Hunting finned X-Wing and other fishy stuff

Ruud · Site Admin

As requested by Ron, here is my approach to finding finned X-Wings.

What the heck is a finned X-Wing?

If you do not know what an X-Wing is, read about it here: http://www.simes.clara.co.uk/programs/sudokutechnique6.htm

A finned X-Wing is almost an X-Wing. The only difference is that one of the 4 cells has some extra candidates that share a box and a row or column (depending on whether the almost X-Wing lies in the rows or in the columns.

This is the picture:

gsf

nice post
it would be nicer if a few real puzzle examples were posted or referenced along with the illustrative pseudo examples

foxglove · Posted: Fri Mar 10, 2006 10:53 pm Post subject: one question

what's the difference between a finned X-Wing and a Turbot?

Ruud · Site Admin

I almost forgot! Laughing

here are a few examples to demonstrate the finned X-Wing:

This sudoku could not be solved without a template check or stronger techniques. It can now be solved with a nice sequence of a naked triple, 2 naked singles, a finned X-Wing and another naked triple that finally breaks it. This sudoku would have been classified as extremely tough, but with finned X-Wing, it is just a hard one.

rkral · Posted: Sat Mar 11, 2006 12:12 pm Post subject:

tarek · Posted: Sat Mar 11, 2006 2:02 pm Post subject:

Hi there Ruud,

I generated this puzzle which is the perfect answer to finned x-wing galore..........

You can add it to you list of examples if you want.......

example4:

rkral · Posted: Sat Mar 11, 2006 4:03 pm Post subject:

Ruud · Site Admin

Thank you for pointing out the finned X-Wing.

My solver spotted this XY-Wing at the exact same candidate position:

tarek · Posted: Sat Mar 11, 2006 6:06 pm Post subject:

Ruud · Site Admin

Hi Tarek,

I am still foiled by an XY-Wing in sample 5, right here:

With XY-Wing disabled, this is the finned X-Wing, as you pointed out:

And now... something completely different...

Now the we have a lot of examples, let's talk about the way to locate them in the grid (from quite a long distance away). All the samples I've seen so far place them in 4 different boxes. Is that a coincidence, or a prerequisite? Any other limitations that I can exploit?

Ruud.

rkral · Posted: Sat Mar 11, 2006 7:22 pm Post subject:

Ruud · Site Admin

tarek · Posted: Sat Mar 11, 2006 11:51 pm Post subject:

I programmed my solver to spot finned fishes (including the sashimi variation) up to to level of squirmbag........The long way I'm afraid...

It is basically like you would explain it to a human.........

Observation 1: The finned x-wing closely resembles the x-wing.......remove the fins & you get an x-wing

an x-wing has exactly 4 cells in 2 rows & 2 columns
You can have a maximum of Two fins (cells) in a finned x-wing.

so: (I'm not too good in pseudo code, the following assumes that the fish is in columns eliminating in rows, swap columns with rows to get the opposite)

1st filter: fish (n=2 x-wing, n=3 swordfish, .........)
2nd filter: Number of cells in a finned fish "Min:(n*2)+1 Max:(n*n)+2" cells in n columns & (n+1 rows or n+2 rows)
3rd filter: Only one column has >n*n cells

observation 2: All Fin(s) should share a box with at least one vertix

4th filter: combining observations 1 & 2
In Only one box would removal of (1-2) cells lead to an n-true fish

---Now you should have a finned n fish, that can eliminate in vertices rows only in the box containing the fin(s). [Note: if you have a mixed normal pattern with a sashimi pattern, this step can combine them easily]

example of the mixed pattern finned swordfish:

Ruud · Site Admin

Thanks Tarek, for your insights.

I now think it is possible to write a generic function to search for N-sized finned formations.

The only irregularity is in the row/column containing the fin. The other rows/columns can be found by the same method as if you were looking for a regular N-sized fish.

So, when we find N-1 rows with a total of N candidates (where N>=2):

then we go look for a row that has at least one candidate in of the columns found in the 'regular' rows, and at least 1 extra candidate in the same tower as one of the other columns.

This method would cover every size and both normal finned and sashimi variations, I think.

Any comments?

Ruud.

rkral · Posted: Sun Mar 12, 2006 7:06 pm Post subject: