The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |..5|.2.|.3.|
 |31.|..9|.6.|
 |..9|...|8.1|
 |---+---+---|
 |.2.|.9.|...|
 |7..|1.3|..2|
 |...|.5.|.4.|
 |---+---+---|
 |4.6|...|2..|
 |.5.|2..|.18|
 |.3.|.7.|6..|
 *-----------*


Play/Print this puzzle online

[SpAce]

Just another POC of yesterday's topic. (Not a very practical one, though. It was kind of tricky to find the "Hidden BUG" here, but it was there -- and the chains were very easy after that.)

Code: Select all

.--------------.---------------------.----------------.
| 8  47   5    |  6      2      1    | b49+7   3   79 |
| 3  1    2    | d47+8  a8+4    9    |  47     6   5  |
| 6  47   9    |  5      3      7-4  |  8      2   1  |
:--------------+---------------------+----------------:
| 5  2   c34+8 | c48+7   9     a67+4 |  1     c78  36 |
| 7  69   48   |  1     d46+8   3    |  5      89  2  |
| 1  69   38   |  78     5      2    |  79     4   36 |
:--------------+---------------------+----------------:
| 4  8    6    |  3      1      5    |  2      79  79 |
| 9  5    7    |  2      46     46   |  3      1   8  |
| 2  3    1    |  9      7      8    |  6      5   4  |
'--------------'---------------------'----------------'

HBUG+7

Code: Select all

a: (4)r2c5,r4c6
   ||
b: (7)r1c7 - r6c7 = r6c4 - (7=64)r48c6
   ||
c: (87)r4c348 - (7=64)r48c6
   ||
d: (8)r2c4,r5c5 - (8=4)r2c5

=> -4 r3c6; stte

(Only the starting points of the chains marked on the grid.)

[Cenoman]

Code: Select all

 +------------------+--------------------+------------------+
 |  8    47   5     |  6     2     1     |  479   3    79   |
 |  3    1    2     | v478*  48*   9     | w47    6    5    |
 |  6    47   9     |  5     3    a47    |  8     2    1    |
 +------------------+--------------------+------------------+
 |  5    2   A348*  | u478*  9     47-6  |  1     78 zB36   |
 |  7    69   48*   |  1    Z468*  3     |  5     89   2    |
 |  1   x69   38    |  78    5     2     | x79    4   y36   |
 +------------------+--------------------+------------------+
 |  4    8    6     |  3     1     5     |  2     79   79   |
 |  9    5    7     |  2     46   b46    |  3     1    8    |
 |  2    3    1     |  9     7     8     |  6     5    4    |
 +------------------+--------------------+------------------+

DP(48)r2c45, b5p15, r45c3 using mixed external-internals
(4)r3c6 - (4=6)r8c6
(3)r4c3 - (3=6)r4c9
(7)r4c4 - r2c4 = r2c7 - (7=96)r6c27 - r6c9 = (6)r4c9
(6)r5c5
=> -6 r4c6; ste

[Ngisa]

Code: Select all

+-------------------+---------------------+--------------------+
| 8     e47     5   | 6       2       1   | 479     3      f79 |
| 3      1      2   | 478     48      9   | 47      6       5  |
| 6     d47     9   | 5       3      c47  | 8       2       1  |
+-------------------+---------------------+--------------------+
| 5      2      348 | 478     9      b467 | 1       78      36 |
| 7     j69     48  | 1     ka6-48    3   | 5      i89      2  |
| 1      69     38  | 78      5       2   | 79      4       36 |
+-------------------+---------------------+--------------------+
| 4      8      6   | 3       1       5   | 2      h79     g79 |
| 9      5      7   | 2       46      46  | 3       1       8  |
| 2      3      1   | 9       7       8   | 6       5       4  |
+-------------------+---------------------+--------------------+


(6)r5c5 = (6-7)r4c6 = r3c6 - r3c2 = r1c2 - r1c9 = r7c9 - (7=9)r7c8 - r5c8 = (9-6)r5c2 = (6)r5c5 =>
- 48r5c5; stte

Clement

[999_Springs]

Code: Select all

+-----------+-------------+-----------+
| 8 47  5   | 6   2   1   | 479 3  79 |
| 3 1   2   | 478 48  9   | 47  6  5  |
| 6 47  9   | 5   3   47  | 8   2  1  |
+-----------+-------------+-----------+
| 5 2  A348 |A478 9   46-7| 1  A78 36 |
| 7 69  48  | 1   468 3   | 5   89 2  |
| 1 69 B38  |B78  5   2   | 79  4  36 |
+-----------+-------------+-----------+
| 4 8   6   | 3   1   5   | 2   79 79 |
| 9 5   7   | 2   46  46  | 3   1  8  |
| 2 3   1   | 9   7   8   | 6   5  4  |
+-----------+-------------+-----------+

ALS-XZ:

A = 3478r4c348, B = 378r6c34, x=3, z=7 => -7r4c6 stte

[blue]

For SpAce: More HBUG/BUG-Lite fun ...

