The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |7.1|...|9..|
 |.8.|...|.2.|
 |9..|..6|1.7|
 |---+---+---|
 |...|4.9|7..|
 |...|...|...|
 |..2|6.3|...|
 |---+---+---|
 |5.4|8..|..1|
 |.3.|...|.6.|
 |..9|...|4.5|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*---------------------------------------------------------------*
| 7     2456c  1     | 235  23458  458 | 9      f3458   3468d   |
| 346   8      356   | 179  179    17  | 356     2       346    |
| 9     245    35    | 235  23458  6   | 1      f3458    7      |
|--------------------+-----------------+------------------------|
| 1368  156    3568  | 4    1258   9   | 7       1358    2368   |
| 13468 145679 35678 | 1257 12578  58  | 23568   134589  234689 |
| 148   14579  2     | 6    1578   3   | 58      14589   489    |
|--------------------+-----------------+------------------------|
| 5     67b    4     | 8    3679  b27  | 23     a39-7a   1      |
| 128   3      78    | 1579 14579  45  | 28      6       289    |
|d1268  167    9     | 137  1367  c127 | 4      e378     5      |
*---------------------------------------------------------------*

Kraken Box 3 Digit 8:  (Read from right to left)

7 r7c8 - (7=2) r7c6 - r9c6 = (2-8) r9c1 = r9c8 - 8 r13c8;

7 r7c8 - (7=6) r7c2 - r1c2 = 6r1c9             - 8 r1c9;

Leren

[SpAce]

Code: Select all

.------------------------.------------------.-----------------------.
|  7       2456    1     | 235   23458  458 | 9      3458    3468   |
|  346     8       356   | 179   179    17  | 356    2       346    |
|  9       245     35    | 235   23458  6   | 1      3458    7      |
:------------------------+------------------+-----------------------:
|  1368    156     3568  | 4     1258   9   | 7      1358    2368   |
|  13468   145679  35678 | 1257  12578  58  | 23568  134589  234689 |
|  148     14579   2     | 6     1578   3   | 58     14589   489    |
:------------------------+------------------+-----------------------:
|  5       6-7     4     | 8     3679   27  | 23    b3(7)9   1      |
|  128     3      a[78]  | 1579  14579  45  | 28     6       289    |
| a126[8]  167      9    | 137   1367   127 | 4     b3(78)   5      |
'------------------------'------------------'-----------------------'

M-Wing:

(78)b7p67 = (87)r97c8 => -7 r7c2; btte (1 PP)

as a simple chain: Show

(7=8)r8c3 - r9c1 = (8-7)r9c8 = (7)r7c8 => -7 r7c2; btte

[SpAce]

Code: Select all

Kraken Box 3 Digit 8:  (Read from right to left)

7 r7c8 - (7=2) r7c6 - r9c6 = (2-8) r9c1 = r9c8 - 8 r13c8;
7 r7c8 - (7=6) r7c2 - r1c2 = 6r1c9             - 8 r1c9;

Ignoring your perverse way of printing krakens, why would you write a two-way kraken in the first place? It reminds me of the SudokuWiki solver's confusing Digit Forcing Chains and two-way Nishios which could all be written as normal AICs. Just like yours which happens to be a loop too:

(7=6)r7c2 - r1c2 = (6-8)r1c9 = r13c8 - r9c8 = (8-2)r9c1 = r9c6 - (2=7)r7c6 - loop

=> -7 r7c58, -6 r459c2, -34 r1c9, -8 r456c8, -16 r9c1; stte

[eleven]

I looked for a loop in the "SK cells":

Code: Select all

 *--------------------------------------------------------------------------------*
 |  7      *2456     1       |  235    23458   458   |  9      #3458     68-34    |
 | #346     8       #356     |  179    179     17    | *356     2       *346      |
 |  9       245      35      |  235    23458   6     |  1      #3458     7        |
 |---------------------------+-----------------------+----------------------------|
 |  1368    15-6     3568    |  4      1258    9     |  7       135-8    2368     |
 |  13468   14579-6  35678   |  1257   12578   58    |  23568   13459-8  234689   |
 |  148     14579    2       |  6      1578    3     |  58      1459-8   489      |
 |---------------------------+-----------------------+----------------------------|
 |  5      #67       4       |  8      3679    27    |  23      379      1        |
 |  12-8    3       *78      |  1579   14579   45    | #28      6       #289      |
 |  1268    1-67     9       |  137    1367    127   |  4      *378      5        |
 *--------------------------------------------------------------------------------*

