## Need help with Swordfish

### Need help with Swordfish

I've gotten up to X-wing in the solving guide as well as in Tom Davis' dissertation, but I'm having trouble making the leap from there to swordfish. Would one (or more) of you explain it in more detail (step by step) or in a different way so that perhaps I can get a grasp on this technique? If you explain the logic behind it (i.e. WHY those candidates are eliminated), then I think I will have an easier time understanding and finding the pattern.

Let me try a somewhat unconventional way of explaining Swordfish. First, since you understand x-wing, lets look at an example:
and lets focus on the number 8. Careful study of the grid will reveal an x-wing in r34c36, eliminating 8 from r3c458 and r4c45. But let's take another look at this deduction. Let us write down all of the different places one can find 8 in the different columns:

C1 : (126)

C2 : (9)

C3 : (34)

C4 : (13467)

C5 : (13467)

C6 : (34)

C7 : (5)

C8 : (23)

C9 : (8)

For example C4 : (13467) means you can find an 8 in column 4 in rows 1,3,4,6,7.

Forget about the original grid and only look at this column of numbers. If this was a sudoku column, you would say, "hey, there's a naked pair (34),(34) in C3 and C6," and then you would eliminate 3 from C4,C5,C8 and 4 from C4,C5. But if you translate everything back to the sudoku grid, these are exactly the deductions of the x-wing, and for that matter, the naked pair exactly corresponds to the cells of the x-wing. This is not a coincidence.

Every (column based) x-wing will correspond to a naked pair when you write down the where entries can go in a column. If you are using SudoCue, copy in this puzzle and switch the view to CN-view. Look at row 8. You will see exactly the list I gave above.

Now let's move on to swordfish. If an x-wing corresponds to a naked pair, then a swordfish must correspond to a naked triple. Let's see an example:
In this puzzle, we will focus on the number 1.

Let's write down where the 1's can go in each column (or we use the CN-view of SudoCue to do the same job)

C1 : (29)

C2 : (128)

C3 : (4)

C4 : (69)

C5 : (368)

C6 : (26)

C7 : (35)

C8 : (7)

C9 : (135)

Here we have to look a little harder, but eventually we spot the naked triple (29), (69), (26) in C1,C4,C6. This allows us to eliminate 2 from C2 and 6 from C5. In the original grid, this corresponds to removing 1 from r2c2 and r6c5.
For more information on this approach, see this

By the way, the reason why I like this approach is that it makes it much easier to spot these patterns and extend the pattern. For instance, you can probably guess that a jellyfish will correspond to a naked quad. The downside of the approach (especially if you're working on paper) is that you might have to right down all of these columns and that can be downright boring. Moreover, sometimes it's hard to see the connection between the column output and the original grid. But, it's food for thought and perhaps somebody else will offer up a more conventional explanation.

Code: Select all

```
.---------------------.---------------------.---------------------.
| 1678 167 4 | 178 178 9 | 3 5 2 |
| 18 3 2 | 4 6 5 | 7 18 9 |
| 9 157 578* | 12378- 12378- 138* | 6 18- 4 |
:---------------------+---------------------+---------------------:
| 5 147 78* | 138- 1348- 138* | 2 9 6 |
| 16 2 3 | 5 9 16 | 8 4 7 |
| 468 46 9 | 268 248 7 | 5 3 1 |
:---------------------+---------------------+---------------------:
| 37 9 1 | 378 378 2 | 4 6 5 |
| 347 457 57 | 1367 137 136 | 9 2 8 |
| 2 8 6 | 9 5 4 | 1 7 3 |
'---------------------'---------------------'---------------------'
```

C1 : (126)

C2 : (9)

C3 : (34)

C4 : (13467)

C5 : (13467)

C6 : (34)

C7 : (5)

C8 : (23)

C9 : (8)

For example C4 : (13467) means you can find an 8 in column 4 in rows 1,3,4,6,7.

Forget about the original grid and only look at this column of numbers. If this was a sudoku column, you would say, "hey, there's a naked pair (34),(34) in C3 and C6," and then you would eliminate 3 from C4,C5,C8 and 4 from C4,C5. But if you translate everything back to the sudoku grid, these are exactly the deductions of the x-wing, and for that matter, the naked pair exactly corresponds to the cells of the x-wing. This is not a coincidence.

Every (column based) x-wing will correspond to a naked pair when you write down the where entries can go in a column. If you are using SudoCue, copy in this puzzle and switch the view to CN-view. Look at row 8. You will see exactly the list I gave above.