Code: Select all

+-------------+------------------+-----------------+
| 8  47  5    | 6     2     1    | 49+7  3     9-7 |
| 3  1   2    | 78+4  48    9    | 47    6     5   |
| 6  47  9    | 5     3     47   | 8     2     1   |
+-------------+------------------+-----------------+
| 5  2   38+4 | /478  9     67+4 | 1     78    36  |
| 7  69  /48  | 1     68+4  3    | 5     89    2   |
| 1  69  38   | 78    5     2    | 79    4     36  |
+-------------+------------------+-----------------+
| 4  8   6    | 3     1     5    | 2     79    79  |
| 9  5   7    | 2     46    46   | 3     1     8   |
| 2  3   1    | 9     7     8    | 6     5     4   |
+-------------+------------------+-----------------+

(BUG-Lite + 5) in all unfilled cells except for r4c4 and r5c3

7r1c7 =[BUG-Lite]= (4r2c4|4r5c5|4r4c36) - (4=78)r46c4 - (78=4)r2c4 - (4=7)r2c7 => -7r1c9; stte

... or, an "HBUG+8"

Code: Select all

+-------------+------------------+-----------------+
| 8  47  5    | 6     2     1    | 49+7  3     9-7 |
| 3  1   2    | 78+4  48    9    | 47    6     5   |
| 6  47  9    | 5     3     47   | 8     2     1   |
+-------------+------------------+-----------------+
| 5  2   38+4 | 4+78  9     67+4 | 1     78    36  |
| 7  69  4+8  | 1     68+4  3    | 5     89    2   |
| 1  69  38   | 78    5     2    | 79    4     36  |
+-------------+------------------+-----------------+
| 4  8   6    | 3     1     5    | 2     79    79  |
| 9  5   7    | 2     46    46   | 3     1     8   |
| 2  3   1    | 9     7     8    | 6     5     4   |
+-------------+------------------+-----------------+

Code: Select all

       7r1c7
        ||
(4r2c4|4r5c5|4r4c36) - (4=78)r46c4 - (78=4)r2c4 - (4=7)r2c7     => -7r1c9; stte
        ||                         /            /
      78r35c4 --------------------             /
        ||                                    /
     896r5c382 - (68=4)r5c5 - r4c4 = 4r2c4 --

... and the HBUG/BUG-Lite is a DP with no solution.

[SpAce]

For SpAce: More HBUG/BUG-Lite fun ...

Thanks! Awesome... I truly couldn't imagine that there might be another one lying around! It was hard enough to find the first one.

(BUG-Lite + 5) in all unfilled cells except for r4c4 and r5c3

7r1c7 =[BUG-Lite]= (4r2c4|4r5c5|4r4c36) - (4=78)r46c4 - (78=4)r2c4 - (4=7)r2c7 => -7r1c9; stte

... or, an "HBUG+8"

Very nice! And impressive. I couldn't get anywhere with the 4r5c3 "placement" which was the first thing I tried to find a hidden BUG. If I counted correctly, there are only two cells where a valid placement can be made without resulting in stte (4r5c3 and 8r2c5). The former gave nothing directly, so I gave up on that. The latter gave a BUG+4 which I used.

It's very interesting that your second HBUG-placement (4r4c4) is actually a false one. I didn't think of that possibility (which of course is really dumb -- if the technique is used for real then it must obviously work whether a "placement" is true or not because you can't know without cheating). It's also the first real example of a placement cell with more than two candidates, which I only hypothesized earlier when I said: "Btw, if generalized, I don't think the defining difference is in the number of original candidates in the cells but how many are left once the guardians are removed."

