The New Sudoku Players' Forum

[SteveG48]

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 *-----------*
 |...|6..|..8|
 |.9.|..8|.73|
 |81.|2.3|...|
 |---+---+---|
 |6..|...|.5.|
 |58.|...|.19|
 |.3.|...|..6|
 |---+---+---|
 |...|8.2|.97|
 |94.|5..|.3.|
 |3..|..1|...|
 *-----------*


[Cenoman]

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 +-------------------+------------------------+-------------------+
 |  47    5    3     |  6       1479    479   |  19     2    8    |
 |  24    9    246   |  14      145     8     |  156    7    3    |
 |  8     1    67    |  2       579     3     |  569    46   45   |
 +-------------------+------------------------+-------------------+
 |  6    a27   19    |  13479*  12489   49    |  2378*  5    24   |
 |  5     8   b247   |  347*    246     46    |  237*   1    9    |
 |  24-7  3    19    |  1479    12489   5     |  278    48   6    |
 +-------------------+------------------------+-------------------+
 |  1     6    5     |  8       3       2     |  4      9    7    |
 |  9     4    28    |  5       67      67    |  28     3    1    |
 |  3     27   278   |  49      49      1     |  56     68   25   |
 +-------------------+------------------------+-------------------+

UR(37)r45c47 using externals: (7)r4c2 == r5c3 => -7 r6c1; ste

[P.O.]

basics:

Hidden Text: Show

Code: Select all

( n1r7c1   n1r8c9   n3r7c5   n3r1c3   n4r7c7 )

intersections:
 ((((6 0) (7 2 7) (5 6)) ((6 0) (9 2 7) (2 5 7)))
 (((5 0) (9 7 9) (2 5 6 8)) ((5 0) (9 9 9) (2 5)))
 ( n5r6c6   n5r1c2   n6r7c2   n5r7c3 ))

PAIR ROW: ((8 5 8) (6 7)) ((8 6 8) (6 7)) 
(((8 3 7) (2 7 8)) ((8 7 9) (2 6 8)) ((9 4 8) (4 7 9)) ((9 5 8) (4 6 7 9)))

intersection:
((((7 0) (4 4 5) (1 3 4 7 9)) ((7 0) (5 4 5) (3 4 7)) ((7 0) (6 4 5) (1 4 7 9))))

TRIPLET BOX: ((4 2 4) (2 7)) ((5 3 4) (2 4 7)) ((6 1 4) (2 4 7))
(((4 3 4) (1 2 4 7 9)) ((6 3 4) (1 2 4 7 9)))

QUAD COL: ((4 7 6) (2 3 7 8)) ((5 7 6) (2 3 7)) ((6 7 6) (2 7 8)) ((8 7 9) (2 8))
(((1 7 3) (1 2 9)) ((2 7 3) (1 2 5 6)) ((9 7 9) (2 5 6 8)))

( n2r1c8 )

intersection:
((((4 0) (3 8 3) (4 6)) ((4 0) (3 9 3) (4 5))))

X-WING COL: n2 (2 9) (4 9)
(((4 5 5) (1 2 4 8 9)) ((4 7 6) (2 3 7 8)) ((9 3 7) (2 7 8)))


Code: Select all

4r145c6 => r6c1 <> 7
 r1c6=4 - r1c1{n4 n7}
 r4c6=4 - r4c9{n4 n2} - r4c2{n2 n7}
 r5c6=4 - r4n4{c456 c9} - r6n4{c8 c1}
 
ste.


