## Fascinating Chain

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

### Fascinating Chain

1...5.......7.1.64..4...1...3...8.4.5...4...7...6...9...7...4...6...3.......1...8 Yes I've learned how to get SadMan to export codes with dots.
This was one of those 19s that Pat suggested I look at. After 3 singles you get this great picture (Dunno how I lost a couple of gridlines but I'm sure you can follow it.)

T1.png (3.68 KiB) Viewed 920 times
The first interesting thing is that there are only two places in Box1 where a 6 could go, and they both chain through to put a 6 in every box of the puzzle. I've marked them in as one chain of dots and the other as * The same thing happens if you start at Box9. The other interesting thing is that this now means that every box, row and column which does not have a solved 6 in it, has exactly two places that could be a 6. This suggests skyscrapers and kites but I can't find any.

Has this kind of pattern got a name, and how would you go about attacking it? As usual, I have found a solution with a Test.
Yogi
2017 Supporter

Posts: 190
Joined: 05 December 2015
Location: New Zealand

### Re: Fascinating Chain

Code: Select all
`*--------------------------------------------------------------------------------*| 1       2789   *23689    | 23489   5      *2469     | 23789   2378    239      || 2389    2589    23589    | 7       2389    1        | 23589   6       4        || 236789  25789   4        | 2389    23689   29-6     | 1       23578   2359     ||--------------------------+--------------------------+--------------------------|| 2679    3       129-6    | 1259    279     8        | 25-6    4       1256     || 5       1289   *12689    | 1239    4       29       |*2368    1238    7        || 2478    12478   128      | 6       237     257      | 2358    9       1235     ||--------------------------+--------------------------+--------------------------|| 2389    12589   7        | 2589    2689    259-6    | 4       1235    123569   || 2489    6       12589    | 24589   2789    3        | 2579    1257    1259     || 2349    2459    2359     | 2459    1      *245679   |*235679  2357    8        |*--------------------------------------------------------------------------------*`

The only non-basic move in the solution to this puzzle is a SwordFish in 6's r159 c367 => - 6 r3c6, r4c37, r7c6.

The Swordfish pattern is the cells marked *. You can eliminate all 6's in columns 367 except those in the * cells.

Fish are probably the most widely discussed and well understood patterns in the world of Sudoku. A Swordfish is a fish of size 3.

Here are links to the discussions of Swordfish in my usually recommended teaching sites : here and here.

There is also an enormous thread on this site called The Ultimate Fish Guide which can be found here.

Here are some practice puzzles, which have Swordfish moves:

1......345..3.2.78...8........6.5..3..5...4..3.....6.298.2.6.1.............78.9.. | 4 r247 c235
..5.7.2.........498....5.7.91...6..7.4.9.8..2..645..8..8..................1.43... | 2 r369 c124
3.15..............74...6.3..8.6.7..4...9.....27..5..8......126.........861..23.5. | 9 r369 c379
.31..6..56....7......59....8..1....27.......3.4...38..12763.........1.....84..3.. | 9 r247 c678
..........8..63..4..2.....8..5.......46..25.....9...3172...54.......7.93.932....5 | 1 r258 c145
..6..........756.....2.3591.5..149.38..9.2.....37......25..94..9...2..3.......... | 7 r147 c189
.......5..46.518.....9..4.6.3.8......2.3..6.9417..9.......68.142.......85.1...... | 7 r358 c568
6.913...........1...4...5.74..8...798.2.............6......3..82....19.3...4296.. | 5 r148 c236
16.54..7...8..1.3..3.8.....7...5..696..9.2.57.............3..4........16...1645.. | 2 r239 c158

Leren
Last edited by Leren on Wed Jun 08, 2016 9:05 pm, edited 6 times in total.
Leren