"HBUG+8"

Code: Select all

       7r1c7
        ||
(4r2c4|4r5c5|4r4c36) - (4=78)r46c4 - (78=4)r2c4 - (4=7)r2c7     => -7r1c9; stte
        ||                         /            /
      78r35c4 --------------------             /
        ||                                    /
     896r5c382 - (68=4)r5c5 - r4c4 = 4r2c4 --

This demonstrates nicely why the BUG-Lite is better for presentation, even though calling it Lite is kind of funny when it's only one or two cells smaller than a full BUG. Like I said in the earlier thread, I think it could also be called HBUG+5+3, if one wants to distinguish it from a more normal BUG-Lite and still skip the +3 chains. The downside is that it requires the reader to realize that the +5 part is a BUG-Lite, which is not necessarily obvious.

... and the HBUG/BUG-Lite is a DP with no solution.

I guess this observation is related to the "idle talk" part of your earlier post. It seemed interesting, but I kind of missed your point there. Is there a distinction between no-solution and binary-solution BUG-type DPs? I've thought that normal BUGs and BUG-Lites can be either kind. That's another unintuitive thing about BUGs, by the way. I bet most people would think that BUGs are always binary-solution DPs, and I thought so too until Leren thankfully educated me.

[Cenoman]

Another kind of fun:

Code: Select all

 +------------------+--------------------+------------------+
 |  8    47*  5     |  6     2     1     | a479#  3    79*  |
 |  3    1    2     | b478#  48    9     |  47*   6    5    |
 |  6    47*  9     |  5     3    c47*   |  8     2    1    |
 +------------------+--------------------+------------------+
 |  5    2    348   |  478*  9    d467*  |  1    a78# e36   |
 |  7    69   48    |  1     468   3     |  5     89   2    |
 |  1    69  f38    | f78*   5     2     |  9-7*  4   f36   |
 +------------------+--------------------+------------------+
 |  4    8    6     |  3     1     5     |  2     79   79   |
 |  9    5    7     |  2     46    46    |  3     1    8    |
 |  2    3    1     |  9     7     8     |  6     5    4    |
 +------------------+--------------------+------------------+

In the 7s, 9-link oddagon (*) having three guardians (#):
(7)r1c7|r4c8==(7)r2c4 - r3c6 = (7-6)r4c6 = r4c9 - (6=387)r6c349 => -7 r6c7; ste

[blue]

Another kind of fun:

I always smile when another of your oddagon eliminations.

---

For SpAce: Another "heavy" BUG-Lite, leading to a single elimination and an stte finish.

Code: Select all

+-------------+------------------+----------------+
| 8  /47  5   | 6     2     1    | 79+4   3   79  |
| 3  1   2    | /478  /48   9    | /47    6   5   |
| 6  /47  9   | 5     3     /47  | 8      2   1   |
+-------------+------------------+----------------+
| 5  2   34+8 | 78+4  9     46+7 | 1      78  3(6)|
| 7  69  48   | 1     46+8  3    | 5      89  2   |
| 1 (6)9 38   | 78    5     2    | 79     4   3-6 |
+-------------+------------------+----------------+
| 4  8   6    | 3     1     5    | 2      79  79  |
| 9  5   7    | 2     46    46   | 3      1   8   |
| 2  3   1    | 9     7     8    | 6      5   4   |
+-------------+------------------+----------------+

(BUG-Lite + 5) in cells not marked with '/' => -6r6c9; stte

Code: Select all

 4r1c7 --------------------------
   ||                             \
(4r4c4|8r5c5) ----                 \
   ||              \                \
 8r4c3 - (8=4)r5c3 - 4r5c5           \
   ||                  ||             \
   ||                4r2c5 - r2c7 = (4-9)r1c7 = 9r6c7 - (9=6)r6c2
   ||                  ||
   ||                4r8c5 - (4=6)r8c6 - 6r4c6 = 6r4c9
   ||                                  /
 7r4c6 -------------------------------

... and the HBUG/BUG-Lite is a DP with no solution.

I guess this observation is related to the "idle talk" part of your earlier post. It seemed interesting, but I kind of missed your point there. Is there a distinction between no-solution and binary-solution BUG-type DPs? I've thought that normal BUGs and BUG-Lites can be either kind.

Yes ... related to the "idle talk".
There's no distinction, when it comes to the BUG-logic being valid -- the bit about "if it has one solution, then it has two or more".

When a BUG+n pattern leads to an elimination, the usual thing to do, is say that the elimination is valid, based on a/the assumption that the puzzle has a unique solution.
If you knew up front (or could easily show) that the BUG part of the BUG+n was a no-solution DP, then (of course) you could claim the elimination without relying on uniqueness.

