The New Sudoku Players' Forum

[stumble]

This is bb1-9-2008VeryHard original

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.------------------------.------------------------.------------------------.
| 6       378     278    | 4       18      5      | 12378   127     9      |
| 39      358     1      | 2       89      7      | 6       4       38     |
| 29      4       2789   | 169     3       1689   | 1278    5       278    |
:------------------------+------------------------+------------------------:
| 8       9       27     | 17      1247    13     | 127     6       5      |
| 24      67      3      | 1567    124678  168    | 9       127     278    |
| 5       1       267    | 679     26789   689    | 278     3       4      |
:------------------------+------------------------+------------------------:
| 139     2       69     | 1679    5       169    | 347     8       367    |
| 19      68      4      | 3       1679    2      | 5       79      67     |
| 7       356     569    | 8       69      4      | 23      29      1      |
'------------------------'------------------------'------------------------'


This is as far as I got:

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.------------------.------------------.------------------.
| 6     37    78   | 4     18    5    | 23    127   9    |
| 39    5     1    | 2     89    7    | 6     4     38   |
| 2     4     789  | 169   3     1689 | 17    5     78   |
:------------------+------------------+------------------:
| 8     9     2    | 17    4     3    | 17    6     5    |
| 4     67    3    | 5     1678  168  | 9     17    2    |
| 5     1     67   | 679   2     69   | 8     3     4    |
:------------------+------------------+------------------:
| 139   2     69   | 1679  5     169  | 4     8     367  |
| 19    8     4    | 3     1679  2    | 5     79    67   |
| 7     36    5    | 8     69    4    | 23    29    1    |
'------------------'------------------'------------------'


Sudoku Explainer wants me to do a Swordfish on 9, but SE’s Swordfish doesn’t look legitimate to me, at least the way I understood Swordfish rules. Does anyone have a solution I could understand?

[daj95376]

You have three basic Swordfish options. Two are complementary/conjugate or some other co-name that I can't remember. If you choose the Swordfish in <7>, then Locked Candidates eliminate the need for either Swordfish in <9>.

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 +--------------------------------------------------------------------+
 |  6      37     78    |  4      18     5     |  23     127    9     |
 |  39     5      1     |  2      89     7     |  6      4      38    |
 |  2      4      789   |  169    3      1689  |  17     5      78    |
 |----------------------+----------------------+----------------------|
 |  8      9      2     |  17     4      3     |  17     6      5     |
 |  4      67     3     |  5      1678   168   |  9      17     2     |
 |  5      1      67    |  679    2      69    |  8      3      4     |
 |----------------------+----------------------+----------------------|
 |  139    2      69    |  1679   5      169   |  4      8      367   |
 |  19     8      4     |  3      1679   2     |  5      79     67    |
 |  7      36     5     |  8      69     4     |  23     29     1     |
 +--------------------------------------------------------------------+


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 Swordfish c258\r158   <> 7    [r1c3],[r8c9]
 +-----------------------------------+
 |  . *7 -7  |  .  .  .  |  . *7  .  |
 |  .  .  .  |  .  .  7  |  .  .  .  |
 |  .  .  7  |  .  .  .  |  7  .  7  |
 |-----------+-----------+-----------|
 |  .  .  .  |  7  .  .  |  7  .  .  |
 |  . *7  .  |  . *7  .  |  . *7  .  |
 |  .  .  7  |  7  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  7  .  .  |  .  .  7  |
 |  .  .  .  |  . *7  .  |  . *7 -7  |
 |  7  .  .  |  .  .  .  |  .  .  .  |
 +-----------------------------------+


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 Swordfish c346\r367   <> 9    [r7c1]
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  .  9  |
 |  9  .  .  |  .  9  .  |  .  .  .  |
 |  .  . *9  | *9  . *9  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  9  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  9  .  .  |
 |  .  .  .  | *9  . *9  |  .  .  .  |
 |-----------+-----------+-----------|
 | -9  . *9  | *9  . *9  |  .  .  .  |
 |  9  .  .  |  .  9  .  |  .  9  .  |
 |  .  .  .  |  .  9  .  |  .  9  .  |
 +-----------------------------------+


