Looking for a rule: finned x wing

Advanced methods and approaches for solving Sudoku puzzles

Looking for a rule: finned x wing

Postby Luke » Sat Oct 21, 2006 3:00 am

This puzzle has a "finned X-wing" according to the Sanraid solver. I'm baffled. If anyone is so inclined I'd like to see a stated rule for this technique.

Here's the pattern, victim number is 7:


Code: Select all
*-----------------------------------------------------------*
 | 6     19    2     | 3     19    5     | 4     8     7     |
 | 578   19    4     | 28    67    1679  | 3     159   1259  |
 | 578   3     57    | 28    4     179   | 19    6     1259  |
 |-------------------+-------------------+-------------------|
 | 3    *678   568   |*17    2     179   | 1679  159   4     |
 | 57    4     1     | 6     379   8     | 2     3579  359   |
 | 9     2     67    | 4     5     137   | 167   137   8     |
 |-------------------+-------------------+-------------------|
 | 2     5   #367    |*17    8     1367  | 179   4     139   |
 | 4    *67   9      | 5     1367  2     | 8     137   13    |
 | 1    *78   378    | 9     37    4     | 5     2     6     |
 *-----------------------------------------------------------*


Thanx!

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Re: Looking for a rule: finned x wing

Postby Myth Jellies » Sat Oct 21, 2006 8:35 am

I like showing finned reductions in the following way...
Code: Select all
*-----------------------------------------------------------*
 | 6     19    2     | 3     19    5     | 4     8     7     |
 | 578   19    4     | 28    67    1679  | 3     159   1259  |
 | 578   3     57    | 28    4     179   | 19    6     1259  |
 |-------------------+-------------------+-------------------|
 | 3    *678   568   |*17    2     179   | 1679  159   4     |
 | 57    4     1     | 6     379   8     | 2     3579  359   |
 | 9     2     67    | 4     5     137   | 167   137   8     |
 |-------------------+-------------------+-------------------|
 | 2    *5   -367    |*17    8     1367  | 179   4     139   |
 | 4    #67   9      | 5     1367  2     | 8     137   13    |
 | 1    #78   378    | 9     37    4     | 5     2     6     |
 *-----------------------------------------------------------*

The starred cells represent a potential x-wing which would eliminate all the sevens in the non-starred cells in rows 4 and 7. Just like the bigger seafood (swordfish, jellyfish) you can ignore the fact that not every vertex of the potential x-wing contains a 7.

The only thing preventing the potential x-wing from being a real x-wing are the sevens marked with the hash marks, known as the fin.

Therefore you can reason that either the fin contains a seven, or the potential x-wing is true. Since the seven in r7c3 sees the entire fin, both the fin and the potential x-wing inhibit it, therefore r7c3 cannot be a seven.
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Re: Looking for a rule: finned x wing

Postby unkx80 » Sat Oct 21, 2006 8:38 am

Code: Select all
*-----------------------------------------------------------*
 | 6     19    2     | 3     19    5     | 4     8     7     |
 | 578   19    4     | 28    67    1679  | 3     159   1259  |
 | 578   3     57    | 28    4     179   | 19    6     1259  |
 |-------------------+-------------------+-------------------|
 | 3    *678   568   |*17    2     179   | 1679  159   4     |
 | 57    4     1     | 6     379   8     | 2     3579  359   |
 | 9     2     67    | 4     5     137   | 167   137   8     |
 |-------------------+-------------------+-------------------|
 | 2    *5   #367    |*17    8     1367  | 179   4     139   |
 | 4    %67   9      | 5     1367  2     | 8     137   13    |
 | 1    %78   378    | 9     37    4     | 5     2     6     |
 *-----------------------------------------------------------*


I relabelled this diagram. Does it help?

Another way of looking at it is: Assume that the # square is a 7. Then the bottom two * squares and the % squares cannot be 7. This implies that in columns 2 and 4, the only possible placement for 7 is at row 4, a contradiction. Therefore 7 can be eliminated from the # square.
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Re: Looking for a rule: finned x wing

Postby tarek » Sat Oct 21, 2006 9:46 am

unkx80 wrote:I relabelled this diagram. Does it help?

On this forum, I noticed that the players tag Eliminated cells with "-", fins with "#" & vertices with "*".......

unkx80 wrote:Another way of looking at it is: Assume that the # square is a 7. Then the bottom two * squares and the % squares cannot be 7. This implies that in columns 2 and 4, the only possible placement for 7 is at row 4, a contradiction. Therefore 7 can be eliminated from the # square.

Correct:D , that is the logic behind it, the pattern above makes it easier to spot.