The BUG-Lite above, BTW, has two solutions.
With that, there's no way to fill the '/' cells that is both self-consistent and compatible with the BUG-Lite.

That's another unintuitive thing about BUGs, by the way. I bet most people would think that BUGs are always binary-solution DPs, and I thought so too until Leren thankfully educated me.

The situation isn't helped by things like this: HoDoKu -- copying a link provided by rjamil in another thread.

[SpAce]

Hi Cenoman,

Another kind of fun:
In the 7s, 9-link oddagon (*) having three guardians (#):
(7)r1c7|r4c8==(7)r2c4 - r3c6 = (7-6)r4c6 = r4c9 - (6=387)r6c349 => -7 r6c7; ste

That's a very interesting Oddagon! Those three non-guardians in box 5 make it look like it can't be valid, but it sure is (I think). However, would you agree that it's kind of degenerate, considering it contains a simpler DP (7r2&6c7) requiring just two of those guardians (r2c4 and r4c8)? (Which can be turned into a normal AIC without any DPs.) That, however, doesn't take away the conceptual and entertainment value of this strange pattern, which I'm sure was your whole point!

I guess this would be a bit more conventional variant:

Code: Select all

.-------------.---------------------.-------------------.
| 8  47   5   |   6      2     1    | a49(#7)  3     79 |
| 3  1    2   |   478*   48    9    |  47*     6     5  |
| 6  47   9   |   5      3     47   |  8       2     1  |
:-------------+---------------------+-------------------:
| 5  2    348 |   478*   9    b46#7 |  1       78*  b36 |
| 7  69   48  |   1      468   3    |  5       89    2  |
| 1  69  c38  | ac8(#7)  5     2    |  9-7*    4    c36 |
:-------------+---------------------+-------------------:
| 4  8    6   |   3      1     5    |  2       79    79 |
| 9  5    7   |   2      46    46   |  3       1     8  |
| 2  3    1   |   9      7     8    |  6       5     4  |
'-------------'---------------------'-------------------'


5-link Oddagon (7)r24,c47,b6 with three guardians:

(7)r1c7|r7c4 == (76)r4c69 - (6=387)r6c934 => -7 r6c7; stte

(Or Almost-Skyscraper (7)R24\c47b6 with spoiler #7r4c6 and the same chain.)

[SpAce]

Hi blue,

For SpAce: Another "heavy" BUG-Lite, leading to a single elimination and an stte finish.

That's very interesting as well! I can't find a corresponding HBUG for it either. Can you? Or does it have to do with the fact that the BUG-Lite has two solutions, unlike the ones before which had none? My brain starts hurting with this stuff

Anyway, I still tried to look for those externals to see if the chains could be simplified, but I don't think it made much difference, except by avoiding the double-kraken (if I didn't make mistakes). The end result in this case is probably more complicated and error-prone anyway with a mixed sets of guardians. Here's what I got:

Code: Select all

.----------------.----------------------.-----------------.
| 8   /47   5    |   6      2      1    |  79+4  3   79   |
| 3   1     2    | bd/4#78  /8#4   9    | a/4#7  6   5    |
| 6   /47   9    |   5      3      /7#4 |  8     2   1    |
:----------------+----------------------+-----------------:
| 5   2    e34+8 |   78+4   9     c46+7 |  1     78  3(6) |
| 7   69    48   |   1     d46+8   3    |  5     89  2    |
| 1  (6)9   38   |   78     5      2    |  79    4   3-6  |
:----------------+----------------------+-----------------:
| 4   8     6    |   3      1      5    |  2     79  79   |
| 9   5     7    |   2      46     46   |  3     1   8    |
| 2   3     1    |   9      7      8    |  6     5   4    |
'----------------'----------------------'-----------------'

blue's BUG-Lite+5 using mixed +internals/#externals

Code: Select all

a: (#7)r2c7 - (7=96)r6c72
   ||
b: (#7)r2c4 - r3c6 = (76)r4c69
   ||
c: (+7-6)r4c6 = (6)r4c9
   ||
c: (#8)r2c4|(+8)r5c5 - (8=796)r6c472
   ||
d: (+8)r4c3 - (8=7)r4c8 - (7=96)r6c72


=> -6 r6c9; stte

Does that make any sense? Cenoman, feel free to comment too. You're the master of mixing and matching internals/externals in the most efficient ways!

