## POM Analysis of the X-Wing: The Filet-O-Fish Rule

Advanced methods and approaches for solving Sudoku puzzles
Hi tarek,

Sorry, I just don't see what you're trying to do. Maybe someone else can give specific help. In the mean time, try ...
Code: Select all
`+----------+-----------+-----------+ | 1  .  .  |  .  .  1  |  .  1 -1  | | .  1  .  |  1  .  .  |  .  .  .  | | .  .  .  |  .  .  .  |  .  1  .  | +----------+-----------+-----------+ | .  1  .  |  1  .  .  |  1  .  .  | | .  .  .  |  .  1  .  |  .  1  .  | | .  . *1  |  .  *  .  |  .  . *1  | +----------+-----------+-----------+ | .  . *1  |  .  *  .  | #1  . *1  | | .  .  *  |  . *1  .  | #1  . *1  | | 1  .  .  |  .  .  1  |  1  . +1  | +----------+-----------+-----------+ `

... for elimination r9c9<>1. (Initial post incorrectly also had r9c7<>1)
Last edited by ronk on Wed Jan 25, 2006 6:52 pm, edited 1 time in total.
ronk
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Location: Southeastern USA

[Edited: Section deleted as it serves no purpose now]

The swordfish i demonstrated is in columns eliminating in rows, the vertex in Box 9 can be any of the 1s demrcated by *, that allows 3 Finned Swordfishes at the same time to coexist(According to my understanding up until now). (cell r7c7 is a valid vertix leaving the other two as Fins, eliminating r7c9, then r8c7 is the vertex with other 2 as fins eliminating r8c9,......)
Last edited by tarek on Wed Jan 25, 2006 8:51 pm, edited 1 time in total.

tarek

Posts: 2699
Joined: 05 January 2006

tarek wrote:To tell u the truth, I don't know how u made the elimination in r9c7, it is not on a LINE with any of the verteces you've demonstrated.
Sorry, my mistake.

The swordfish i demonstrated is in columns eliminating in rows, the vertex in Box 9 can be any of the 1s demrcated by *, that allows 3 Finned Swordfishes at the same time to coexist(According to my understanding up until now). (cell r7c7 is a valid vertix leaving the other two as Fins, eliminating r7c9, then r8c7 is the vertex with other 2 as fins eliminating r8c9,......)
OK, I see now. From my POV, you are illustrating an overlay (pun intended) of three separate steps. Your deductions of r7c9<>1, r8c9<>1, and r9c9<>1 are correct, and so is the method AFAIK.

Coloring allows you to pin all the 1s ...
Code: Select all
`+----------+-----------+-----------+ | A  .  .  |  .  .  a  |  .  1  1  | | .  a  .  |  A  .  .  |  .  .  .  | | .  .  .  |  .  .  .  |  .  1  .  | +----------+-----------+-----------+ | .  A  .  |  a  .  .  |  1  .  .  | | .  .  .  |  .  A  .  |  .  a  .  | | .  .  a  |  .  .  .  |  .  .  A  | +----------+-----------+-----------+ | .  .  A  |  .  .  .  |  1  .  1  | | .  .  .  |  .  a  .  |  1  .  1  | | a  .  .  |  .  .  A  |  1  .  1  | +----------+-----------+-----------+ `

r1c8, r1c9, r4c7, r9c7, and r9c9 all see both conjugate colors 'A' and 'a', eliminating candidate 1s at those locations. Consequently r3c8=1, making 'a' represent false and 'A' represent true locations. Therefore r8c7=1.
ronk
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Location: Southeastern USA

Thanx ronk

tarek

Posts: 2699
Joined: 05 January 2006

I was having a hard time seeing what you were getting at, as well, tarek. Now I see it.

