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enxio27
Master

Joined: 17 Mar 2007
Posts: 165

 Posted: Fri Sep 28, 2007 7:08 pm    Post subject: 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.
rep'nA
Hooked

Joined: 19 Jan 2007
Posts: 49
Location: Union City, California

Posted: Mon Oct 01, 2007 9:46 am    Post subject:

Let me try a somewhat unconventional way of explaining Swordfish. First, since you understand x-wing, lets look at an example:
 Code: .---------------------.---------------------.---------------------. | 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     | '---------------------'---------------------'---------------------'

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:
 Code: *-----------------------------------------------------------*  | 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    |  *-----------------------------------------------------------*

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.
 Code: *-----------------------------------------------------------*  | 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    |  *-----------------------------------------------------------*

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
Pete
Gold Member

Joined: 13 May 2006
Posts: 113
Location: Cincinnati Ohio, USA

 Posted: Sun Oct 07, 2007 11:25 am    Post subject: rep'na, Thank you so much, I never saw it quite this way before. this seems much easier for me. Pete_________________"It gets dark at night" - Olbers
rep'nA
Hooked

Joined: 19 Jan 2007
Posts: 49
Location: Union City, California

Posted: Mon Oct 08, 2007 10:00 pm    Post subject:

 Pete wrote: rep'na, Thank you so much, I never saw it quite this way before. this seems much easier for me. Pete

You're welcome, 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
enxio27
Master

Joined: 17 Mar 2007
Posts: 165

Posted: Tue Oct 30, 2007 3:04 pm    Post subject:

 rep'nA wrote: If an x-wing corresponds to a naked pair, then a swordfish must correspond to a naked triple.

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.

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?

 Quote: 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 can see that, but hopefully a fair amount of practice will eliminate the need to write it all down each time.

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.
rep'nA
Hooked

Joined: 19 Jan 2007
Posts: 49
Location: Union City, California

Posted: Wed Oct 31, 2007 12:47 pm    Post subject:

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?
 Quote: 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 can see that, but hopefully a fair amount of practice will eliminate the need to write it all down each time.

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.

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
enxio27
Master

Joined: 17 Mar 2007
Posts: 165

Posted: Wed Oct 31, 2007 2:18 pm    Post subject:

 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.

Ok, now you have my curiosity up. Please elaborate!

 Quote: 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.

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?

 Quote: 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 haven't even gotten as far as sea creatures yet, but I can see the likelihoood that eventually a pattern emerges.

 Quote: 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.

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.
Sarah
Regular

Joined: 28 Nov 2006
Posts: 17
Location: Milky Way Galaxy [for now]

 Posted: Sat Nov 03, 2007 2:32 am    Post subject: Thanks for posting the approach. I think this will be much easier for my daughter to grasp.
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