## Valid Swordfish??

Post the puzzle or solving technique that's causing you trouble and someone will help

### Valid Swordfish??

Hello.

I am quite new to Sudoku and have been trying to go beyond the basic techniques so that I can have a go at some of the harder puzzles. I understand the X-wing, and even the XY-Wing, but the Swordfish is still confusing me. I read these http://angusj.com/sudoku/hints.php#swordfish & http://www.sadmansoftware.com/sudoku/swordfish.htm

"Look for three columns with only two candidates for a given digit. If these fall on exactly three common rows, and each of those rows has at least two candidate cells, then all three rows can be cleared of that digit - except in the defining cells. This is the original, "restrictive" definition. It has since been realised that a more relaxed definition is possible, in that the three columns can each have two or three candidates for the given digit - as long as they fall on the three common rows."

So I thought I had discovered a Swordfish in a puzzle I was really struggling with, but I ended up with an error and wasnt able to complete. So I was wondering if my Swordfish was correct. I chose columns A B and C, as the defining cells fell on 3 rows. I cancelled the candidates on the ? squares R7>C2 & C5 and R8> C9.

Was this right? Here http://angusj.com/sudoku/hints.php#swordfish it seems to imply that you can remove candidates from rows and columns that lie between defining cells.

If this was right, then maybe I just made a schoolboy error and messed up somewhere else.
Attachments
suduko_swordfish.png (89.01 KiB) Viewed 507 times
oojafink

Posts: 4
Joined: 04 February 2013

oojafink wrote:
I was wondering if my Swordfish was correct

I chose columns A B and C, as the defining cells fell on 3 rows

the 5 is indeed in 3 rows
in each of those 3 columns (columns 1,2,9)
however
not the same 3 rows

Pat

Posts: 3700
Joined: 18 July 2005

### Re: Valid Swordfish??

Sorry, I dont understand. The 'tops' and 'bottom' of my defined columns fall on rows 2-9, 2-9, and 7-9. Do you mean they all have to be either 2-9 or 7-9??
oojafink

Posts: 4
Joined: 04 February 2013

### Re: Valid Swordfish??

OK, I just did some more reading and I now think I understand my mistake. I have to be able to draw three imaginary lines across three rows between my defining cells. in my example, the defining cell at R7>C9 isn't 'anchored' to anything else.
oojafink

Posts: 4
Joined: 04 February 2013

### Re: Valid Swordfish??

Hello

I'd like to see the original puzzle to see if I can solve it using a different technique - are you able to post a snapshot of it?

Regards, Steve
StevenLudmon

Posts: 2
Joined: 31 January 2013

### Re: Valid Swordfish??

Hi Steve

The original puzzle can be seen as the starting cells have a grey background. It's very possible I was making life hard for myself anyway, as I'm still quite new to Sudoku and I'm certain that sometimes I'm missing out things like hidden or even naked double/triples! I'm also making stupid errors like missing out certain candidates when doing an initial pencil-in, or even adding them when they shouldnt be there.
oojafink

Posts: 4
Joined: 04 February 2013

### Re: Valid Swordfish??

Hm, looks like something for this thread.
eleven

Posts: 1971
Joined: 10 February 2008

### Re: Valid Swordfish??

eleven wrote:Hm, looks like something for this thread.
I'm not so sure. All of the 5's have a blue background Presumably some of them were gray to begin with, and are only showing up blue because 5 is the currently active digit. With the 5's it is valid.

JasonLion
2017 Supporter

Posts: 640
Joined: 25 October 2007
Location: Silver Spring, MD, USA

### Re: Valid Swordfish??

Hi oojafink, I thought that the grey background cells were the originals but I wasn't sure about the 5's as they are all blue. Were any of the 5's given?
StevenLudmon

Posts: 2
Joined: 31 January 2013

### Re: Valid Swordfish??

Of course, you are right. So i get a puzzle, which is quite nasty for non pencilmark players.
The triple in row 2 is hard to spot for them, as well as the complementary hidden quad 1358.

Probably easier to find is the w-wing 46 in r2c7/r8c4 with the strong link for 4 in column 3.
Code: Select all
` +-------+-------+-------+ | . . 2 | . 8 5 | 9 . . | | . . @ | 2 . 9 | # . . | | . 8 9 | . . 1 | 5 . 2 | +-------+-------+-------+ | 2 9 5 | 8 3 6 | 1 4 7 | | 6 4 8 | 7 1 2 | 3 5 9 | | 7 3 1 | 5 9 4 | 2 . . | +-------+-------+-------+ | 9 . 3 | 1 . 8 | . 2 . | | 8 2 @ | # 5 3 | . 9 1 | | . . 6 | 9 2 7 | 8 3 . | +-------+-------+-------+`

If r2c3=4, then r2c7 must be 6.
If r8c3=4, then r8c4 must be 6.
So at least one of r2c7 and r8c4 is 6, therefore r8c7 (and r2c4) cannot be 6.
This gives a 6 in r8c4 and you get here.
Code: Select all
` +-------+-------+-------+ | Y . 2 | X 8 5 | 9 . . | | . . . | 2 . 9 | . . . | | X 8 9 | X . 1 | 5 . 2 | +-------+-------+-------+ | 2 9 5 | 8 3 6 | 1 4 7 | | 6 4 8 | 7 1 2 | 3 5 9 | | 7 3 1 | 5 9 4 | 2 . . | +-------+-------+-------+ | 9 . 3 | 1 . 8 | . 2 . | | 8 2 . | . 5 3 | . 9 1 | | . . 6 | 9 2 7 | 8 3 . | +-------+-------+-------+`

Now you might notice, that only 34 is left for the X-ed cells r1c4,r3c14.
Because they are part of a unique rectangle pattern (2 cells in 2 rows, 2 in 2 columns, 2 in 2 boxes), r1c1 (Y) cannot be 34, if the puzzle is unique.
So it must be 1 and the puzzle is solved.
eleven

Posts: 1971
Joined: 10 February 2008

### Re: Valid Swordfish??

You seem to have two mistakes. First, you don't have a <2> in [box 2]. It's included in the grid below. Second, your column and row counts for your Swordfish. I've marked the cells (*) containing <5> in your columns ABC. These cells occur in four rows. They can only occur in three rows for a basic Swordfish to exist.

Code: Select all
`    A      B                                                      C +-----------------------------------------------------------------------+ |  134    167    2      |  346    8      5      |  9      1367   1346   | | *1345  *1567   47     |  2346   467    9      |  467    13678  13468  | |  34     8      9      |  346    467    1      |  5      367    2      | |-----------------------+-----------------------+-----------------------| |  2      9      5      |  8      3      6      |  1      4      7      | |  6      4      8      |  7      1      2      |  3      5      9      | |  7      3      1      |  5      9      4      |  2      68     68     | |-----------------------+-----------------------+-----------------------| |  9     *57     3      |  1      456    8      |  467    2     *456    | |  8      2      47     |  46     456    37     |  467    9     *13456  | | *145   *157    6      |  9      2      37     |  8      137   *1345   | +-----------------------------------------------------------------------+ # 71 eliminations remain`

Regards, Danny A. Jones
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006