The New Sudoku Players' Forum

[morl]

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..2|.5.|3..
.4.|1.3|.9.
3..|4.2|..1
---+---+---
.76|...|82.
1..|...|..6
.35|...|41.
---+---+---
7..|3.6|..8
.9.|8.5|.7.
..3|.7.|1..

..2.5.3...4.1.3.9.3..4.2..1.76...82.1.......6.35...41.7..3.6..8.9.8.5.7...3.7.1..

[SpAce]

Hidden Text: Show

Original, faulty, attempt:

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.------------------------.------------------.------------------------.
|  j68+9*   1        2   | 679   5     789  |  3       68*      4    |
|   568^    4        78  | 1     68    3    |  2567^   9        257^ |
|   3      j68+5*^  i789 | 4     689   2    | a67#5   j68+5*^   1    |
:------------------------+------------------+------------------------:
|   4       7        6   |d59    3     1    |  8       2      fc59   |
|   1       28      h89  | 2579  2489  4789 |gb579     3        6    |
|   289     3        5   | 2679  2689  789  |  4       1       f79   |
:------------------------+------------------+------------------------:
|   7      (2)5^     14  | 3     1249  6    |  259^    45^      8    |
|k(+6)-2    9        14  | 8     14    5    |  26      7        3    |
|   68+25*  68+25*   3   |d29    7     49   |  1       456^    e259  |
'------------------------'------------------'------------------------'

Almost-X-Chain(5)(^) & BUG-Lite(68)(*) using mixed internals/externals

[(5)r7c7 = r79c8 - r3c8 =#= r2c79 - r2c1 = (5)r3c2] - (5=2)r7c2
||
(5*)r3c7 - r5c7 = r4c9^ - (5=92)r49c4 - (2|^5=9)r9c9 - r46c9 = r5c7 - r5c3 = r3c3 - (9|*5)r1c1,r3c28 =DP[68]= (6)r8c1

=> -2 r8c1; stte

Edit: S**t. I just realized that my solution had an obvious mistake! It seems that I'd ignored the (5)r9c9 as another spoiler to the X-Chain. Back to the drawing board.

Edit2: Fortunately that wasn't too hard to fix... I think.

Code: Select all

.----------------------------.------------------.------------------------.
|  j68+9*      1         2   | 679   5     789  |  3       68*      4    |
|   568^       4         78  | 1     68    3    |  2567^   9        257^ |
|   3         j68+5*^   i789 | 4     689   2    | a67#5   j68+5*^   1    |
:----------------------------+------------------+------------------------:
|   4          7         6   |d59    3     1    |  8       2      fc59   |
|   1          28       h89  | 2579  2489  4789 |gb579     3        6    |
|   289        3         5   | 2679  2689  789  |  4       1       f79   |
:----------------------------+------------------+------------------------:
|   7         (2)5^      14  | 3     1249  6    |  259^   A45^      8    |
|k(+6)-2       9         14  | 8     14    5    |  26      7        3    |
|  B68+(2)5*  B68+(2)5*  3   |d29    7     49   |  1      A456^   Ae29#5 |
'----------------------------'------------------'------------------------'

Almost-almost-X-Chain(5)(^) & BUG-Lite(68)(*) using mixed internals/externals

[(5)r7c7 =#= r79c8 - r3c8 =#= r2c79 - r2c1 = (5)r3c2] - (5=2)r7c2
||
(5*)r3c7 - r5c7 = r4c9^ - (5=92)r49c4 - (2|^5=9)r9c9 - r46c9 = r5c7 - r5c3 = r3c3 - (9|*5)r1c1,r3c28 =DP[68]= (6)r8c1
||
(546)b9p928 - (5|6=82)r9c12

=> -2 r8c1; stte

[Cenoman]

A bit out of the rules, in three steps using uniqueness techniques (including SpAce's DP)

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 +----------------------+-----------------------+---------------------+
 |  689*   1      2     |  679    5      789    |  3      68*   4     |
 |  568    4      78    |  1      68     3      |  2567   9     257   |
 |  3      568*   789   |  4      689    2      |  567    568*  1     |
 +----------------------+-----------------------+---------------------+
 |  4      7      6     |  59     3      1      |  8      2     59    |
 |  1      28     89    |  2579   2489   4789   |  579    3     6     |
 |  289    3      5     |  2679   2689   789    |  4      1     79    |
 +----------------------+-----------------------+---------------------+
 |  7      25     14    |  3      1249   6      |  259    45    8     |
 |  26     9      14    |  8      14     5      |  26     7     3     |
 |  2568*  2568*  3     |  29     7      49     |  1      456   259   |
 +----------------------+-----------------------+---------------------+

1. UR(14)r78c35 => -14r7c5

2a. DP(68)b1p18, r13c8, r9c12 using internals b1 (9r1c1, 5r3c2) and single external 6r9c8 (common to r9 and c8 pairs)
(9)r1c1
(6)r9c8 - r8c7 = (6)r8c1
(5)r3c2 - (5=2)r7c2 - (2=6)r8c1
=> -6 r1c1

2b. same DP, same guardians
(9)r1c1
(6)r9c8 - (6=8)r1c8
(5-6)r3c2 = (6-8)r9c2 = (8)r9c1
=> -8 r1c1; ste

[SpAce]

A bit out of the rules, in three steps using uniqueness techniques (including SpAce's DP)

Very nice, once again! I think it could be counted as a two-stepper, because the latter part could be written as a single split-node kraken. I don't think it even gets too messy that way. For example:

Step 2:

(9)r1c1
||
(6)r9c8 - r8c7,r9c2 = (68)r8c1,r1c8
||
(5)r3c2 - (5=28)r75c2 - (2|8)r8c1,r9c2 = (68)r89c1

=> -6|8 r1c1; stte

[Cenoman]

I think it could be counted as a two-stepper, because the latter part could be written as a single split-node kraken. I don't think it even gets too messy that way. For example:

Step 2:

(9)r1c1
||
(6)r9c8 - r8c7,r9c2 = (68)r8c1,r1c8
||
(5)r3c2 - (5=28)r75c2 - (2|8)r8c1,r9c2 = (68)r89c1

=> -6|8 r1c1; stte

Hi SpAce,
I'm not that fond of split nodes. I'd prefer this other way (an almost skyscraper) to get the same result (r1c1=9)

1. UR(14)r78c35 => -14r7c5; 2 placements & basics

2. DP(68)b1p18, r13c8, r9c12 using internals b1 (9r1c1, 5r3c2) and single external 6r9c8 (common to r9 and c8 pairs)
(9)r1c1
(5)r3c2 - (5=2)r7c2 - r5c2 = (2)r6c1
(6)r9c8 - [SS(6)r8c7=r8c1-r1c1==r1c8] = (6)r1c4 - (68=9)r1c18
=> -9 r6c1; ste

[eleven]

A bit out of the rules ...

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     +----------------------+-----------------------+---------------------+
     | #68+9   1      2     |  67-9   5      78-9   |  3     #68    4     |
     |  568    4      78    |  1      68     3      |  2567   9     257   |
     |  3     b68+5   78-9  |  4     e68+9   2      |  567   d68+5  1     |
     +----------------------+-----------------------+---------------------+
     |  4      7      6     |  59     3      1      |  8      2     59    |
     |  1      28     89    |  2579   2489   4789   |  579    3     6     |
     |  289    3      5     |  2679   2689   789    |  4      1     79    |
     +----------------------+-----------------------+---------------------+
     |  7     a25     14    |  3      1249   6      |  259   c45    8     |
     | #26     9      14    |  8      14     5      | #26     7     3     |
     |  2568   2568   3     |  29     7      49     |  1    c#456   259   |
     +----------------------+-----------------------+---------------------+

Same step 1: UR 14 (in my eyes simpler than some basics)

Note, that if 9 is missing in r1c1, not both r8c1 and r9c8 can be 6 (else two 8's in row 1). In this case none of them can be 6, because one forces the other.
So we have 9r1c1 or ((2r8c1 -> 5r7c2) and 5r79c8) => 68r3c28 -> 9r3c5 => -9r1c46,r3c3

Maybe SpAce likes to express that in a chain

Ah, i can do that myself:
Almost turbot fish 6 r1c18,r8c17,r9c8 -> -6r8c1,r9c8, i.e. 2r8c1 & 45r79c8
9r1c1 == 5r7c2,r8c1 & 45r79c8 - (5=9)r3c258 => -9r1c46,r3c2

(but who would understand that ?)

[SpAce]

Same step 1: UR 14 (in my eyes simpler than some basics)

Definitely easier to spot than triples or quads in almost all cases.

Note, that if 9 is missing in r1c1, not both r8c1 and r9c8 can be 6 (else two 8's in row 1). In this case none of them can be 6, because one forces the other.
So we have 9r1c1 or ((2r8c1 -> 5r7c2) and 5r79c8) => 68r3c28 -> 9r3c5 => -9r1c46,r3c3

Maybe SpAce likes to express that in a chain

I would have had to, because otherwise I wouldn't understand it Fortunately you (partly) saved me from the trouble:

Ah, i can do that myself:
Almost turbot fish 6 r1c18,r8c17,r9c8 -> -6r8c1,r9c8, i.e. 2r8c1 & 45r79c8
9r1c1 == 5r7c2,r8c1 & 45r79c8 - (5=9)r3c258 => -9r1c46,r3c2

(but who would understand that ?)

Well... I read your first explanation several times without really grasping your logic. The chain, however, made it easy. It'd be even easier for me to see it all in one package:

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.---------------------.--------------------.-------------------.
|ca68(9)*  1     2    |b7#6-9  5     b78-9 |  3      c68*  4   |
|  568     4     78   | 1      68     3    |  2567    9    257 |
|  3      h568   78-9 | 4     h68(9)  2    |  567    h568  1   |
:---------------------+--------------------+-------------------:
|  4       7     6    | 59     3      1    |  8       2    59  |
|  1       28    89   | 2579   2489   4789 |  579     3    6   |
|  289     3     5    | 2679   2689   789  |  4       1    79  |
:---------------------+--------------------+-------------------:
|  7     gf25    14   | 3      29     6    |  259    g45   8   |
|ed26      9     14   | 8      14     5    |ec26*     7    3   |
|  2568    2568  3    | 29     7      49   |  1    gfc456* 259 |
'---------------------'--------------------'-------------------'

(9)r1c1 = (97-6)r1c46 = [(6)r1c1=#=r1c8-r9c8=(6)r8c7] - r8c1 = (2,6)r8c17 - (2|6)r7c2,r9c8 = (5)r7c2&(45)r79c8 - (5=689)r3c285 => -9 r1c46,r3c3

PS. About naming conventions. Your Turbot Fish could also be seen as an Empty Rectangle, but is it more common to call it just a Turbot Fish when there are only two members in the hinge box? Personally I'd rather call it ER just because Turbot Fish is a less specific term (covering Skyscrapers and Kites as well). Am I in the minority, though? Hodoku, for example, would not call it ER by default (but it's an option which I've turned on).