The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|.51|...|
 |24.|..3|...|
 |.75|.9.|6..|
 |---+---+---|
 |6.2|..5|.7.|
 |.54|.3.|26.|
 |.3.|2..|1.5|
 |---+---+---|
 |..9|.4.|52.|
 |...|3..|.16|
 |...|52.|...|
 *-----------*


Play/Print this puzzle online

[SpAce]

Code: Select all

.----------------.-------------------.-----------------.
| a38+9  689  36 | a(+7)-48  5   1   | 78   a34+  2    |
|  2     4    1  |    6      78  3   | 789   5    789  |
| a38+   7    5  | ca(48)+   9   2   | 6    a34+  1    |
:----------------+-------------------+-----------------:
|  6    b89   2  |  c(8)9    1   5   | 3     7    4    |
|  1     5    4  |    789    3   78  | 2     6    89   |
| b789   3    78 |    2      6   4   | 1     89   5    |
:----------------+-------------------+-----------------:
|  378   68   9  |    1      4   678 | 5     2    378  |
|  5     2    78 |    3      78  9   | 4     1    6    |
|  4     1    36 |    5      2   678 | 789   89   3789 |
'----------------'-------------------'-----------------'

BUG-Lite(348)r13c148 using internals:

(7==9)r13c148 - b4p[7=2] - (9=84)r43c4 => -48 r1c4; stte

(Added) ...or using mixed #external/+internal:

Code: Select all

.----------------.----------------------.----------------.
| b38+9  689  36 |   4+7-8   5      1   | 78   34+  2    |
|  2     4    1  |   6      a7(#8)  3   | 789  5    789  |
|  38+   7    5  |   4-8+    9      2   | 6    34+  1    |
:----------------+----------------------+----------------:
|  6    c89   2  | c(8)9     1      5   | 3    7    4    |
|  1     5    4  |   789     3      78  | 2    6    89   |
| b789   3    78 |   2       6      4   | 1    89   5    |
:----------------+----------------------+----------------:
|  378   68   9  |   1       4      678 | 5    2    378  |
|  5     2    78 |   3       78     9   | 4    1    6    |
|  4     1    36 |   5       2      678 | 789  89   3789 |
'----------------'----------------------'----------------'

(8)r2c5 == (9)r[1-6]c1 = (9,8)r4c24 => -8 r13c4; stte

(A simple X-Chain would do the same, of course.)

[Ngisa]

Code: Select all

+--------------------+------------------+--------------------+
| 389    689    368  | 478    5     1   | 78     34     2    |
| 2      4      1    | 6      78    3   | 789    5      789  |
| 38     7      5    | 48     9     2   | 6      34     1    |
+--------------------+------------------+--------------------+
| 6      89     2    | 89     1     5   | 3      7      4    |
| 1      5      4    | 789    3    c78  | 2      6     d89   |
| 789    3     f78   | 2      6     4   | 1      e89     5   |
+--------------------+------------------+--------------------+
| 378    68     9    | 1      4    b678 | 5      2      378  |
| 5      2      8-7  | 3     a78    9   | 4      1      6    |
| 4      1      3678 | 5      2    b678 | 789    389    3789 |
+--------------------+------------------+--------------------+


(7=8)r8c5 - r79c6 = r5c6 - r5c9 = r6c8 - (8=7)r6c3 => - 7r8c3; stte

Clement

[SpAce]

(7=8)r8c5 - r79c6 = r5c6 - r5c9 = r6c8 - (8=7)r6c3 => - 7r8c3; stte

Hi Clement! That's very nice. You could make it even shorter and simpler by targeting (8)r6c3. Then you don't need the 7s at all and can use a simple X-Chain.