Nice to see that everything still works, even in the presence of two x-wings (or one big jellyfish) and a naked/hidden single .
Myth Jellies

Posts: 593
Joined: 19 September 2005

I should have posted it as follows,
Code: Select all
`+----------+-----------+-----------+ | 1  .  .  |  .  .  1  |  .  1  1  | | . *1  .  | *1  .  .  |  .  .  .  | | .  .  .  |  .  .  .  |  .  1  .  | +----------+-----------+-----------+ | . *1  .  | *1  .  .  | *1  .  .  | | .  .  .  |  .  1  .  |  .  1  .  | | .  .  1  |  .  .  .  |  .  .  1  | +----------+-----------+-----------+ | .  . -1  |  .  .  .  | *1  . +1  | | .  .  .  |  .  1  .  | #1  .  1  | | 1  .  .  |  .  .  1  | #1  .  1  | +----------+-----------+-----------++----------+-----------+-----------+ | 1  .  .  |  .  .  1  |  .  1  1  | | . *1  .  | *1  .  .  |  .  .  .  | | .  .  .  |  .  .  .  |  .  1  .  | +----------+-----------+-----------+ | . *1  .  | *1  .  .  | *1  .  .  | | .  .  .  |  .  1  .  |  .  1  .  | | .  .  1  |  .  .  .  |  .  .  1  | +----------+-----------+-----------+ | .  .  1  |  .  .  .  | #1  .  1  | | .  .  .  |  . -1  .  | *1  . +1  | | 1  .  .  |  .  .  1  | #1  .  1  | +----------+-----------+-----------++----------+-----------+-----------+ | 1  .  .  |  .  .  1  |  .  1  1  | | . *1  .  | *1  .  .  |  .  .  .  | | .  .  .  |  .  .  .  |  .  1  .  | +----------+-----------+-----------+ | . *1  .  | *1  .  .  | *1  .  .  | | .  .  .  |  .  1  .  |  .  1  .  | | .  .  1  |  .  .  .  |  .  .  1  | +----------+-----------+-----------+ | .  .  1  |  .  .  .  | #1  .  1  | | .  .  .  |  .  1  .  | #1  .  1  | |-1  .  .  |  .  . -1  | *1  . +1  | +----------+-----------+-----------+`

As MythJellies & ronk mentioned, apparantly it holds even though there are 2 X-Wings present , if the X-Wing (r24c24) eliminations came 1st then the eliminations above could not happen using a finned swordfish as we lose the r4c7 vertex. The other X-Wing(r19c16) can eliminate the 1s in box 9 row 9 leving only 2 simultaneous finned swordfishes (and a useless almost finned swordfish).

the presence of the hidden (then naked) 1 in r3 did not prevent thr eliminations

Tarek

tarek

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Joined: 05 January 2006

& another issue;

If we have a non grouped vertex in a COMPLETE (Swordfis, Jellyfish & Squirmbag) & no other vertex in its box; doesn't that mean that with it Simultaneously there are 2 ALMOST finned patterns (i.e. Sashimi).

If that is true then that would imply that the orignal Vertex candidate will end-up as a hidden single in its box.

As it turns into a naked single then it will eliminate all candidates sharing a line with it (killing itself & leaving the skeleton of the lower-class fish, a Seppuku in keeping with Samurai theme ).

if that is the case could we make a generalization out of this for every Complete (NXN) swordfish with a non grouped vertex with no other vertex in the same box as follows:

if a candidate forms a complete (NxN) Swordfish, the non grouped vertex cell that has no other vertex cell in the same box MUST have ONLY that candidate.

It seems logical, because with the specific NxN sworfish mentioned above, there will be always a complete (lower class fish) that will do the same job eventually but in 2 extra steps.
Last edited by tarek on Fri Jan 27, 2006 8:48 am, edited 1 time in total.

tarek

Posts: 2699
Joined: 05 January 2006

here is an example (#429 from the top1465):
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`*-----------------------------------------------------------------*|%2     %56    *69    | 7     *59     3     | 4      8      1     || 1      8      7     | 29     4      259   | 359    6      39    || 59     3      4     | 1      6      8     | 259    2579   279   ||---------------------+---------------------+---------------------|| 8      27     3     | 4     *279    1     | 6     *279    5     || 6      2457   29    | 8      23579  259   | 1      23479  23479 || 59     2457   1     | 6      23579  259   | 8      23479  23479 ||---------------------+---------------------+---------------------|| 4      1      5     | 3     *29     6     | 7     *29     8     || 37     9      26    | 25     8      47    | 235    1      2346  || 37     26     8     | 259    1      47    | 2359   23459  23469 |*-----------------------------------------------------------------*`

