The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|3.2|...|
 |...|4.5|...|
 |..9|.7.|6..|
 |---+---+---|
 |.5.|...|.4.|
 |..3|7.1|9..|
 |9..|...|..2|
 |---+---+---|
 |8..|...|..5|
 |..7|.3.|4..|
 |.3.|...|.8.|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*------------------------------------------------*
| 1467 167  5   | 3   69   2    | 8   179   1479 |
| 1367 1678 168 | 4   69   5    | 2   1379  1379 |
| 234  24   9   | 1   7    8    | 6   5     34   |
|---------------+---------------+----------------|
| 167  5    168 |a29  28  b3-9  | 137 4     137  |
| 24   24   3   | 7   5    1    | 9   6     8    |
| 9    178  18  | 6   48   34   | 5   137   2    |
|---------------+---------------+----------------|
| 8    169  24  | 2-9 124  4679 | 137 1379  5    |
| 5    169  7   | 8   3   c69   | 4   2    d169  |
| 16   3    24  | 5   124 f4679 | 17  8    e1679 |
*------------------------------------------------*

(9) r4c4 = r4c6 - (9=6) r8c6 - r8c9 = (6-9) r9c9 = (9) r9c6 => - 9 r4c6, r7c4; stte

Leren

[SpAce]

Code: Select all

.-----------------.--------------------.----------------------.
| 1467  167   5   | 3    69     2      | 8    179    1479     |
| 1367  1678  168 | 4    69     5      | 2    1379   1379     |
| 234   24    9   | 1    7      8      | 6    5      34       |
:-----------------+--------------------+----------------------:
| 167   5     168 | 29   28     3-9    | 137  4      137      |
| 24    24    3   | 7    5      1      | 9    6      8        |
| 9     178   18  | 6    48     34     | 5    137    2        |
:-----------------+--------------------+----------------------:
| 8     169   24  | 2-9  124    467-9  | 137  1379   5        |
| 5     19-6  7   | 8    3    a(6)[9]  | 4    2     a1[6]9    |
| 16    3     24  | 5    124   b467(9) | 17   8    b(6)[9]-17 |
'-----------------'--------------------'----------------------'

M-Ring:

(9,6)r8c69 = (6,9)r9c96 - loop => -9 r4c6,r7c46; -6 r8c2, -17 r9c9; stte

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 1467  167   5     | 3     69    2     | 8     179   1479  |
 | 1367  1678  168   | 4     69    5     | 2     1379  1379  |
 | 234   24    9     | 1     7     8     | 6     5     34    |
 *-------------------+-------------------+-------------------|
 | 167   5     168   | 29    28    39    | 137   4     137   |
 | 24    24    3     | 7     5     1     | 9     6     8     |
 | 9     178   18    | 6     48    34    | 5     137   2     |
 *-------------------+-------------------+-------------------|
 | 8    a169   24    | 2-9   124   467-9 |d137  d1379  5     |
 | 5    b169   7     | 8     3    c69    | 4     2    c169   |
 | 16    3     24    | 5     124   4679  |d17    8     1679  |
 *-----------------------------------------------------------*


9r7c2 = r8c2 - (9=16)r8c69 - (1=379)b9p127 => -9 r7c46 ; stte

Or, slightly shorter,

9r7c2 = (9-1)r8c2 = (1379)b9p1267 => -9 r7c46

[SpAce]

Hi Steve,

9r7c2 = r8c2 - (9=16)r8c69 - (1=379)b9p127 => -9 r7c46 ; stte

This works, but it's also a loop, so you could get more eliminations (not that they're needed). I count at least -6 r8c2, -17 r9c9, which were also included in my loop.