[Sudtyro2]

Code: Select all

+------------------+-----------------+--------------+
|  389   689  36   |  478*  5    1   | 78  34  2    |
|  2     4    1    |  6     78*  3   | 789 5   789  |
|  38    7    5    | b48#   9    2   | 6   34  1    |
+------------------+-----------------+--------------+
|  6    d89*  2    | c89*   1    5   | 3   7   4    |
|  1     5    4    | b789#  3    78  | 2   6   89   |
| a789#  3    7-8* |  2     6    4   | 1   89  5    |
+------------------+-----------------+--------------+
|  378   68   9    |  1     4    678 | 5   2   378  |
|  5     2    78*  |  3     78*  9   | 4   1   6    |
|  4     1    36   |  5     2    678 | 789 89  3789 |
+------------------+-----------------+--------------+

In 8s, a 7-link oddagon(*) with three guardians(#).
[8r6c1 == r35c4] - r4c4 = 8r4c2 => -8r6c3; stte

SteveC

[SpAce]

In 8s, a 7-link oddagon(*) with three guardians(#).
[8r6c1 == r35c4] - r4c4 = 8r4c2 => -8r6c3; stte

Hi Steve! Very nice! Did you notice that you could do it with just two guardians by using a Grouped Oddagon (i.e. considering r13c4 as a group node)? Doesn't make any practical difference here because r35c4 works as a unit in the chain, but in other situations it might help a lot to have fewer guardians to worry about. Here it would just give you a slightly simpler chain (no group node) and a redundant routing option (r5c9=r6c8). So, no mentionable benefits in this case, but I just thought it wouldn't hurt to remember that possibility when using oddagons.

[Sudtyro2]

Thx, SpAce, for the helpful feedback. Funny that I was concentrating on the grouped guardians and didn't see the grouped oddagon option. But, I did initially see the r13c4 group as a node in a (longer) alternative X-chain solution for the same elimination (plus one):
8r8c3 = r8c5 - r2c5 = [r13c4] - r4c4 = 8r4c2 => -8r6c3,r7c2; stte.

SteveC

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 389   689   36    | 478   5     1     | 78    34    2     |
 | 2     4     1     | 6     78    3     | 789   5     789   |
 | 38    7     5     | 48    9     2     | 6     34    1     |
 *-------------------+-------------------+-------------------|
 | 6    d89    2     |c89    1     5     | 3     7     4     |
 | 1     5     4     | 789   3    b78    | 2     6     89    |
 | 789   3    e78    | 2     6     4     | 1     89    5     |
 *-------------------+-------------------+-------------------|
 | 378   68    9     | 1     4    a678   | 5     2     378   |
 | 5     2    f78    | 3     7-8   9     | 4     1     6     |
 | 4     1     36    | 5     2    a678   | 789   89    3789  |
 *-----------------------------------------------------------*


X-chain 8r79c6 = r5c6 - r4c4 = r4c2 - r6c3 = 8r8c3 => -8 r8c5 ; stte

[Cenoman]

Hard to find something different !

Code: Select all

 +-------------------+-------------------+--------------------+
 |  389   689   36   | b478   5    1     |  78    34   2      |
 |  2     4     1    |  6    a78   3     |  789*  5    789*   |
 |  38    7     5    |  48    9    2     |  6     34   1      |
 +-------------------+-------------------+--------------------+
 |  6     89    2    |  89    1    5     |  3     7    4      |
 |  1     5     4    |Cc78-9  3   B78    |  2     6   z89     |
 |  789   3     78   |  2     6    4     |  1    y89   5      |
 +-------------------+-------------------+--------------------+
 |  378   68    9    |  1     4    678   |  5     2    378    |
 |  5     2     78   |  3     78   9     |  4     1    6      |
 |  4     1     36   |  5     2   A678   |  789* x89   3789*  |
 +-------------------+-------------------+--------------------+

UR(79)r29c79 using externals
(7)r2c5 - r1c4 = (7)r5c4
(7)r9c6 - r5c6 = (7)r5c4
(9)r9c8 - r6c8 = (9)r5c9
=> -9 r5c4; ste

[Leren]

Where there is an X chain there is often a fish.