Code: Select all

 Swordfish r289\c158   <> 9    [r7c1]
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  .  9  |
 | *9  .  .  |  . *9  .  |  .  .  .  |
 |  .  .  9  |  9  .  9  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  9  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  9  .  .  |
 |  .  .  .  |  9  .  9  |  .  .  .  |
 |-----------+-----------+-----------|
 | -9  .  9  |  9  .  9  |  .  .  .  |
 | *9  .  .  |  . *9  .  |  . *9  .  |
 |  .  .  .  |  . *9  .  |  . *9  .  |
 +-----------------------------------+


If you still don't like either Swordfish example for [r7c1]<>9, then pretend you have an Empty Rectangle in [r2b8] of the last example. You'll get the same results as the finned Franken X-Wing that's also present!

[wintder]

Sudoku Explainer wants me to do a Swordfish on 9, but SE’s Swordfish doesn’t look legitimate to me, at least the way I understood Swordfish rules. Does anyone have a solution I could understand?

The general swordfish pattern is 3X3.

That suggests 9 cells with the candidate. They don't have to be all filled. The least possible is six filled, as long as there are two valid positions in each row and column of the pattern.

This is an example of a minimal swordfish, not finned, not sashimi.

Code: Select all

. x .|. . .|. x .
. . .|. . .|. . .
. . .|. . .|. . .
-----+-----+-----
. . .|. . .|. . .
. . .|. x .|. x .
. . .|. . .|. . .
-----+-----+-----
. . .|. . .|. . .
. . .|. . .|. . .
. x .|. x .|. . .

[Carcul]

[r8c5]-1-[r1c5]=1=[r1c8]-1-[r5c8]=1=[r4c7]=7=[r4c4]-7-[r67c4]=7|1=[r7c46]-1-[r8c5],

=> r8c5<>1 and the puzzle is solved.

[stumble]

Sudoku Explainer wants me to do a Swordfish on 9, but SE’s Swordfish doesn’t look legitimate to me, at least the way I understood Swordfish rules. Does anyone have a solution I could understand?

The general swordfish pattern is 3X3.

That suggests 9 cells with the candidate. They don't have to be all filled. The least possible is six filled, as long as there are two valid positions in each row and column of the pattern.

This is an example of a minimal swordfish, not finned, not sashimi.

Code: Select all

. x .|. . .|. x .
. . .|. . .|. . .
. . .|. . .|. . .
-----+-----+-----
. . .|. . .|. . .
. . .|. x .|. x .
. . .|. . .|. . .
-----+-----+-----
. . .|. . .|. . .
. . .|. . .|. . .
. x .|. x .|. . .

This minimal is how I've been attempting to make Swordfish. I wasn't aware you could 'leave out' candidates in a row when you're setting up. I thought I'd tried it that way and gotten an error in the past.

[stumble]

If you still don't like either Swordfish example for [r7c1]<>9, then pretend you have an Empty Rectangle in [r2b8] of the last example. You'll get the same results as the finned Franken X-Wing that's also present!

Thanks again daj, I'm keeping your Swordfish for examples. I didn't know their rules were as flexible as that. but I don't understand your Empty Rectangle hint. Well... I don't understand Empty Rectangles anyway. This would be a good chance to learn if you'd expand on your comment a bit.

[daj95376]

I don't understand your Empty Rectangle hint. Well... I don't understand Empty Rectangles anyway. This would be a good chance to learn if you'd expand on your comment a bit.

Okay. First, let's remove a few of the Swordfish markings in my last example and add a couple new ones. Add an AIC on <9> as well.

Code: Select all

(9) [r2c1]=[r2c5]-[r89c5]=[r7c46]-[r7c1]
 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  .  9  |
 | *9  .  .  |  . *9  .  |  .  .  .  |
 |  .  .  9  |  9  .  9  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  9  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  9  .  .  |
 |  .  .  .  |  9  .  9  |  .  .  .  |
 |-----------+-----------+-----------|
 | -9  .  9  | *9  . *9  |  .  .  .  |
 |  9  .  .  |  . *9  .  |  .  9  .  |
 |  .  .  .  |  . *9  .  |  .  9  .  |
 +-----------------------------------+


Code: Select all

If [r2c1]=9, then [r7c1]<>9.
If [r2c1]<>9, then the AIC forces [r7c1]<>9. Either way, the elimination occurs.