Or, slightly shorter,

9r7c2 = (9-1)r8c2 = (1379)b9p1267 => -9 r7c46

The last node has multiple possible digit arrangements and not all of them work as intended. As you know, my fix would be a comma: (137,9)b9p6172 or (1,379)b9p6172. Since I know you don't like that option, the best approach is the normal way:

Code: Select all

9r7c2 = (9-1)r8c2 = r8c9 - (1=379)b9p126 - loop => -9 r7c46, -6 r8c2, -17 r9c9

or shorter and simpler (my preference):

Code: Select all

(9)r7c2 = (91-6)r8c29 = (69)b9p92 - loop => -9 r7c46, -6 r8c2, -17 r9c9

or shortest but not simplest:

Code: Select all

(9,1)r78c2 = (16,9)b9p692 - loop => -9 r7c46, -6 r8c2, -17 r9c9

[SteveG48]

Code: Select all

.-----------------.--------------------.----------------------.
| 1467  167   5   | 3    69     2      | 8    179    1479     |
| 1367  1678  168 | 4    69     5      | 2    1379   1379     |
| 234   24    9   | 1    7      8      | 6    5      34       |
:-----------------+--------------------+----------------------:
| 167   5     168 | 29   28     3-9    | 137  4      137      |
| 24    24    3   | 7    5      1      | 9    6      8        |
| 9     178   18  | 6    48     34     | 5    137    2        |
:-----------------+--------------------+----------------------:
| 8     169   24  | 2-9  124    467-9  | 137  1379   5        |
| 5     19-6  7   | 8    3    a(6)[9]  | 4    2     a1[6]9    |
| 16    3     24  | 5    124   b467(9) | 17   8    b(6)[9]-17 |
'-----------------'--------------------'----------------------'

M-Ring:

(9,6)r8c69 = (6,9)r9c96 - loop => -9 r4c6,r7c46; -6 r8c2, -17 r9c9; stte

Oooh, that's nice. Still, I think it would be easier to follow if you wrote it (9=6)r8c6 - r8c9 = (6-9)r9c9 = r9c6 loop .

[Ngisa]

Code: Select all

+---------------------+-------------------+---------------------+
| 1467    167     5   | 3     69     2    | 8      179     1479 |
| 1367    1678    168 | 4     69     5    | 2      1379    1379 |
| 234     24      9   | 1     7      8    | 6      5       34   |
+---------------------+-------------------+---------------------+
|b167     5      c168 |e29  d28      39   | 137    4       137  |
| 24      24      3   | 7    5       1    | 9      6       8    |
| 9       178     18  | 6    48      34   | 5      137     2    |
+---------------------+-------------------+---------------------+
| 8      g169     24  |f29   124     4679 | 137    1379    5    |
| 5      h69-1    7   | 8    3       69   | 4      2      i169  |
|a16      3       24  | 5    124     4679 | 7-1    8       1679 |
+---------------------+-------------------+---------------------+


(1=6)r9c1 - r4c1 = (6-8)r4c3 = (8-2)r4c5 = r4c4 - (2=9)r7c4 - r7c2 = (9-1)r8c2 = (1)r8c9 => - 1r8c2,r7c4; stte

Clement

[SteveG48]

9r7c2 = (9-1)r8c2 = (1379)b9p1267 => -9 r7c46
The last node has multiple possible digit arrangements and not all of them work as intended. As you know, my fix would be a comma: (137,9)b9p6172 or (1,379)b9p6172.

Interesting. I'm normally on the lookout for that (especially since I know you're watching ). If you read the chain in the forward direction, the 1 has to be in r8c9 and there is no problem. If you read it in the reverse direction, the chain still works because if (1379) is not true in the node then r8c9 can't be a 1. However, the logic doesn't work because if (1379) is true, then the 9 might not be in the right place.

As you know, my fix would be a comma: (137,9)b9p6172 or (1,379)b9p6172. Since I know you don't like that option, the best approach is the normal way:

Actually, according to your stated preferences, you wouldn't fix it with the comma either, right? You'd use the slightly longer normal way (as would I).

[RSW]

This is the first puzzle I've knowingly encountered with a 7-fish. I was tinkering with my solver program code this week, and just for fun, I changed the search order to start searching for the biggest fish first, to see what it would find.