6r1c2 = 6r2c13 - (6=3458)r2c79,r13c8 - 8r9c8 = r8c79 - (8=7)r8c13 - (7=6)r79c2, loop
=> -34r1c9, -8r456c8, -8r8c1, -7r9c2, -6r349c2; stte

[Ngisa]

Code: Select all

+------------------------+----------------------+-------------------------+
| 7       2456     1     | 235     23458    458 | 9       3458     3468   |
| 346     8        356   | 179     179      17  | 356     2        346    |
| 9       245      35    | 235     23458    6   | 1       3458     7      |
+------------------------+----------------------+-------------------------+
| 1368    156      3568  | 4       1258     9   | 7       1358     2368   |
| 13468   145679   35678 | 1257    12578    58  | 23568   134589   234689 |
| 148     14579    2     | 6       1578     3   | 58      14589    489    |
+------------------------+----------------------+-------------------------+
| 5      d6-7      4     | 8      c23679    27  | 23     b379      1      |
| 128     3       a78    | 12579   124579   45  | a28     6       a289    |
| 1268    167      9     | 137     1367     127 | 4       378      5      |
+------------------------+----------------------+-------------------------+


(7=289)r8c379 - (9)r7c8 = (9-6)r7c5 = (6)r7c2 => -7r7c2; btte

Clement

[SpAce]

I looked for a loop in the "SK cells"

That was my first instinct too, after seeing the shape of the givens. Good job finding one! I gave up when I found the short btte solution. Here's my new attempt (around the same theme, but not sticking to the SK-cells):

Code: Select all

.------------------------------.------------------.---------------------------.
|   7          a245[6]   1     | 235   23458  458 | 9     b345(8)  b(6)[8]-34 |
|   346         8        356   | 179   179    17  | 356    2        346       |
|   9           245      35    | 235   23458  6   | 1     b345(8)   7         |
:------------------------------+------------------+---------------------------:
|   1368        15-6     3568  | 4     1258   9   | 7      135-8    2368      |
|   13468       14579-6  35678 | 1257  12578  58  | 23568  13459-8  234689    |
|   148         14579    2     | 6     1578   3   | 58     1459-8   489       |
:------------------------------+------------------+---------------------------:
|   5         d(6)7      4     | 8     3679   27  | 23     379      1         |
|   128         3        78    | 1579  14579  45  | 28     6        289       |
| d[6](8)-12  d(6)17     9     | 137   1367   127 | 4     c37[8]    5         |
'------------------------------'------------------'---------------------------'

(6)r1c2 = (68)b3p328 - r9c8 = (86)b7p728 - loop

=> -34 r1c9, -8 r456c8, -12 r9c1, -6 r45c2; stte

as a simple chain: Show

(6)r1c2 = (6-8)r1c9 = r13c8 - r9c8 = (8-6)r9c1 = (6)r79c2 - loop

=> -34 r1c9, -8 r456c8, -12 r9c1, -6 r45c2; stte

PS. What I really like about your loop (and it's often the case with your loops!) is that it actually needs those multiple eliminations for stte (unlike mine, or the one I extracted from Leren's solution, both of which would work just as well as normal chains with a single elimination). If I understand correctly, yours needs three from the elimination list: -8 r8c1 and -67 r9c2.

I think it adds value to a loop, because it means that the looping structure is actually significant. Such multi-elimination solutions (where no single elimination works by itself) are harder to find and recognize as such anyway. What's your secret formula for producing them on a regular basis?

[eleven]

What's your secret formula for producing them on a regular basis?

It's not secret, Mathimagics shows it in his avatar: e^(i*pi) + 1 = 0

[SpAce]

What's your secret formula for producing them on a regular basis?

It's not secret, Mathimagics shows it in his avatar: e^(i*pi) + 1 = 0

That explains! I use: P(A|B) = (P(B|A) * P(A)) / P(B). Not so elegant and often produces unintuitive results