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Re: Looking for a rule: finned x wing

Postby unkx80 » Sat Oct 21, 2006 11:03 am

tarek wrote:On this forum, I noticed that the players tag Eliminated cells with "-", fins with "#" & vertices with "*".......


Thanks for the note.:)

tarek wrote:
unkx80 wrote:Another way of looking at it is: Assume that the # square is a 7. Then the bottom two * squares and the % squares cannot be 7. This implies that in columns 2 and 4, the only possible placement for 7 is at row 4, a contradiction. Therefore 7 can be eliminated from the # square.

Correct:D , that is the logic behind it, the pattern above makes it easier to spot.


I had a lot of trouble understanding finned fish, until I found the reasoning behind it on aeb's site. Knowing this reasoning allowed me to know what pattern to look out for.
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Postby ravel » Sat Oct 21, 2006 12:38 pm

Code: Select all
*-----------------------------------------------------------*
 | 6     19    2     | 3     19    5     | 4     8     7     |
 | 578   19    4     | 28    67    1679  | 3     159   1259  |
 | 578   3     57    | 28    4     179   | 19    6     1259  |
 |-------------------+-------------------+-------------------|
 | 3    &678   568   |#17    2     179   |^1679 -159  -4     |
 | 57    4     1     | 6     379   8     | 2     3579  359   |
 | 9     2     67    | 4     5     137   |^167   137   8     |
 |-------------------+-------------------+-------------------|
 |-2     5   -367    |#17    8     1367  |^@179  4     139   |
 |-4    &67  -9      |-5     1367  2     | 8    @137   13    |
 | 1    &78   378    | 9     37    4     | 5     2     6     |
 *-----------------------------------------------------------*
I cannot spot this as finned (sashimi) x-wing, simply because there is no potential x-wing. Instead i see it as grouped strong links.

A systematic way to find them can be the following. First locate the strong links for 7. There are only 2: r4c4=r7c4 and r7c7=r8c8. They can be combined to 2 strong links r4c4=r7c4-r7c7=r8c8, saying that r4c4 or r8c8 has to be 7, so r4c8 and r8c8 cannot be 7 (but there is no 7). The next can be to combine 3 strong links, but this is not possible in this case.

Then look for grouped strong links, which can be connected with strong links (look at all cells, that can be seen by the ends of the strong links). There are 2: r7c7=r46c7, combined r4c4=r7c4-r7c7=r46c7, i.e. one of r4c4, r4c7 or r6c7 must be 7, and r4c89 cannot (no 7 there again). And r4c2=c89c2, combined r7c4=r4c4-r4c2=c89c2, here 7 can be eliminated from r71c3.

You also can combine them to 3 links: r8c8=r7c7-7c4=r4c4-r4c2=c89c2, saying, that r8c13<>7.
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Postby tarek » Sat Oct 21, 2006 1:32 pm

ravel wrote:I cannot spot this as finned (sashimi) x-wing, simply because there is no potential x-wing. Instead i see it as grouped strong links.


I agree that the Sashimi variation is trickier to spot, you can use anything in your arsenal that does the trick (turbot fish, multiple colouring....).

This should be easier to spot...a finned swordfish (not a sashimi) where you can construct a swordfish from true vertices...the fin is the only extra
Code: Select all
*-----------------------------------------------------------------*
| 5      9      68    | 1     *48     7     | 346   *348    2     |
| 3      2      68    | 568    9      456   | 46     1      7     |
| 4      1      7     | 268    3      26    | 5      9      68    |
|---------------------+---------------------+---------------------|
| 2      367    19    | 35689  58     13569 | 367    3578   4     |
| 16    #346    5     | 2368   7      12346 | 9      38     68    |
| 8     *3467  -49    | 3569  *45     34569 | 2      357    1     |
|---------------------+---------------------+---------------------|
| 69    *46     2     | 379    1      39    | 8     *47     5     |
| 19     8      14    | 579    6      59    | 47     2      3     |
| 7      5      3     | 4      2      8     | 1      6      9     |
*-----------------------------------------------------------------*
Eliminating 4 From r6c3 (Finned Swordfish in Columns 258 with 1 fin in Box 4)

The previously posted sashimi X-wing is not THE TRICKIEST Sashimi finned fish to spot....you may remember these from the big fish thread ravel....
Code: Select all
*-----------------------------------------------------------------*
| 1358   7      138   | 2      6      4     | 35     389    389   |
| 2      9      4     | 3      5      78    | 6      78     1     |
| 3568   68     368   | 1      78     9     | 357    4      2     |
|---------------------+---------------------+---------------------|
|-379    5      2     | 6      789    78    | 1      37     4     |
|*3678   68    #3678  |*4      1      2     | 9      5     *367   |
|*4      1     #679   |*79     3      5     | 8      2     *67    |
|---------------------+---------------------+---------------------|
| 6789   2      678   | 5      79     36    | 4      1      389   |
| 16789  4      16789 | 89     2      36    | 37     3789   5     |
|*89     3      5     |*789    4      1     | 2      6     *789   |
*-----------------------------------------------------------------*
Eliminating 7 From r4c1 (Finned Swordfish in Rows 569 with 2 fins in Box 4)