Code: Select all

    1    2    3     4  5   6      7   8    9     
 +---------------+-------------+---------------+
1| 1467 1467 5   | 3  69  2    | 8   179  1479 |
2| 1367 1678 168 | 4  69  5    | 2   1379 1379 |
3| 1234 124  9   | 1  7   8    | 6   5    34   |
 +---------------+-------------+---------------+
4| 167  5    168 | 29 28  39   | 137 4    137  |
5| 24   24   3   | 7  5   1    | 9   6    8    |
6| 9    178  18  | 6  48  34   | 5   137  2    |
 +---------------+-------------+---------------+
7| 8    169  24  | 29 124 4679 | 137 1379 5    |
8| 5    169  7   | 8  3   69   | 4   2    169  |
9| 16   3    24  | 5  124 4679 | 17  8    1679 |
 +---------------+-------------+---------------+

7-Fish (aka ???): In rows  1 2 4 6 7 8 & 9, digit 1 must go in columns  1 2 3 5 7 8 & 9
Therefore candidate 1 can be removed from all other cells in columns  1 2 3 5 7 8 & 9
Removing candidate 1 from r3c1 r3c2.


Note, this doesn't reduce the puzzle to basics. A further advanced step is needed.

[Leren]

According to the Ultimate Fish Guide here a 7 Fish is called a Leviathan. Leren

[Cenoman]

Code: Select all

 +----------------------+--------------------+----------------------+
 |  1467   167    5     |  3    69    2      |  8     179    1479   |
 |  1367   1678   168   |  4    69    5      |  2     1379   1379   |
 |  234    24     9     |  1    7     8      |  6     5      34     |
 +----------------------+--------------------+----------------------+
 |  167    5      168   |  29   28    39     |  137   4      137    |
 |  24     24     3     |  7    5     1      |  9     6      8      |
 |  9      178    18    |  6    48    34     |  5     137    2      |
 +----------------------+--------------------+----------------------+
 |  8     b169    24    |  29   124  c67-49  | d137  d1379   5      |
 |  5      19-6   7     |  8    3     69     |  4     2      169    |
 | a16     3      24    |  5    24-1  4679   | e17    8      69-17  |
 +----------------------+--------------------+----------------------+

Loop (1=6)r9c1 - r7c2 = (6-7)r7c6 = r7c78 - (7=1)r9c7@ => -1 r9c5, -17 r9c9, -49r7c6, -6r8c2; ste

[RSW]

According to the Ultimate Fish Guide here a 7 Fish is called a Leviathan. Leren

Thanks. I've now added that info to the program.

[SpAce]

M-Ring: (9,6)r8c69 = (6,9)r9c96 - loop => -9 r4c6,r7c46; -6 r8c2, -17 r9c9; stte

Oooh, that's nice. Still, I think it would be easier to follow if you wrote it (9=6)r8c6 - r8c9 = (6-9)r9c9 = r9c6 loop .

I know, and I mostly agree. Yet I have a few reasons (excuses?) why I still do it my way.

reasons 1-3: Show

First, if there's a chance to write something as a one-linker (a symmetric one too), I can't help but take it In this case all but one of the rc-digits were 6 or 9 as well, which made it even more fun. So few patterns can be (easily) written as one-linkers anyway that I think they sort of deserve that distinction.

Second, that longer chain fragment is already included in Leren's solution, so I wouldn't want to repeat it. (Btw, I'm really surprised he, being an M-Wing/Ring specialist, apparently missed the M-Ring possibility this time. Or maybe he was nice enough to leave it for others to find.) Anyway, in general most people write their chains that way, so I don't know how much it would add value if I did too (see next reason).

Third, using (and seeing) tricky expressions regularly makes one used to them. They weren't always easy for me either but with enough practice they've become a second nature. I realize that practicing them is not necessarily fun for the audience, especially when they're not necessary, but it does help when having to write (and read) actually complex AICs. I surely could write some of my chains more simply, but it would limit my own learning. I also think it adds more value if someone provides a bit different kinds of examples showcasing rarer expert features. That being said, I surely don't recommend or wish that everyone starts writing chains like I do. One is probably enough.

Fourth, it's not actually that hard to read. The trick is to focus on the single link and to look into both directions from there, kind of like a kraken:

Code: Select all

(6,9)r8c96         (6)r8c9 - (6=9)r8c6 
|| |          <->  ||           |
(6,9)r9c96         (6-9)r9c9 = (9)r9c6


Looking at it that way is also a good reminder that AICs aren't unidirectional chains. They're static logic structures where each link must work independently and both ways. I know perfectly well that I don't need to tell you any of that, but remembering that perspective might partly help to avoid this too (though I'm definitely not immune to it myself):

9r7c2 = (9-1)r8c2 = (1379)b9p1267 => -9 r7c46
The last node has multiple possible digit arrangements and not all of them work as intended.