Now let's move on to swordfish. If an x-wing corresponds to a naked pair, then a swordfish must correspond to a naked triple. Let's see an example:

Code: Select all

```
*-----------------------------------------------------------*
| 35 18 35 | 4 7 9 | 6 2 18 |
| 178 178 4 | 26 26 18 | 3 9 5 |
| 9 2 6 | 35 18 35 | 148 47 1478 |
|-------------------+-------------------+-------------------|
| 57 3 1 | 257 248 578 | 45 6 9 |
| 258 48 25 | 9 3 6 | 145 47 147 |
| 567 467 9 | 157 14 157 | 2 8 3 |
|-------------------+-------------------+-------------------|
| 23 5 23 | 8 9 4 | 7 1 6 |
| 4 16 8 | 37 16 37 | 9 5 2 |
| 16 9 7 | 16 5 2 | 48 3 48 |
*-----------------------------------------------------------*
```

Let's write down where the 1's can go in each column (or we use the CN-view of SudoCue to do the same job)

C1 : (29)

C2 : (128)

C3 : (4)

C4 : (69)

C5 : (368)

C6 : (26)

C7 : (35)

C8 : (7)

C9 : (135)

Here we have to look a little harder, but eventually we spot the naked triple (29), (69), (26) in C1,C4,C6. This allows us to eliminate 2 from C2 and 6 from C5. In the original grid, this corresponds to removing 1 from r2c2 and r6c5.

Code: Select all

```
*-----------------------------------------------------------*
| 35 18 35 | 4 7 9 | 6 2 18 |
| 178* 178- 4 | 26 26 18* | 3 9 5 |
| 9 2 6 | 35 18 35 | 148 47 1478 |
|-------------------+-------------------+-------------------|
| 57 3 1 | 257 248 578 | 45 6 9 |
| 258 48 25 | 9 3 6 | 145 47 147 |
| 567 467 9 | 157* 14- 157* | 2 8 3 |
|-------------------+-------------------+-------------------|
| 23 5 23 | 8 9 4 | 7 1 6 |
| 4 16 8 | 37 16 37 | 9 5 2 |
| 16* 9 7 | 16* 5 2 | 48 3 48 |
*-----------------------------------------------------------*
```

**thread**on the player's forum.By the way, the reason why I like this approach is that it makes it much easier to spot these patterns and extend the pattern. For instance, you can probably guess that a jellyfish will correspond to a naked quad. The downside of the approach (especially if you're working on paper) is that you might have to right down all of these columns and that can be downright boring. Moreover, sometimes it's hard to see the connection between the column output and the original grid. But, it's food for thought and perhaps somebody else will offer up a more conventional explanation.

"Obviousness is always the enemy to correctness."-Bertrand Russell

You're welcome, Pete!Pete wrote:rep'na,

Thank you so much,

I never saw it quite this way before.

this seems much easier for me.

Pete

Two extra comments: 1) There is a version of this to catch (basic) finned fish (but it gets impractical for the ultimate fish, if you know what those are).

2) One can also use these grids to turn some medusa 3D-chains into xy-chains. I'd give citations, but I find them to be not so

*user friendly*(if you must, see e.g., Denis Berthier's

**thread**over on the player's forum). So if anyone is interested, I would be happy to explain in greater detail.

"Obviousness is always the enemy to correctness."-Bertrand Russell

It took me a while to understand what you meant by "naked pair" and "naked triple", but I finally got the idea. You're right about it being unconventional.rep'nA wrote: If an x-wing corresponds to a naked pair, then a swordfish must correspond to a naked triple.

How do you decide (working with pencil and paper) which candidate to look for a swordfish for, or do you try them all until you find one or eliminate all possibility of a swordfish?

I can see that, but hopefully a fair amount of practice will eliminate the need to write it all down each time.The downside of the approach (especially if you're working on paper) is that you might have to write down all of these columns and that can be downright boring.

I'm going to give the swordfish collection another try. I definitely messed them up the first time around and got stuck on all of them, even though I KNEW there was a swordfish in there.

You've hit on the key point...practice. When I work on pencil and paper, I also use navy beans to help me 'filter' candidates. Through time, I've learned to eliminate two kinds of candidates from consideration (as far as the above stuff goes): candidates with very few possible placements and candidates with very many possible placements. But this is just a general rule. With practice, I've learned to identify what patterns will be most likely to give me a fish deduction.enxio27 wrote: How do you decide (working with pencil and paper) which candidate to look for a swordfish for, or do you try them all until you find one or eliminate all possibility of a swordfish?I can see that, but hopefully a fair amount of practice will eliminate the need to write it all down each time.The downside of the approach (especially if you're working on paper) is that you might have to write down all of these columns and that can be downright boring.

One nice thing about writing things down for each candidate is that you can use some of the interesting tricks discoverd by Denis Berthier that pass between different candidates.

"Obviousness is always the enemy to correctness."-Bertrand Russell

Ok, now you have my curiosity up. Please elaborate!rep'nA wrote: You've hit on the key point...practice. When I work on pencil and paper, I also use navy beans to help me 'filter' candidates.

This is a useful start. Do you find that the likely candidates correspond to those contained in actual triples/quads, or does that make them less likely?Through time, I've learned to eliminate two kinds of candidates from consideration (as far as the above stuff goes): candidates with very few possible placements and candidates with very many possible placements.

I haven't even gotten as far as sea creatures yet, but I can see the likelihoood that eventually a pattern emerges.But this is just a general rule. With practice, I've learned to identify what patterns will be most likely to give me a fish deduction.

I'll have to give his thread another try after I've gotten a little practice with this. Maybe next time I can get past his bristles enough to learn something.One nice thing about writing things down for each candidate is that you can use some of the interesting tricks discoverd by Denis Berthier that pass between different candidates.