And this truly astonishing HEADLESS finned swordfish (aka 0 true vertices)
Code: Select all
*-----------------------------------------------------------------*
| 567    2456   247   |*1      8      467   |-4567  *9     *3     |
| 1678   468    3     | 5      2479   4679  | 1468  #267   #478   |
| 15678  9      147   | 3      247    467   | 14568 #267   #4578  |
|---------------------+---------------------+---------------------|
| 138    238    12    | 6      47     38    | 47     5      9     |
| 4      7      5     | 89     39     2     | 68     36     1     |
| 368    368    9     |*47     1      5     | 2     *37    *48    |
|---------------------+---------------------+---------------------|
| 39     34     8     | 2      4579   479   | 57     1      6     |
| 2      1      6     |*78     35     38    | 9     *4     *57    |
| 579    45     47    | 49     6      1     | 3      8      2     |
*-----------------------------------------------------------------*
Eliminating 7 From r1c7 (Finned Swordfish in Columns 489 with 4 fins in Box 3)

The same logic remains though, for the Sashimi's above I use (as did Myth) ANY N*N points that have the framework of true fish except for the fins that are in the way & you would have there a finned fish.

so we end up with 3 varieties: Classic, Sashimi, Headless (or extreme sashimi:D )

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Last edited by tarek on Sat Oct 21, 2006 10:32 am, edited 1 time in total.
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Postby daj95376 » Sat Oct 21, 2006 2:25 pm

Code: Select all
 *-----------------------------------------------------------*
 | 6     19    2     | 3     19    5     | 4     8     7     |
 | 578   19    4     | 28    67    1679  | 3     159   1259  |
 | 578   3     57    | 28    4     179   | 19    6     1259  |
 |-------------------+-------------------+-------------------|
 | 3    B678   568   |*17    2     179   |*1679  159   4     |
 |G57    4     1     | 6    B379   8     | 2     3579  359   |
 | 9     2     67    | 4     5     137   |#167   137   8     |
 |-------------------+-------------------+-------------------|
 | 2     5    -367   |*17    8     1367  |*179   4     139   |
 | 4     67    9     | 5     1367  2     | 8     137   13    |
 | 1    G78    378   | 9    ~37    4     | 5     2     6     |
 *-----------------------------------------------------------*

There appears to be a complex finned X-Wing at [r47c47] with fin [r6c7]

Code: Select all
X-Wing                                                                        => [r7c3]<>7
[r6c7]=7 => [r8c8]=7 => coloring BG => [r9c5]<>7 => Locked Candidates [r7c46] => [r7c3]<>7

Ironically, the direct approach seems to be the simplest.

Code: Select all
[r7c3]=7 => [r8c8]=7,[r9c5]=7,[r5c1]=7 => [b1]=INVALID => [r7c3]<>7
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Postby ronk » Sat Oct 21, 2006 3:42 pm

tarek wrote:so we end up with 3 varieties: Classic, Sashimi, Headless (or extreme sashimi:D )

What happened to 'Finned?'
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Postby tarek » Sat Oct 21, 2006 4:19 pm

ronk wrote:
tarek wrote:so we end up with 3 varieties: Classic, Sashimi, Headless (or extreme sashimi:D )

What happened to 'Finned?'
oh, all these 3 are finned fish & I will keep naming all 3 as FINNED, it is just an attempt at categorising them according to difficulty:

1. Classic (you can construct a fish from true vertices, i.e. NOT sashimi)
2. Sashimi (you can't construct a fish from true vertices, i.e. NOT Classic)
3. Headless (it is an extreme Sashimi in that the Elimination line has NO true vertices)
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Postby ronk » Sat Oct 21, 2006 5:11 pm

I was taking "classic" to be a finless fish. And saying "finned sashimi" and "finned headless" seems redundant IMO.

So I'd prefer classic, finned (meaning not sashimi and not headless), sashimi and headless as the category names.
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Postby Mike Barker » Sat Oct 21, 2006 5:53 pm

I've always considered that there are 4 kinds of fish. A basic fish is what Ron calls "classic", finned fish include a fin with true vertices and the sashimi version, big fin fish which are the "headless" variety, and then the Franken fish which is a finned (either type) "headless" fish. You can read up on some of these more exotic fish here.
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Postby tarek » Sat Oct 21, 2006 7:03 pm

tarek wrote:
ronk wrote:So I'd prefer classic, finned (meaning not sashimi and not headless), sashimi and headless as the category names.

