As promised, I implemented the Swordfish classic Sudoku solving technique in my Perfect Sudoku software and generated a few puzzles.

**I just posted one of them on the Daily Sudoku page**.
However, I ran my generator and generated a couple of thousands Killer Sudokus and

**NONE** of them required Swordfish, just as I speculated before. Surely, in some of them you could use Swordfish, but they could also be solved by other Killer and/or classic Sudoku techniques. I will keep trying to generate one that REQUIRE Swordfish and will post it if I get it.
By the way, I consider X-Wing to be a simplified version of Swordfish, so everything I just said applies to X-Wing too.
Let me know how you like this “fiendish” classic Sudoku puzzles…

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## 8 Comments

A killer sudoku can be designed to require all the classic sudoku techniques. Consider any classic sudoku puzzle. Surround each of the starting ‘givens’ with a 1-cell cage, and surround the unknown cells with a single cage with sum = 405 – sum of the givens. You now have converted a classic sudoku into a killer sudoku. Hence all the classic techniques could be required to solve a killer sudoku. It is just that the killer sudoku puzzles currently designed do not typically require them.

fdkr, what you’re saying makes complete sense. However, there is one problem – I personally consider Killer Sudokus with singleton cages to be invalid. You will notice that Killers that I post never have 1-cell cages (except the first few I posted back in September, before I enhanced my algorithm).

> and surround the unknown cells with a single cage with sum = 405 – sum of the givens

You need to take into account that in proper killer sudoku/sum number place/samunamupure you cannot have cages larger than 9 cells, so the maximum cage sum can only be 45. If you want to allow duplicates inside cages and thus cages of any size, that’s another game called “murderer sudoku”… (Just kidding!)

I don’t know what are you talking about(!!!) because the X-wing and Swordfish techniques are absolutely unknown for me. Who is available to teach me about them? A very simple explanation with a small example will be appreciated. Best regards.

Fernando Castro

Fernando,

Swordfish: consider digit 1 (for this example). Find “n” columns that have digit 1 as a candidate in only “n” different rows. If you manage to do that, that’s a swordfish and you can erase digit 1 as a candidate from those n rows, except from those n columns :). I know it’s confusing, but when you replace “n” with “2” it becomes much simpler and that is called X-Wing.

Basically, in X-Wing you only find a “rectangle” – 4 cells that constitute a rectangle (or a square) that can have digit 1 as a candidate, but no other rows in those two columns (that constitute the rectangle) can have digit 1. If so, then you can erase digit 1 from those 2 rows that constitute the rectangle .

Of course, you can interchange rows and columns in this explanation. 🙂

I don’t get this swordfish/x-wing thing either. I’ve read all the explanations, studied all the examples, but I just don’t get it.

Cindy, look at the explanation and the image shown in this post: http://www.djape.net/?p=98

You look at the 4 numbers that are highlighted in red. You should conclude that 2 of those cells must be equal to 1. And since they obviously can’t be in the same row nor column, they must be on the diagonals of that little rectangle – hence the name “X-wing”. But the name isn’t important.

Obviously, the reason for 2 of those 4 cells being 1 is that in columns 4 and 7 YOU MUST HAVE NUMBER 1 somewhere, and those are the only cells that have number 1 as a candidate in those columns.

So once you’ve concluded that – the consequence is that in rows 4 and 8 number 1 can’t be anywhere else except in 2 of those 4 cells – so you eliminate number 1 from all cells from rows 4 and 8 except from columns 4 and 7 :).

In the given example, this indirectly solves R4C9 = 9.

fdkr’s proof (14th Nov) that a killer sudoku can be made to require all the solving elements of classic sudoku impressed me with it’s simplicity and directness. But it kinda got me to thinking. I’m not saying that the conclusion is necessarily incorrect but I was wondering if the proof itself holds up?

1) Is it safe to ignore cage sums in the proof?

I know it seems that it’s just to simplify the proof, but as Udosuke says, totalling all the remaining sums in one cage is illegal and sometimes we use (il)legality as solving logic.

Consider, for example,

Row A cells 1 and 2 must contain a 3,7 pair order unknown. Rows G 1 and 2 must also contain

a 3,7 pair. If those four cells are the last to be solved then in classic sudoku we have an invalid puzzle ( multiple solutions), but in killer that’s not necessarily true.

Consider too, instead of summing all the remaining cells we had each as a singleton then you have no solving to do at all! So at what point can we ignore cage sums/distribution in the proof?

2) It seems to me that X-Wing itself is different between killer and classic. For example

Row A Cells 1 and 2 must contain a 3,7 pair order unknown.

Row G cells 1 and 2 must contain a 3,8 pair order unknown Some intervening cells are value unknown.

It seems to me that in killer that’s an X-Wing on the 3s , but in classic it’s not.

If I’m correct, that’s a fairly substantial difference.

Do I have that right? and do these points impact on the validity of the proof?

Regards and best wishes to all,

Stan