Now, everything hinges on the strong link in [r2] and the grouped strong link in [b8]. The grouped strong link in [b8] occurs because of the four empty cells [r89c46] -- in a rectangular arrangement. I'm pretty sure this is how the technique gets its name. In any event, it's an Empty Rectangle in [r2b8].

For fish lovers, it's also a finned Franken X-Wing r2b8\c15 with fin cells [r7c46].

[ronk]

Now, everything hinges on the strong link in [r2] and the grouped strong link in [b8]. The grouped strong link in [b8] occurs because of the four empty cells [r89c46] -- in a rectangular arrangement. I'm pretty sure this is how the technique gets its name. In any event, it's an Empty Rectangle in [r2b8].

I think most sudoku hobbyists here consider the empty rectangle (ER) to be just [b8] ... and there are two more in [b2] and [b7]. Even [b1] may legitimately be considered an ER.

[stumble]

Not sure if this question belongs here, but it’s a continuation of my confusion about Swordfish, so I’ll plunk it in here. This is a DIFFERENT puzzle than I started with above.
BB1-12-08SuperHard original

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.---------------------.---------------------.---------------------.
| 1      67     2689  | 29     3      28    | 24679  246    5     |
| 239    4      239   | 1259   6      25    | 279    8      1279  |
| 2689   5      2689  | 7      29     4     | 269    3      1269  |
:---------------------+---------------------+---------------------:
| 256    9      4     | 8      25     1     | 3      7      26    |
| 2356   16     12356 | 259    24579  257   | 24568  246    268   |
| 25     8      7     | 3      245    6     | 1      9      2     |
:---------------------+---------------------+---------------------:
| 568    2      568   | 4      57     9     | 678    1      3678  |
| 4689   3      689   | 26     1      27    | 26789  5      26789 |
| 7      16     1569  | 256    8      235   | 269    26     4     |
'---------------------'---------------------'---------------------'


after my ‘basic’ ministrations:

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.---------------.---------------.---------------.
| 1    7    26  | 9    3    8   | 4    26   5   |
| 39   4    239 | 1    6    5   | 279  8    79  |
| 689  5    689 | 7    2    4   | 69   3    1   |
:---------------+---------------+---------------:
| 2    9    4   | 8    5    1   | 3    7    6   |
| 36   16   136 | 2    9    7   | 5    4    8   |
| 5    8    7   | 3    4    6   | 1    9    2   |
:---------------+---------------+---------------:
| 68   2    5   | 4    7    9   | 68   1    3   |
| 4    3    89  | 6    1    2   | 789  5    79  |
| 7    16   169 | 5    8    3   | 269  26   4   |
'---------------'---------------'---------------'


And now below is my attempt at a Swordfish on 6. ‘*’ denotes my Swordfish parameters. ‘-‘ denotes the 6’s it cancelled that agreed with the official solution. ‘!’ denotes the ‘6s’ it looks like the Swordfish SHOULD remove, but do not agree with the official solution. Can someone tell me where I’m going wrong in formulating my Swordfish layout? or interpreting its targets?

Code: Select all

.---------------.---------------.---------------.
| 1    7    2-6 | 9    3    8   | 4    26   5   |
| 39   4    239 | 1    6    5   | 279  8    79  |
| 689* 5    689*| 7    2    4   | 69*  3    1   |
:---------------+---------------+---------------:
| 2    9    4   | 8    5    1   | 3    7    6   |
| 36*  16!  136*| 2    9    7   | 5    4    8   |
| 5    8    7   | 3    4    6   | 1    9    2   |
:---------------+---------------+---------------:
| 68*  2    5   | 4    7    9   | 68*  1    3   |
| 4    3    89  | 6    1    2   | 789  5    79  |
| 7    16   19-6| 5    8    3   | 269! 26   4   |
'---------------'---------------'---------------'


Eventually I used:
XyChainOn6 r3c7-r2c9-r8c9-r8c3-r7c1=>r7c7<>6
which broke the puzzle.

