Swordfish or X-wing

Advanced methods and approaches for solving Sudoku puzzles

Swordfish or X-wing

Postby ArkieTech » Mon Jan 01, 2007 5:32 pm

Code: Select all
 *-----------*
 |..4|9..|28.|
 |...|.5.|.3.|
 |...|...|7.5|
 |---+---+---|
 |.62|..9|1.8|
 |..1|4.5|3..|
 |8.3|1..|47.|
 |---+---+---|
 |7.6|...|...|
 |.8.|.7.|...|
 |.15|..2|8..|
 *-----------*
 *--------------------------------------------------*
 | 5    3    4    | 9    16   7    | 2    8    16   |
 | 16  -29   7    | 28   5    18   | 69   3    4    |
 | 16  *29   8    | 23   146  134  | 7   *169  5    |
 |----------------+----------------+----------------|
 | 4    6    2    | 7    3    9    | 1    5    8    |
 | 9    7    1    | 4    8    5    | 3    26   26   |
 | 8    5    3    | 1    2    6    | 4    7    9    |
 |----------------+----------------+----------------|
 | 7    4    6    | 358 *19   138  |#59  *129  123  |
 | 2    8    9    | 35   7    134  | 56   146  136  |
 | 3    1    5    | 6   *49   2    | 8   *49   7    |
 *--------------------------------------------------*

From the original puzzle above I worked through a unique loop and wound up here.
I think this is a swordfish with a fin at r7c7 and a removal candidate at r2c2.
Or -- is r7c7 a fin to an x-wing with r3c8 the removal candidate?
Or -- is it both?
Or -- neither?
I am having difficulty getting my arms around swordfishes and their many patterns.

dan
dan
User avatar
ArkieTech
 
Posts: 2954
Joined: 29 May 2006
Location: NW Arkansas USA

Re: Swordfish or X-wing

Postby ronk » Mon Jan 01, 2007 6:35 pm

ArkieTech wrote:
Code: Select all
 *--------------------------------------------------*
 | 5    3    4    | 9    16   7    | 2    8    16   |
 | 16  -29   7    | 28   5    18   | 69   3    4    |
 | 16  *29   8    | 23   146  134  | 7   *169  5    |
 |----------------+----------------+----------------|
 | 4    6    2    | 7    3    9    | 1    5    8    |
 | 9    7    1    | 4    8    5    | 3    26   26   |
 | 8    5    3    | 1    2    6    | 4    7    9    |
 |----------------+----------------+----------------|
 | 7    4    6    | 358 *19   138  |#59  *129  123  |
 | 2    8    9    | 35   7    134  | 56   146  136  |
 | 3    1    5    | 6   *49   2    | 8   *49   7    |
 *--------------------------------------------------*

(...)
I think this is a swordfish with a fin at r7c7 and a removal candidate at r2c2.
Or -- is r7c7 a fin to an x-wing with r3c8 the removal candidate?
Or -- is it both?
Or -- neither?

To be a valid, an exclusion must be true 1) if all fin cells are false, and 2) if each fin cell is individually true. Since r2c2 does not directly "see" the fin, the exclusion r2c2<>9 -- while correct -- is not attributable to your (degenerate sashimi) swordfish. And I don't think there's a different fish on your grid either.

However, r7c4<>8 can be deduced with a relatively simple chain ...
Code: Select all
 5    3    4    | 9    16   7    | 2    8    16
 16  *29   7    |*28   5    148  |*69   3    146
 16   29   8    | 23   146  134  | 7    1469 5
----------------+----------------+---------------
 4    6    2    | 7    3    9    | 1    5    8
 9    7    1    | 4    8    5    | 3    26   26
 8    5    3    | 1    2    6    | 4    7    9
----------------+----------------+---------------
 7    4    6    |*358  19   138  |*59   129  123
 2    8    9    | 35   7    134  | 56   146  1346
 3    1    5    | 6    49   2    | 8    49   7

 r7c4-8-r2c4-2-r2c2-9-r2c7=9=r7c7=5=r7c4, implies r7c4<>8

... followed by cascading singles to solve the puzzle.

P.S. It might be better to post a question like yours in the Help with particular puzzles forum.
ronk
2012 Supporter
 
Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Postby daj95376 » Mon Jan 01, 2007 6:49 pm

I'll let someone else answer your question about the fish. In case the answer comes back 'no', then consider this alternate solution.

Code: Select all
# after SSTS:
# XY-Chain on [r2c7] => [r2c2]<>9 (and [r3c8]<>9, but not necessary)
# Singles complete the puzzle
 *-----------------------------------------------------------*
 | 5     3     4     | 9     16    7     | 2     8     16    |
 | 16    2-9   7     | 28    5     148   |*69    3     146   |
 | 16   d29    8     |c23    146   134   | 7     146-9 5     |
 |-------------------+-------------------+-------------------|
 | 4     6     2     | 7     3     9     | 1     5     8     |
 | 9     7     1     | 4     8     5     | 3     26    26    |
 | 8     5     3     | 1     2     6     | 4     7     9     |
 |-------------------+-------------------+-------------------|
 | 7     4     6     | 358   19    138   | 59    129   123   |
 | 2     8     9     |b35    7     134   |a56    146   1346  |
 | 3     1     5     | 6     49    2     | 8     49    7     |
 *-----------------------------------------------------------*


[Edit: Oops. ronk and I were preparing replies at the same time. I'll leave mine anyway.]
daj95376
2014 Supporter
 
Posts: 2624
Joined: 15 May 2006

Postby ArkieTech » Mon Jan 01, 2007 6:56 pm

Ronk wrote:
To be a valid, an exclusion must be true 1) if all fin cells are false, and 2) if each fin cell is individually true. Since r2c2 does not directly "see" the fin, the exclusion r2c2<>9 -- while correct -- is not attributable to your (degenerate sashimi) swordfish. And I don't think there's a different fish on your grid either.

However, r7c4<>8 can be deduced with a relatively simple chain ...

The removal candidate must see the fin. That is helpful.

Thanks

I will post to the puzzle help next time.

dan
dan
User avatar
ArkieTech
 
Posts: 2954
Joined: 29 May 2006
Location: NW Arkansas USA


Return to Advanced solving techniques

cron