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[ArkieTech]

Code: Select all

 *-----------*
 |.58|.32|...|
 |.37|..4|...|
 |2..|9..|...|
 |---+---+---|
 |.9.|1..|.3.|
 |..1|.2.|9..|
 |.4.|..6|.5.|
 |---+---+---|
 |...|..9|..2|
 |...|7..|36.|
 |...|24.|71.|
 *-----------*


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[Ngisa]

Code: Select all

+-------------------+-------------------+-------------------+
| 4       5     8   | 6      3      2   | 1       9     7   |
| 9       3     7   |e58     1      4   | 68-5    2     568 |
| 2       1     6   | 9     d578   d578 |cb458   b48    3   |
+-------------------+-------------------+-------------------+
| 568     9     25  | 1      578    578 | 2468    3     468 |
| 35      68    1   | 4      2      35  | 9       7     68  |
| 7       4     23  | 38     9      6   | 28      5     1   |
+-------------------+-------------------+-------------------+
| 1       7     345 | 38-5   6      9   |a458    b48    2   |
| 58      2     49  | 7      58     1   | 3       6     49  |
| 3568    68    359 | 2      4      358 | 7       1     589 |
+-------------------+-------------------+-------------------+


(5)r7c7 = UR(48)r37c78 - (48=5)r3c7 - r3c56 = (5)r2c4 => - 5r2c7,r7c4; stte

Clement

[SpAce]

Code: Select all

                     c                  c      c
  .---------------.------------------.-----------------.
  | 4     5   8   |  6     3     2   |  1      9   7   |
  | 9     3   7   |  5-8   1     4   |  568    2   568 |
b | 2     1   6   |  9    *578  *578 | *458   *48  3   |
  :---------------+------------------+-----------------:
  | 68    9   25  |  1     578   578 |  2468   3   468 |
  | 35    68  1   |  4     2     35  |  9      7   68  |
b | 7     4   23  | *38    9     6   | *28     5   1   |
  :---------------+------------------+-----------------:
b | 1     7   345 | *358   6     9   | *458   *48  2   |
  | 58    2   49  |  7     58    1   |  3      6   49  |
  | 3568  68  359 |  2     4     358 |  7      1   589 |
  '---------------'------------------'-----------------'

Swordfish 3x4: (8)r367\c478b2 => -8 r2c4; stte

[SpAce]

(5)r7c7 = UR(48)r37c78 - (48=5)r3c7 - r3c56 = (5)r2c4 => - 5r2c7,r7c4; stte

Hi Clement! That's a very nice solution! I'm kind of pissed that I didn't see that myself I'd just change a couple of things in your notation:

1. (48=5)r3c7 should be (4|8=5)r3c7. You've been advised about that by many people on many occasions, but you refuse to accept that fact. Why? The way you write those cases is logically wrong as per the conventions followed here, and I for one have explained the reason to you. I know it's a bit unintuitive but it's still true. You'd improve your notation style a lot if you fixed that simple thing.

2. UR(48)r37c78 is a bit ambiguous (partly because URs are, so it's not all your fault). If you're using a UR as a normal boolean term in an AIC, you should mention the specific UR type (in this case Type 1). Otherwise the surrounding links don't make sense. So, one way to write your chain correctly could be something like this:

(5)r7c7 = [UR Type 1 (48)r37c78] - (4|8=5)r3c7 - r3c56 = (5)r2c4

Most of us use URs a bit differently, though, as a kind of an explanation to a derived link (i.e. not as a boolean term by itself). Then you don't have to worry about the type, and it's often simpler anyway. One way to do it like that here could be this (note the '=' on both sides, without spaces; it's still a single strong link, but with an inlined explanation):

(5)r7c7 =UR(48)r37c78= (5)r3c7 - r3c56 = (5)r2c4

or more simply (since the UR pattern is pretty easy to see on the grid):

(5)r7c7 =UR= (5)r3c7 ...

Or the "Cenoman style" (external explanation for the derived link):

UR (48)r37c78 using internals:

(5)r7c7 == (5)r3c7 ...

Edit: corrected typo

[Cenoman]

Code: Select all

 +--------------------+--------------------+--------------------+
 |  4      5    8     |  6     3     2     |  1      9    7     |
 |  9      3    7     |  5-8*  1     4     |  568*   2   a568#  |
 |  2      1    6     |  9     578   578   | b458#   48*  3     |
 +--------------------+--------------------+--------------------+
 |  68     9    25    |  1     578   578   |  2468   3    468   |
 |  35     68   1     |  4     2     35    |  9      7    68    |
 |  7      4    23    |da38#   9     6     | c28     5    1     |
 +--------------------+--------------------+--------------------+
 |  1      7    345   |zD358*  6     9     | b458#   48*  2     |
 |  58     2    49    |  7     58    1     |  3      6    49    |
 |  3568   68   359   |  2     4     358   |  7      1    589   |
 +--------------------+--------------------+--------------------+

In the 8s, 5-link-oddagon (*) having four guardians (#)
(8)r2c9|r6c4 == (8)r3c7|r7c7 - r6c7 = (8)r6c4 => -8 r2c4; ste