Code: Select all

*-------------------------------------------*
| 389  689  36  |*478  5  1   | 78  34 2    |
| 2    4    1   | 6   *78 3   | 789 5  789  |
| 38   7    5   |*48   9  2   | 6   34 1    |
|---------------+-------------+-------------|
| 6   F89   2   |*89   1  5   | 3   7  4    |
| 1    5    4   | 789  3  78  | 2   6  89   |
| 789  3    7-8 | 2    6  4   | 1   89 5    |
|---------------+-------------+-------------|
| 378  68   9   | 1    4  678 | 5   2  378  |
| 5    2   *78  | 3   *78 9   | 4   1  6    |
| 4    1    36  | 5    2  678 | 789 89 3789 |
*-------------------------------------------*

Finned Franken Swordfish in 8's r48b2 c345 with a fin Cell r4c2 => - 8 r6c3; stte

Leren

[SpAce]

Where there is an X chain there is often a fish.

Shouldn't that be "always"? I'm pretty sure every X-Chain is a fish, but obviously every fish is not an X-Chain.

[Leren]

SpAce wrote : ... I'm pretty sure every X-Chain is a fish ...

Haven't ever given it any thought but what about a 4 cell Skyscraper ? It's obviously an X chain but is it a Fish ? It might be two Siamese finned fish but that's as close I can come after about 5 minutes of thought. Leren

[SpAce]

SpAce wrote : ... I'm pretty sure every X-Chain is a fish ...

Haven't ever given it any thought but what about a 4 cell Skyscraper ? It's obviously an X chain but is it a Fish ? It might be two Siamese finned fish but that's as close I can come after about 5 minutes of thought. Leren

Thanks for reminding that it's not quite as simple as I implied. You're right that a Skyscraper (or any longer X-Chain with similarly placed endpoints) might need two fishes to get all the same eliminations. However, if the Siamese extension is accepted then I think the combo is considered a single fish (at least Hodoku does), which of course is somewhat illogical as Siamese twins are still two individuals. I guess it makes sudoku sense, though, since the whole point of the extension is to see it as a single pattern. (The Remora extension is probably even more controversial in that regard, but I don't really have experience with them).

Either way I think my point is still valid, though it could have been worded better. It's more accurate to say that every X-Chain can be converted into one or more fishes, but to get the exact same eliminations you might need more than one (or to use the Siamese extension).

Btw, I think the UFG is a bit inaccurate and incomplete about its Skyscraper conversion:

Code: Select all

 *  X  * | .  .  . | .  /  .          /  X  / | .  .  . | .  *  .
**  X ** | .  .  . | .  #  .          #  X  # | .  .  . | . **  .
 *  X  * | .  .  . | .  /  .          /  X  / | .  .  . | .  *  .
---------+---------+---------        ---------+---------+---------
 .  /  . | .  .  . | .  /  .          .  *  . | .  .  . | .  *  .
 .  /  . | .  .  . | .  /  .          .  *  . | .  .  . | .  *  .
 .  /  . | .  .  . | .  /  .          .  *  . | .  .  . | .  *  .
---------+---------+---------        ---------+---------+---------
 .  /  . | .  .  . | .  /  .          .  *  . | .  .  . | .  *  .
 *  X  * | *  *  * | *  X  *          /  X  / | /  /  / | /  X  /
 .  /  . | .  .  . | .  /  .          .  *  . | .  .  . | .  *  .
 Fig 2D: cc\rb                        Fig 2D inverse: rb\cc
 rr\cb transpose                      cb\rr transpose
 turbot fish (skyscraper)             turbot fish (ER + conjugate link)
 sashimi mutant x-wing

First, it's only showing the Grouped Skyscraper which doesn't run into the mentioned problem (eliminations possible in one box only). Also, it's calling it "sashimi mutant x-wing" which I think has a couple of slight problems. One, it should be "franken" and not "mutant". Two, the term "sashimi" is rarely used with non-basic fishes (even if they fit the definition). Three, as per tarek's own definitions and usage, "sashimi" doesn't automatically imply "finned", so it's missing that keyword. Four, the non-grouped Skyscraper is more easily seen as a basic (Siamese Finned Sashimi) X-Wing, so it should be shown as a special case for that reason too. (Well, the last point is kind of moot as the Grouped Skyscraper would be even easier as a basic Finned (possibly Sashimi) X-Wing without the Siamese twist).