Yes ... related to the "idle talk".
There's no distinction, when it comes to the BUG-logic being valid -- the bit about "if it has one solution, then it has two or more".

Ok, that makes sense!

When a BUG+n pattern leads to an elimination, the usual thing to do, is say that the elimination is valid, based on a/the assumption that the puzzle has a unique solution.
If you knew up front (or could easily show) that the BUG part of the BUG+n was a no-solution DP, then (of course) you could claim the elimination without relying on uniqueness.

Ah, that's indeed a relevant difference! Of course.

The BUG-Lite above, BTW, has two solutions.
With that, there's no way to fill the '/' cells that is both self-consistent and compatible with the BUG-Lite.

Yes, I noticed that immediately when I tried to find a corresponding HBUG (and failed). That's why I asked above if they're possibly related.

The situation isn't helped by things like this: HoDoKu -- copying a link provided by rjamil in another thread.

Indeed! The available teaching materials do a poor job in that regard (even though Hodoku material is generally among the best), and the effect snowballs when no one checks the facts and the false information keeps getting shared. Fortunately it usually makes little difference in practice, but it's still wrong.

[Cenoman]

Hi Space

Those three non-guardians in box 5 make it look like it can't be valid, but it sure is (I think). However, would you agree that it's kind of degenerate...

...a bit more conventional variant: 5-link Oddagon (7)r24,c47,b6 with three guardians...

Why do things simple when you can do them complex ?

I suspected that with its 14 candidates in digit 7, this puzzle had many other oddagons. I started searching 5-links , then 7-links but found only some with uneasy sets of guardians. And spotting the 9-links, I found it funny and stop searching others.

Of course yours is much better. Simply I did not see it !

There are a lot of paths to find in this puzzle.
Besides 999_Springs nice ALS-XZ, I would have expected an AIC as such simple as: (7=8)r4c8 - (8=9)r5c8 - (9=6)r5c2 - r5c5 = (6)r4c6 => -7 r4c6; ste

In more complex solutions, there was also DP(47) r1c27, r2c47, r3c26, r4c46 with four guardians 9r1c7, 8r2c4, 8r4c4, 6r4c6

Hidden Text: Show

(9)r1c7 - r6c7 = (9-6)r6c2 = r6c9 - r4c9 = (6)r4c6
(8-7)r2c4 = (7)r3c6
(8)r4c4 - (8=7)r6c4
(6)r4c6
=> -7r4c6; ste

Combining this DP(47) with DP(48) of my first post, one get's a MUG (478) b12345, also with four guardians: 9r1c7, 3r4c3, 6r4c6, 6r5c5

Code: Select all

 +--------------------+-----------------------+------------------+
 |  8    47*    5     |     6     2     1     |  479*  3    79   |
 |  3    1      2     |     478*  48*   9     |  47*   6    5    |
 |  6    47*    9     |     5     3     47*   |  8     2    1    |
 +--------------------+-----------------------+------------------+
 |  5    2      348*  |     478*  9   Zd46-7* |  1     78 Yc36   |
 |  7    69     48*   |     1     468*  3     |  5     89   2    |
 |  1    69  XAb38    | WzBb78    5     2     |Ya79    4  Xb36   |
 +--------------------+-----------------------+------------------+
 |  4    8      6     |     3     1     5     |  2     79   79   |
 |  9    5      7     |     2     46    46    |  3     1    8    |
 |  2    3      1     |     9     7     8     |  6     5    4    |
 +--------------------+-----------------------+------------------+

MUG (478) b12345 using externals
(7)r6c7 - (7=386)r6c369 - r4c9 = (6)r4c6
(8)r6c3 - (8=7)r6c4
(7)r6c4
(8)r6c4 - (8=36)r6c39 - r4c9 = (6)r4c6
=> -7 r4c6; ste

[Cenoman]

Hi SpAce,

a separate response to another subject.

blue's BUG-Lite+5 using mixed +internals/#externals

a: (#7)r2c7 - (7=96)r6c72
||
b: (#7)r2c4 - r3c6 = (76)r4c69
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c: (+7-6)r4c6 = (6)r4c9
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c: (#8)r2c4|(+8)r5c5 - (8=796)r6c472
||
d: (+8)r4c3 - (8=7)r4c8 - (7=96)r6c72

=> -6 r6c9; stte

Does that make any sense? Cenoman, feel free to comment too....