I understand the logic behind what you're saying & the fear to turn this into SUSHI........I'm inclined to go with your suggestion or to keep everything as "finned" only.

Mike & ronk,
So with the Franken type should we do it as follows...
Code: Select all
1. Classic Fish (true fish, no fins)
2. Finned Fish (true fish with fins)
3. Sashimi Fish (virtual fish with fins)
4. Headless Fish (0 true vertices line Sashimi)
5. Franken Fish (Fins not limited to 1 box)


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Postby ronk » Sat Oct 21, 2006 8:14 pm

tarek wrote:So with the Franken type should we do it as follows...
Code: Select all
1. Classic Fish (true fish, no fins)
2. Finned Fish (true fish with fins)
3. Sashimi Fish (virtual fish with fins)
4. Headless Fish (0 true vertices line Sashimi)
5. Franken Fish (Fins not limited to 1 box)

I think so but I should reread some threads to be certain ... with MJ's Filet-o-Fish and vidarino's Big Fish threads at the top of the list.

BTW ... multiple fin cells in one box is one fin, is it not?
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Postby Havard » Sun Oct 22, 2006 12:11 am

Feeling a bit responsible for the "headless" and "franken" terms, I would like to add my 2 c.:)

I think the easiest way to describe these methods is thinking in terms of covering sets. A classic fish is either n rows or columns that can be "covered" by n columns or rows. (n rows covered by n columns and v.v)

Now for all these "fish" (that has been presented as "fish" on this forum so far) it holds true that the basis sets are always restricted to only columns or only rows. I think it was ronk who first introduced the idea that also using a box as part of the basis-sets could find a "smaller fish", but I don't think the idea of using boxes are yet concidered to be "fish" by the masses. This might change however.:)

Then the rest of the fish-names derives from using not only the opposite lines (row<->column) to cover the original fish, but to use boxes to do this as well, and also having "extra" candidates left in the fish after the number of covering sectors equals the number of basis-sectors.

A "finned" fish (in my opinion) is then a fish that, after you have been able to apply your n covering sectors, you are still left with some candidates. (the fins). These can then "see" some of the candidates within some of the covering sets(that are not part of the fish itself), and these can then be eliminated.

With that definition, you can actually divide ALL fish into finned and not-finned. However, there has been given some names to some of the special cases of covering. The "headless" variant was a result of getting exacly an "n-cover" (no fins) by using a box. I believe the first "headless" fish was a swordfish that had one box and two rows to cover three columns(a "classic" fish-illustration found many places since). In other words, a "headless" fish is also a "perfect fish" or a "non-finned-fish", but expanding the covering to include boxes as well.

Now by adding a "fin" to this, you got something that I think was just called a "finned swordfish", and that is also what I would argue it as. After expanding the fishworld to include boxes as covering sets, that falls nicely into place. (being "one extra" candidate outside the three covering sectors (row, row, box) and that candidate "seeing" some of the candidates inside one of those three sectors)

Now frankenfish was then introduced as the name of a fish using more then one box for covering sets as well as being finned. The first frankenfish was a swordfish of three columns, that used two boxes and one row as covering sets, and had one "fin" that could see one of the two boxes. In other words a "finned-more-than-one-box-used-for-cover"-fish, but then again, if truly accepting boxes as cover, it would really only be a "finned" fish.:)

I guess the thing about this that differs most from "public opinion" is the definiton I use for a "fin". My definition is: After you have covered a fish with N sectors with N other sectors, you are left with some candidates, these are concidered "fins" The rule that will always apply to fins are then that: any candidates that are part of any of the covering sectors, but not part of the basis sectors, that can see all the fins, can be eliminated This POV will then be completly in line with what was concidered "fins" in the early fishes, but will IMO be more flexible to deal with the more complex sea-creatures that we are facing. (not having to talk about 16 fins when having to use a lot of boxes for covering sectors) Note also that this POV will limit most sea-creatures ( even of huge proportions) to just one fin. Two can also happen sometimes, but three is outright rare!:)

The exciting new ways for sealife to go is in my opinion the possiblity ronk has introduced to use a mixture of sectors to make the basis of the fish. If the saying goes "there is always a smaller fish", then can we look away when something thought to be a jellyfish can be shown to be a "swordfish" concisting of two rows and a box... ?:)

We'll just have to wait and see I guess!:)

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