Posts: 4110
Joined: 03 June 2012

### Re: Fascinating Chain

Table C is your Fascinating Chain, digit 6 with mark [*] as elimination.
Outside [2] of row and column are to detect [*].
As you said, [*] are false if r1c3=6 or r3c1=6 is true
Table A is a puzzle which leads table B of digit 4 with mark [*] as elimination,
Code: Select all
`table A           table B            table C                  2     2            2    2    2                     ---+---+---       ---+---+---        ---+---+---..7|1.6|3..     2|.4.|...|.4.      2|..6|..6|......|5.8|...     2|.4.|.4.|...       |...|...|.6.2..|.3.|..1      |.*4|*.4|4..       |6..|.6*|...-----------       -----------        -----------71.|...|.36     2|..*|4..|...       |6.*|...|*.6..8|...|1..     2|4..|.*.|...      2|..6|...|6..53.|...|.24      |...|...|..4       |...|6..|...-----------       -----------       -----------6..|.5.|..2      |...|*.4|4..       |...|.6*|..6...|8.1|...      |**4|...|4*.       |.6.|...|.....5|3.2|6..      |.4.|.4.|.4.      2|...|..6|6..`
Kozo Kataya

Posts: 33
Joined: 06 July 2012

### Re: Fascinating Chain

I’m unhappy, but I will get over it. I spent some hours on and off preparing this reply and then I lost my internet connection before I could save a draft, so I have had to start again. It was quite detailed and I’m not sure I can remember it all, but here goes (again.) I have copied Leren’s suggested puzzles and I will certainly attempt them. However, there are clearly some things about these fish that I don’t yet understand. You identified the swordfish pattern in my puzzle as r159c367, which describes six 6-candidate cells covering three rows and three columns. Each of these cells can see two of the others and they chain around in a closed loop. Fine. But if you look at the remaining 6-candidate cells in my drawing above, they also appear (to me) to form the swordfish r347c159 with the same characteristics. And in the two chains above (the stars and the dots) I have identified all the remaing 6-candidate cells for the puzzle, so I don’t see how the swordfish can eliminate any more instances of candidate 6 or show me which option is the correct one to solve the puzzle.

My own method to solve this puzzle was simplicity itself. I looked at the two possible arrangements of the 4 and 6 in Box2 and proceeded, knowing that one of them had to be correct:

Boxes2.png (2.01 KiB) Viewed 885 times

In the first option, 6r1c6 forces 4r1c4, and in the second, 6r3c5 leads to 6r9c6, which means 4c4 in Box8 and 4r1c6.
The puzzle was solved with the first option, so I did not get to the second one.
Yogi
2017 Supporter

Posts: 190
Joined: 05 December 2015
Location: New Zealand

### re: Swordfish

Yogi wrote:

You identified the swordfish pattern in my puzzle as r159c367

But if you look at the remaining 6s,
they also appear to form the swordfish r347c159

this puzzle does have 2 Swordfish (for 6)
• r159\c367
• c159\r347
and as you said, they are equivalent

Pat

Posts: 3896
Joined: 18 July 2005

### Re: Fascinating Chain

Yes, there is a column based Swordfish c159 r347 for the same eliminations. Neither is more "correct" then any other - when solving I look for row based fish before columns based fish but the other way around is equally valid.

I see Pat has posted the same thing while I was preparing this post.

The third practice puzzle has a full 9 cell row based Swordfish, which doesn't lend itself to a chain interpretation.

Code: Select all
`*---------------------------------------------------------------------------------*| 3       269     1        | 5       47      89       | 4678-9   479     267-9    || 589     2569    2568-9   | 3       47      89       | 145678-9 1479    12567-9  || 7       4      *589      | 2       1       6        |*589      3      *59       ||--------------------------+--------------------------+---------------------------|| 159     8       5-9      | 6       3       7        | 15-9     2       4        || 145     356     3456     | 9       8       2        | 13567    17      13567    || 2       7      *369      | 1       5       4        |*369      8      *369      ||--------------------------+--------------------------+---------------------------|| 458     35      34578    | 478     9       1        | 2        6       37       || 49      239     2347-9   | 47      6       5        | 1347-9   1479    8        || 6       1      *4789     | 478     2       3        |*479      5      *79       |*---------------------------------------------------------------------------------*`

I'm afraid there is no shortcut to learning a large topic like Fish and learning is often a painful process. As you say, you are unhappy but you will get over it - eventually. Join the club, we've all been there.

