Solving Sudoku : Swordfish
This is very similar to using X-Wings, in that it will allow you to use knowledge about rows to remove candidates from columns, and vice versa.
Make sure you're happy with why X-Wings work before moving on to Swordfish!
The complexity here is that you're using knowledge from 3 rows at the same time - and that's what makes them harder to spot. Unlike X-Wings, they don't form a simple rectangle.
|This puzzle is mostly solved - but we've reached a point where simpler methods aren't helping.|
|There's actually a Swordfish in 4s in this puzzle, so we'll explain what it is and how it works.
To begin with, highlighting all of the places where 4 is still a candidate will help to make things easier.
|What we're looking for are sets of values that we can use to make a chain - just like in an X-Wing being a closed chain of four values, a Swordfish needs a closed chain of 6 (or more) values.|
|The Swordfish here is in three rows (3, 5 and 8).|
We'll remove the other values for now to make it a little clearer.
|Just like in the X-Wing example, a value in one position forces the other in the same row to not be that value. Lets put in some arrows to help to show that.|
|See that each of the arrows end in a column that matches one of the other rows?|
|This makes a fairly neat closed chain - and that means we can be sure that every one of those columns is occupied. To show the links, here are the arrows.
|There really are only two possibilites for the positions of the 4s within this loop:|
|Either way the values were arranged, you can see that these three columns are occupied by the contents of those three rows.|
|Once again highlighting the columns, you know that you can remove candidates for 4 from anywhere in those columns other than the three Swordfish rows.|
That's a great deal of work just to remove one candidate - but any progress helps when you're in the toughest puzzles!
|Tip: This only works because the loop is closed! This makes it easier to search for - you know that if you follow a chain and find yourself back at the start, there's a closed loop! It might not mean you can remove any candidates every time, though, which means you have to carry on searching.|
|Here's another example - there's a Swordfish in rows for 1s.:|
Hang on... so this works for any closed loops?
Yup - and it doesn't have to be limited to lines - its possible to connect values that share the same box, but it really does get incredibly complicated! Chances are that you can probably find a simpler method to help you.
Isn't an X-Wing just a closed loop?
Again, yup! An X-Wing and Swordfish are really the same thing - an X-Wing with 2 rows and columns, and a Swordfish on 3 rows and columns.
If you can see where this is heading... yes, it means that it is possible to have a Swordfish-4, which means it uses the connections between 4 lines! (These are sometimes called Jellyfish.) These are incredibly rare indeed, and usually another technique will work without you having to rely on them!