1    1   | .    (1)  .   | 1    .    1   |
+---------------+---------------+---------------+

[SpAce]

yes, the examples where the ERI cell is relative is complicated sorta {making one from scratch is harder}
most of the complication arise when an ERI over lays a "2-string kyte" style elimination like box 3 in this case when the R2C8 is removed we have eliminations seen below.

In other words we can agree that the ERI cell is irrelevant in pure ER patterns where the ERI acts as a strong link. Its absence is only relevant when the ERI acts as a weak link, but then it's actually misleading to talk about an ERI at all because the weak link can exist without an actual "empty rectangle" pattern in the box. Your example could just as well look like this, with only the intersection cell unoccupied in box 3:

Code: Select all

+---------------+---------------+---------------+
|  1    1    1  |  1    1    1  |  1   (1)   1  |
|  .   (1)   .  |  .    .    .  | (1)   .   (1) |
|  1    1    1  |  1    1    1  |  1   (1)   1  |
+---------------+---------------+---------------+
|  .   (1)   .  |  1    1    1  |  1    .    1  |
| (1)  (1)  (1) |  1   -1    1  |  1    .    1  |
|  .   (1)   .  |  1    1    1  |  1    .    1  |
+---------------+---------------+---------------+
|  1    1    1  |  .   (1)   .  |  1    .    1  |
|  1   -1    1  | (1)  (1)  (1) |  1   (1)   1  |
|  1    1    1  |  .   (1)   .  |  1    .    1  |
+---------------+---------------+---------------+

There's no ERI in box 3 but it still works. From that we (or at least I) can conclude that the ERI cell is irrelevant in all cases, because the term ERI makes sense only with ERs and with ERs we only use the strong link property (when the intersection cell is irrelevant). As far as I'm concerned, if the box pattern acts as a weak link, then it's not an ERI (even if it looks like one).

Btw, I kept your grid marking style above, though I think it's non-standard and a bit confusing. In most diagrams I've seen the '.' denotes a cell that may or may not hold the relevant digit (for which you apparently use '1'), and '/' is used for cells that can't be occupied by it (for which you apparently use the '.'). It causes similar confusion as overloading existing terms, which is what got this whole discussion started. That's why I probably misread one of your diagrams earlier. Communication would be so much easier if people just followed a few simple conventions... sigh.

[StrmCkr]

Yeah I was using xsudo to build the examples, lacked time to throw it into a text editor and swap the. Terms to standard ntatom

Same goes for interpreting standard patterns swapimg stuff to digits so I can manipulate them easier in my programs

[rjamil]

Hi StrmCkr and SpAce,

I derived one more combination containing four Empty Rectangles as follows:

Code: Select all

*Dual Geouped Empty Rectangle (1 exemplar, 1 exclusion)
  --------------+-------------+-----------
    /  +z    /  |  .   .   .  |  .  .   .
   +z   .   +z  |  .   .   .  |  . -Z   .
    /  +z    /  |  .   .   .  |  .  .   .
  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  / +z   /
    .  -Z    .  |  .   .   .  | +z  .  +z
    .   .    .  |  .   .   .  |  / +z   /
  --------------+-------------+-----------
    /  +z    /  |  .   .   .  |  / +z   /
   +z   .   +z  |  .   .   .  | +z  .  +z
    /  +z    /  |  .   .   .  |  / +z   /
  --------------+-------------+-----------

.---------------------------------.---------------------------------.---------------------------------.
| 23456789   123456789  23456789  | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 23456789   123456789  23456789  | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 23456789   123456789  23456789  |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 23456789   123456789  23456789  |
:---------------------------------+---------------------------------+---------------------------------:
| 23456789   123456789  23456789  | 123456789  123456789  123456789 | 23456789   123456789  23456789  |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 23456789   123456789  23456789  | 123456789  123456789  123456789 | 23456789   123456789  23456789  |
'---------------------------------'---------------------------------'---------------------------------'

Hodoku suggests two "Finned Franken Swordfish" moves as follows:
1) 1 r79b1 c28b8 fr2c1 fr2c3 => r2c8<>1; and
2) 1 r79b6 c28b8 fr5c7 fr5c9 => r5c2<>1.

But, by looking the above mentioned exemplar as four Empty Rectangles, is it should be called "Dual Grouped Empty Rectangle" with both eliminations at once, i.e., -1r2c5, r5c2?

OR, maybe, is it simply called Grouped Empty Rectangle Transport", where ERI @ r5c8 is treated as Transport ERI?

R. Jamil
----------
Treat pattern name as proper noun.

[SpAce]

Hi rjamil,

I think I made it clear what I think of anything named "Grouped Empty Rectangle". As long as that overloaded name is used, I'm not interested. Most of the ER/ERI stuff is an unnecessary complication anyway, as far as I'm concerned. They're all easy to see as Grouped X-Chains ("grouped" used in its correct meaning) or fishes, which have more generic value, so I don't really see any need for an extra POV with complicated and overloaded names.

Btw, to get both eliminations at once with an X-Chain you can use subchains, as explained by StrmCkr here.

(1)r2c13 = r13c2 - r79c2 = r8c13 - r8c79 = (1)r79c8 => -1 r2c8

(1)r79c2 = r8c13 - r8c79 = r79c8 - r46c8 = (1)r5c79 => -1 r5c2

a:(1)r2c13 = r13c2 - b:(1)r79c2 = r8c13 - r8c79 = a:(1)r79c8 - r46c8 = b:(1)r5c79 => -1 r2c8,r5c2

(The third chain is a combination of the first two with embedded endpoints, i.e. it has two subchains. It works but it's harder to read than two separate chains.)