[Sudtyro]

Code: Select all

.---------------.---------------.---------------.
| 1    7    2-6 | 9    3    8   | 4    26   5   |
| 39   4    239 | 1    6    5   | 279  8    79  |
| 689* 5    689*| 7    2    4   | 69*  3    1   |
:---------------+---------------+---------------:
| 2    9    4   | 8    5    1   | 3    7    6   |
| 36*  16!  136*| 2    9    7   | 5    4    8   |
| 5    8    7   | 3    4    6   | 1    9    2   |
:---------------+---------------+---------------:
| 68*  2    5   | 4    7    9   | 68*  1    3   |
| 4    3    89  | 6    1    2   | 789  5    79  |
| 7    16   19-6| 5    8    3   | 269! 26   4   |
'---------------'---------------'---------------'


The confusion may be that for a general fish, all candidates for a particular digit in N rows/columns must be located in N columns/rows. Your row Swordfish has an "extra" 6 in r5c2.

[daj95376]

I think most sudoku hobbyists here consider the empty rectangle (ER) to be just [b8] ... and there are two more in [b2] and [b7]. Even [b1] may legitimately be considered an ER.

Yes, Havard did originally define an Empty Rectangle as a missing pattern within a box. He then showed how it could be combined with a strong link to perform an elimination. As pointed out by

P.S. I wonder if we can somehow distinguish between Empty Rectangles, the technique, from empty rectangles, the box/box grouped stronglink. I know I was confused ...

No one ever responded to his comment. As far as I'm concerned, the ER technique needs a strong link, and I will continue to designate the ER technique as a strong link combined with a grouped strong link in a box.

[ronk]

I will continue to designate the ER technique as a strong link combined with a grouped strong link in a box.

If that's the ER technique, then what do you call the following with four ERs and four eliminations?

Code: Select all

 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  .  9  |
 |  9  .  .  |  .  9  .  |  .  .  .  |
 | -9  .  9  |  9 -9  9  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  9  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  9  .  .  |
 |  .  .  .  |  9  .  9  |  .  .  .  |
 |-----------+-----------+-----------|
 | -9  .  9  |  9 -9  9  |  .  .  .  |
 |  9  .  .  |  .  9  .  |  .  9  .  |
 |  9  .  .  |  .  9  .  |  .  9  .  |
 +-----------------------------------+

[ArkieTech]

ronk said

If that's the ER technique, then what do you call the following with four ERs and four eliminations?

Code: Select all

 +-----------------------------------+
 |  .  .  .  |  .  .  .  |  .  .  9  |
 | *9  .  .  |  . *9  .  |  .  .  .  |
 | -9  .  9  |  9 -9  9  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  9  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  9  .  .  |
 |  .  .  .  |  9  .  9  |  .  .  .  |
 |-----------+-----------+-----------|
 | -9  .  9  |  9 -9  9  |  .  .  .  |
 | *9  .  .  |  . *9  .  |  . *9  .  |
 | *9  .  .  |  . *9  .  |  . *9  .  |
 +-----------------------------------+ 
 
 
 



Swordfish?

dan

[ronk]

Swordfish?

That is one of several correct answers, but the context of the question implied using at least one ER.

[daj95376]

Swordfish?

That is one of several correct answers, but the context of the question implied using at least one ER.

One ER gets you nothing. Two ERs get you nothing. Three ERs get you one elimination.

Code: Select all

 One Elimination Using Fish Notation and Three ERs
 +-----------------------+
 | / X / | . . . | / X / |
 | X . X | . . . | X . X |
 | / X / | . . . | / X / |
 |-------+-------+-------|
 | . . . | . . . | . . . |
 | . . . | . . . | . . . |
 | . . . | . . . | . . . |
 |-------+-------+-------|
 | . . . | . . . | / X / |
 | . * . | . . . | X . X |
 | . . . | . . . | / X / |
 +-----------------------+


However, I think most sudoku hobbyists here do not seriously consider using three or more ERs as the ER technique. At least, that's not how the technique is demonstrated in Sudopedia. That example uses a strong link combined with an ER pattern -- as I've chosen to do ... and how Havard originally demonstrated.