[jco]

After basics

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.--------------------------------------------------------------------.
| 47     5      3      | 6      1479   479    | 19     2      8      |
| 24     9      246    | 14     145    8      | 156    7      3      |
| 8      1     b67     | 2      579    3      | 569   b46    b45     |
|----------------------+----------------------+----------------------|
| 6      27     19     | 13479  12489  49     | 2378   5      24     |
| 5      8      247    | 347    246    46     | 237    1      9      |
| 247    3      19     | 1479   12489  5      | 278    48     6      |
|----------------------+----------------------+----------------------|
| 1      6      5      | 8      3      2      | 4      9      7      |
| 9      4      28     | 5      67     67     | 28     3      1      |
| 3     a27     28-7   | 49     49     1      | 56     68    a25     |
'--------------------------------------------------------------------'

1. (7=25)r9c29 - (5=467)r3c389 => -7 r9c3; [20 placements and NP(47)r1c16]
----

Code: Select all

.--------------------------------------------------.
|c47   5    3    | 6    19  d47   | 19   2    8    |
| 2    9    46   | 1-4  5    8    | 16   7    3    |
| 8    1    67   | 2    79   3    | 69   4    5    |
|----------------+----------------+----------------|
| 6    2    1    | 37   8    9    | 37   5    4    |
| 5    8    47   | 347  26   6-4  | 237  1    9    |
|b47   3    9    |a147  12   5    | 27   8    6    |
|----------------+----------------+----------------|
| 1    6    5    | 8    3    2    | 4    9    7    |
| 9    4    2    | 5    67   67   | 8    3    1    |
| 3    7    8    | 9    4    1    | 5    6    2    |
'--------------------------------------------------'

2. Skyscraper (4): r6c4 = r6c1 - r1c1 = r1c6 => -4 r2c4, r4c6; ste

[SteveG48]

Mine was basically to same as P.O.'s:

Code: Select all

 *--------------------------------------------------------------------*
 |a47     5      3      | 6      1479  b479    | 19     2      8      |
 | 24     9      246    | 14     145    8      | 156    7      3      |
 | 8      1      67     | 2      579    3      | 569    46     45     |
 *----------------------+----------------------+----------------------|
 | 6    ce27     19     | 13479  12489 c49     | 2378   5     c24     |
 | 5      8     e247    | 347    246   d46     | 237    1      9      |
 | 24-7   3      19     | 1479   12489  5      | 278    48     6      |
 *----------------------+----------------------+----------------------|
 | 1      6      5      | 8      3      2      | 4      9      7      |
 | 9      4      28     | 5      67     67     | 28     3      1      |
 | 3      27     278    | 49     49     1      | 56     68     25     |
 *--------------------------------------------------------------------*


[(7=4)r1c1 - r1c6 = (427)r4c269] = 4r5c6 - (4=27)b4p26 => -7 r6c1 ; ste

[SteveG48]

I like Cenoman's use of the UR, and it brings up a question. The use of a double = to indicate a derived strong link is well accepted. Is a double - to indicate a derived weak link also used? I'd like to write the solution as:

7r4c2 = r4c47 -- r5c47 = 7r5c3. Or better yet, 7r4c2 = r4c47 -[UR]- r5c47 = 7r5c3 . Is this ever done?

[Cenoman]

No objection to use double - , to indicate a derived weak link. But I know quite no opportunity to do so. The main derived weak links embedded in AICs are those provided by AHS's (Almost Hidden Sets). For AHS's, using ALS writing rules needs no specific symbol for their weak link.

I'd be careful with derived weak links between groups such as 7r4c47 and 7r5c47; 7r4c47 is a shortcut for 7r4c4|7r4c7 (similar for r5c47) Writing that those groups are in a weak link means: "if one is True, the other is False" If 7r4c4 is True, there is no native weak link to infer that 7r5c7 is False (similar for each 7 in the UR)

In the present puzzle they are in a weak link, by derivation of the UR strong link between the guardians themselves:
7r4c47 - 7r4c2 =UR= 7r5c3 - 7r5c47
But such a configuration: two guardians only, in the "long" edges of the rectangle (I mean the edges not in mini-lines), and moreover both in the same box is IMHO rather infrequent. So I surmise that such a derived weak link is not an intrinsic feature of DP patterns, whereas derived strong links are (between elements of a comprehensive set of guardians, whether internals, externals or mixed)

Using double - could be helpful to avoid repetition of the same (long) weak link subchain in krakens, nets, or even in a long sequence of moves using it several times. I have never done so, and I cannot remember seeing it.

[SteveG48]

Good points. Thanks.