Interesting. I'm normally on the lookout for that (especially since I know you're watching ).

I bet! (Though I shouldn't be watching, yet here I still am. How hard can taking a break be??) Anyway, don't worry. I know very well that this particular trap is surprisingly hard to avoid even when you're consciously thinking about it. There are still cases when I can't stop second-guessing myself.

If you read the chain in the forward direction, the 1 has to be in r8c9 and there is no problem. If you read it in the reverse direction, the chain still works because if (1379) is not true in the node then r8c9 can't be a 1. However, the logic doesn't work because if (1379) is true, then the 9 might not be in the right place.

Exactly. This was a tricky case because the strong link actually works, as you say. The real problem is with the following weak link, which is easy to miss because it's not explicitly shown in the chain. The link (1379)b9p1267 - (9)r7c246 doesn't work because the 9 could be in r8c9, just like you said.

Actually, according to your stated preferences, you wouldn't fix it with the comma either, right? You'd use the slightly longer normal way (as would I).

Well, I can't guarantee that because I seem to have a bit conflicting preferences You're absolutely right that from a readability or simplicity perspective I'd choose the longer way. To some people's dismay, it's obviously not the only perspective I use, though (Btw, I added something to my last comment of that discussion.)

[SpAce]

This is the first puzzle I've knowingly encountered with a 7-fish. I was tinkering with my solver program code this week, and just for fun, I changed the search order to start searching for the biggest fish first, to see what it would find.

Code: Select all

    1    2    3     4  5   6      7   8    9     
 +---------------+-------------+---------------+
1| 1467 1467 5   | 3  69  2    | 8   179  1479 |
2| 1367 1678 168 | 4  69  5    | 2   1379 1379 |
3| 1234 124  9   | 1  7   8    | 6   5    34   |
 +---------------+-------------+---------------+
4| 167  5    168 | 29 28  39   | 137 4    137  |
5| 24   24   3   | 7  5   1    | 9   6    8    |
6| 9    178  18  | 6  48  34   | 5   137  2    |
 +---------------+-------------+---------------+
7| 8    169  24  | 29 124 4679 | 137 1379 5    |
8| 5    169  7   | 8  3   69   | 4   2    169  |
9| 16   3    24  | 5  124 4679 | 17  8    1679 |
 +---------------+-------------+---------------+

7-Fish (aka ???): In rows  1 2 4 6 7 8 & 9, digit 1 must go in columns  1 2 3 5 7 8 & 9
Therefore candidate 1 can be removed from all other cells in columns  1 2 3 5 7 8 & 9
Removing candidate 1 from r3c1 r3c2.


That's a valid Leviathan, all right, but you do realize that there's a single in r3c4 that gets those same eliminations? It's the Leviathan's complementary fish. Every basic fish has such a counterpart, which is why you'll never find (nor need) anything bigger than a Jellyfish if you search for smaller fishes first. Even though larger fishes exist, as your example demonstrates, there's always a complementary smaller fish available (with the same eliminations).

If the big fish is row-based (like here) then the little fish is column-based, and vice versa. In this case the little fish is a Cyclopsfish 1:c4\r3 => -1 r3c12. The larger the big fish, the smaller the little fish. A Leviathan's complementary fish could be at most an X-Wing (9-7=2) but because there's one given of the digit 1, it's a 1-Fish (8-7=1). The principle is exactly the same as with subsets which also come in pairs (i.e. no need to look for larger than quads -- if you look for both naked and hidden).

Btw, while the row and column numbers in your grid are nice to look at, they make it impossible to copy-paste that grid into Hodoku (without first deleting the row numbers). I recommend removing them when you post grids here.

Note, this doesn't reduce the puzzle to basics. A further advanced step is needed.

Singles rarely solve these puzzles (Neither do any other finless basic fishes for that matter.)