To me, yes that makes sense. In the set of internals listed by blue, 4r4c4 is AIC-resistant (I need a kraken, as well as blue). So you suggest to replace it by the externals of the pair (78)r46c4 in c4. Instead of five internal guardians, you have six mixed guardians (no concern with replacing 4r1c7 by 7r2c7). Now I noticed that 7r2c4 and 8r2c4 have the same parity as 7r4c6 and 8r5c5 respectively. De facto, 7r4c6 and 8r5c5 are external guardians of the pair (78)r46c4 in b5. So I suggest to eventually keep as guardians of this BUG-lite+5 the following four (mixed externals-internals) guardians: #7r2c7, #+7r4c6, #+8r5c5, +8r4c3, with the related four chains according to your proposal. They cover extensively all the pairs and bivalue cells of the BUG-lite.

My turn to raise the question: does that make any sense?

[SpAce]

Why do things simple when you can do them complex ?

I hear you

I suspected that with its 14 candidates in digit 7, this puzzle had many other oddagons. I started searching 5-links , then 7-links but found only some with uneasy sets of guardians. And spotting the 9-links, I found it funny and stop searching others.

It was both funny and interesting, so it was good! Mine was simpler but so "normal" that it didn't really add much value.

In more complex solutions, there was also DP(47) r1c27, r2c47, r3c26, r4c46 with four guardians 9r1c7, 8r2c4, 8r4c4, 6r4c6

Indeed. I originally considered both that and your DP(48) because they were the first patterns that caught my eye in this puzzle. Yet I ended up using the HBUG because of the ongoing discussion. Glad you produced solutions with both of those DPs! (Btw, are they examples of Unique Loops (UL)? "DP" is such a generic name that it would be nice to have a bit more specific one for such simple patterns with only two digits (basically extended URs). Even "BUG-Lite" seems like a too generic name for them.)

Combining this DP(47) with DP(48) of my first post, one get's a MUG (478) b12345, also with four guardians: 9r1c7, 3r4c3, 6r4c6, 6r5c5

That would have actually been my preference because it's always nice to combine things into a MUG (though it's easy to make mistakes, so I'm not very confident with them). However, I gave up on that because it didn't produce a useful set of guardians. Note that the 6r4c6,6r5c5 are natively strongly linked, and so are the externals 78r6c4, so there's not much point in using the others or the combo DP at all, I'm afraid.

a separate response to another subject. ... To me, yes that makes sense. In the set of internals listed by blue, 4r4c4 is AIC-resistant (I need a kraken, as well as blue). So you suggest to replace it by the externals of the pair (78)r46c4 in c4. Instead of five internal guardians, you have six mixed guardians (no concern with replacing 4r1c7 by 7r2c7). Now I noticed that 7r2c4 and 8r2c4 have the same parity as 7r4c6 and 8r5c5 respectively. De facto, 7r4c6 and 8r5c5 are external guardians of the pair (78)r46c4 in b5. So I suggest to eventually keep as guardians of this BUG-lite+5 the following four (mixed externals-internals) guardians: #7r2c7, #+7r4c6, #+8r5c5, +8r4c3, with the related four chains according to your proposal. They cover extensively all the pairs and bivalue cells of the BUG-lite.

My turn to raise the question: does that make any sense?

Yes, it makes perfect sense to me. Thank you, Cenoman! I wanted to do exactly that myself, but my poor brain was already hurting so I didn't want to push it any further, fearing that I could miss something obvious. But, I gladly agree if you think it does work that way. My only concern is that it gets harder and harder to understand the more such equivalences are used to reduce the set of guardians. It's also more error-prone for the writer.

[Cenoman]

. My only concern is that it gets harder and harder to understand the more such equivalences are used to reduce the set of guardians. It's also more error-prone for the writer.

I agree with this general assertion. Care should be taken not to push the process too far.

Nevertheless, I see a nuance between the present case and previous examples. In previous examples, one guardian was discarded because demonstrated (with a chain) to have the same parity as an other one.
In the current BUG+5, choosing the set of four guardians #7r2c7, #+7r4c6, #+8r5c5, +8r4c3 is not "reducing the set of guardians" The double symbol #+ in front of 7r4c6 & 8r5c5 draws attention on their role of double guardians. Posting such a solution could be accompanied of a sentence about the comprehensive pattern covering by the set of guardians.