Leren
Leren

Posts: 4110
Joined: 03 June 2012

Yogi wrote:
My own method to solve this puzzle was simplicity itself. I looked at the two possible arrangements of the 4 and 6 in Box2 and proceeded, knowing that one of them had to be correct---

if you prefer "forcing chains" (and "forcing nets"),
we needn't bother you with Swordfish et al

Pat

Posts: 3896
Joined: 18 July 2005

### One-fish, two-fish

Pat wrote:
Yogi wrote:

You identified the swordfish pattern in my puzzle as r159c367

But if you look at the remaining 6s,
they also appear to form the swordfish r347c159

this puzzle does have 2 Swordfish (for 6)
• r159\c367
• c159\r347
and as you said, they are equivalent

If there is a fish in the columns (rows) there is always a complementary fish (usually of a different order) in the rows (columns).

Personally, I think they are hard to spot and not very useful, so I don't much look for them.

Keith
keith
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Posts: 221
Joined: 03 April 2006

### Re: Fascinating Chain

Table C is your Fascinating Chain, digit 6 with mark [*] as elimination.
Outside [2] of row and column are to detect [*].
if Table A is given, table B [ * ] shows the elimination.
As r4c2345678 between r4c1 and r4c9, and r2345678c6 between r1c6 and r9c6 are eliminated.
Also r23c23 and r78c78 are eliminated.
Because the only 2 candidates can be true along r19c19.
Code: Select all
`table A           table B            table C                  2        2         2    2    2                     ---+---+---       ---+---+---        ---+---+---..6|..6|...     2|..6|..6|...      2|..6|..6|....66|666|66.      |.**|66*|66.       |...|...|.6.666|666|66.      |6**|66*|66.       |6..|.6*|...-----------       -----------        -----------666|666|666      |6**|***|**6       |6.*|...|*.6.66|666|66.      |.66|66*|66.      2|..6|...|6...66|666|66.      |.66|66*|66.       |...|6..|...-----------       -----------       -----------.66|666|666      |.66|66*|**6       |...|.6*|..6.66|666|66.      |.66|66*|**.       |.6.|...|......|..6|6..     2|...|..6|6..      2|...|..6|6..`

Kozo Kataya

Posts: 33
Joined: 06 July 2012

### Re: Fascinating Chain

Well, I have worked through the first three puzzles in Leren's list and not been able to find the swordfish in any of them. However, I did manage to solve them with my own methods and I think this has shown that Keith and Pat have it right: I can live quite happily on a fish-free diet. I had already noted that X-Wings don't do much for me.

There are many strategies for solving Sudoku and there is definitely no one right way to do it. Today I saw a list of 61 types! It's largely a matter of taste which ones we would prefer to use. Because our brains are wired differently, our individual senses of Logic, Reasoning and Rightness make us individually prefer some methods over others.

Vive les Differences!

Yogi
Yogi
2017 Supporter

Posts: 190
Joined: 05 December 2015
Location: New Zealand

### Re: Fascinating Chain

Code: Select all
`*----------------------------------------------------------------------------------*| 1       679       8        | 5       679     79       | 2       3       4        || 5      *469      *469      | 3      *469     2        | 1       7       8        || 247     237-4     237-4    | 8       17-4    147      | 5       6       9        ||----------------------------+--------------------------+--------------------------|| 8      *124      *124      | 6      *124     5        | 7       9       3        || 267     267       5        | 9       237     37       | 4       8       1        || 3       179-4     179-4    | 14      17-4    8        | 6       5       2        ||----------------------------+--------------------------+--------------------------|| 9       8        *47       | 2      *45      6        | 3       1       57       || 2467    123567-4  12367-4  | 14      1359-4  1349     | 8       24      567      || 246     12356-4   1236-4   | 7       8       134      | 9       24      56       |*----------------------------------------------------------------------------------*`

Here is the first puzzle with a Swordfish in 4's r247 c235 for an amazing 11 eliminations (well it is a test puzzle specifically aimed at Swordfish).

Leren

PS to make things easier for you I have added the location of the Swordfish in all the example puzzles in my earlier post.

For example, the second puzzle has the location 2 r369 c124. This means that the Swordfish digit is 2, located in Rows 3, 6 and 9 and you'll find that they only occur in Columns 1, 2 and 4.

Thus you can eliminate all 2's in Columns 1, 2 and 4 except for those in Rows 3, 6 and 9.

All the puzzles are simple row based Swordfish, probably the easiest type to spot. I wasn't trying to make things to hard for you.

Leren
Leren

Posts: 4110
Joined: 03 June 2012