I don't have time to look at the fish POV right now, but it might be possible to combine them too. Probably doesn't make much sense, though. Unless a combo elimination is needed for an OTP solution, it's usually simpler to use smaller patterns with multiple steps for the same effect.

Added:

Hodoku suggests two "Finned Franken Swordfish" moves as follows:
1) 1 r79b1 c28b8 fr2c1 fr2c3 => r2c8<>1; and
2) 1 r79b6 c28b8 fr5c7 fr5c9 => r5c2<>1.

There are lots of different fishes that can get those eliminations, but the exact matches for the corresponding X-Chains (or ER patterns) are mutants with boxes as base sectors and rows & columns as cover sectors (i.e. not the frankens you presented above). They're also easy to combine, especially if seen as finless Obi-Fishes (my preference anyway):

Mutant 3x4 Obi-Fish: (1)B179\r28c28 => -1 r2c8
Mutant 3x4 Obi-Fish: (1)B679\r58c28 => -1 r5c2
Mutant 4x5 Obi-Fish: (1)B1679\r258c28 => -1 r2c8,r5c2

So, as demonstrated, you can indeed get both eliminations at once, using either a Grouped X-Chain (with subchains) or an Obi-Fish. No need to use horrible ER names (or almost equally horrible finned UFG fishes). The single 4x5 Obi-Fish would be my favorite way to present it, being very compact and totally unambiguous.

[rjamil]

Hi SpAce,

Added:
...
So, as demonstrated, you can indeed get both eliminations at once, using either a Grouped X-Chain (with subchains) or an Obi-Fish. No need to use horrible ER names (or almost equally horrible finned UFG fishes). The single 4x5 Obi-Fish would be my favorite way to present it, being very compact and totally unambiguous.

At least now it is clear that the pattern already exists, no matter what name it has.

Here I am sharing some more patterns with teaser (horrible) names that I have derived by adding an ERI with Skyscraper and 2-String Kite patterns:

Code: Select all

Skyscraper + ERI
  --------------+-------------+-----------
    .  +Z    .  |  .  -Z   .  | -Z  /  -Z
    .   /    .  |  .   .   .  |  .  /   .
   -Z   /   -Z  |  .  -Z   .  |  . +Z   .
  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------
    .   /    .  |  /  +z   /  |  .  /   .
    .  +Z    .  | +z   .  +z  |  . +Z   .
    .   /    .  |  /  +z   /  |  .  /   .
  --------------+-------------+-----------
Grouped Skyscraper + ERI
(Finned X-Wing)
  --------------+-------------+-----------
    .  +z    .  |  .   .   .  |  .  /   .
    .  +z    .  |  .   .   .  |  .  /   .
   -Z  +z   -Z  |  .  -Z   .  |  . +Z   .
  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------
    .   /    .  |  /  +z   /  |  .  /   .
    .  +Z    .  | +z   .  +z  |  . +Z   .
    .   /    .  |  /  +z   /  |  .  /   .
  --------------+-------------+-----------
Grouped Skyscraper + ERI
(Sashimi X-Wing)
  --------------+-------------+-----------
    .  +z    .  |  .   .   .  |  .  /   .
    .  +z    .  |  .   .   .  |  .  /   .
   -Z   /   -Z  |  .  -Z   .  |  . +Z   .
  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------
    .   /    .  |  /  +z   /  |  .  /   .
    .  +Z    .  | +z   .  +z  |  . +Z   .
    .   /    .  |  /  +z   /  |  .  /   .
  --------------+-------------+-----------
2-String Kite + ERI Ring                    Grouped 2-String Kite + ERI Ring
  --------------+-------------+-----------  --------------+-------------+-----------
   -Z   /   -Z  |  .   .   .  |  . -Z   .    -Z  +Z   -Z  |  .   .   .  |  . -Z   .
    /   /   +Z  |  /   /   /  |  / +Z   /    +Z   /   +Z  |  /   /   /  |  / +Z   /
   -Z  +Z   -Z  |  .   .   .  |  . -Z   .    -Z  +Z   -Z  |  .   .   .  |  . -Z   .
  --------------+-------------+-----------  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  . -Z   .     .   /    .  |  .   .   .  |  . -Z   .
    .   /    .  |  .   .   .  |  . -Z   .     .   /    .  |  .   .   .  |  . -Z   .
    .   /    .  |  .   .   .  |  . -Z   .     .   /    .  |  .   .   .  |  . -Z   .
  --------------+-------------+-----------  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  / +z   /     .   /    .  |  .   .   .  |  / +z   /
   -Z  +Z   -Z  | -Z  -Z  -Z  | +z -Z  +z    -Z  +Z   -Z  | -Z  -Z  -Z  | +z -Z  +z
    .   /    .  |  .   .   .  |  / +z   /     .   /    .  |  .   .   .  |  / +z   /
  --------------+-------------+-----------  --------------+-------------+-----------

Updated as on 20191012: Added box 1 more eliminations in "2-String Kite + ERI Ring" and "Grouped 2-String Kite + ERI Ring" exemplars.

See example puzzle here.

R. Jamil