The verteces of the complete Swordfish are marked with "*"
Note that r1c3 is an ungrouped vertex with no other vertex in its box
The missing verteces of the 2 Almost finned Swordfishes are marked with "%"
The xwing is in r47c58

The chain of events in the Seppuku would be :
[From the complete swordfish]
Eliminating 9 From r5c3
Eliminating 9 From r5c5
Eliminating 9 From r6c5
Eliminating 9 From r3c8
Eliminating 9 From r5c8
Eliminating 9 From r6c8
Eliminating 9 From r9c8
[From The almost finned swordfish with the missing vertex at r1c1 & the fin being r1c3]
Eliminating 9 From r3c1
[Because r1c3 (the ungrouped vertex) will be a hidden single]
Eliminating 6 From r1c3
[Because r1c3 (the ungrouped vertex) will be a naked single, or because of the xwing]
Eliminating 9 From r1c5 (beheading the swordfish)

All of this from one observation

The x-wing will eventually do the same job but in 2 extra steps

tarek

Posts: 2699
Joined: 05 January 2006

debbo newbie here.

do you start with a clean puzzle as you attack it? or do you do the usual pairing up, populating the squares you can, then put the real brain-power to work?
debbo

Posts: 2
Joined: 20 July 2008

Code: Select all
`+-------------------+-------------------+-------------------+|     2     3     4 |    78    56  5678 |  1579    59  1579 ||     7     8     5 |     9     1     4 |     2     3     6 ||     6     9     1 |    27    25     3 |     8     4    57 |+-------------------+-------------------+-------------------+|   189*     4   389 |     6   235  1259* |   159B     7  1259B ||     5     2     6 |     4     7    19 C|   139A     8   139 A||    19*C     7    39 |   123*     8  259-1 |  1569@  2569     4 |+-------------------+-------------------+-------------------+|    89     1     7 |     5  2346   268 |  3469   269   239 ||     4     5    28 |  2378     9  2678 |   367     1   237 ||     3     6    29 |   127*    24   127* |  4579   259     8 |+-------------------+-------------------+-------------------+`

not sure if this is a valid move need some help on it.
when a=1 the *'s form a sword fish of some kind.?
when b=1 then c is one.
and @=1
there for R6C6 <>1
Some do, some teach, the rest look it up.

StrmCkr

Posts: 841
Joined: 05 September 2006

StrmCkr wrote:when a=1 the *'s form a sword fish of some kind.?

I don't think your *'s form a swordfish. Add [r6c6] and you have a swordfish w/o any eliminations, but I don't think you want that!

Code: Select all
` before 'a'                               after 'a' +-----------------------------------+    +-----------------------------------+ |  .  .  .  |  .  .  .  |  1  .  1  |    |  .  .  .  |  .  .  .  |  1  .  1  | |  .  .  .  |  .  1  .  |  .  .  .  |    |  .  .  .  |  .  1  .  |  .  .  .  | |  .  .  1  |  .  .  .  |  .  .  .  |    |  .  .  1  |  .  .  .  |  .  .  .  | |-----------+-----------+-----------|    |-----------+-----------+-----------| |  1  .  .  |  .  .  1  |  1  .  1  |    | *1  .  .  |  .  . *1  |  .  .  .  | |  .  .  .  |  .  .  1  |  1  .  1  |    |  .  .  .  |  .  .  .  | +1  . +1  | |  1  .  .  |  1  .  1  |  1  .  .  |    | *1  .  .  | *1  . ?1  |  .  .  .  | |-----------+-----------+-----------|    |-----------+-----------+-----------| |  .  1  .  |  .  .  .  |  .  .  .  |    |  .  1  .  |  .  .  .  |  .  .  .  | |  .  .  .  |  .  .  .  |  .  1  .  |    |  .  .  .  |  .  .  .  |  .  1  .  | |  .  .  .  |  1  .  1  |  .  .  .  |    |  .  .  .  | *1  . *1  |  .  .  .  | +-----------------------------------+    +-----------------------------------+`
daj95376
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i was thinking more like a franken mutant
pair of x wings linked by the *'s (box 4+5) & (5+8)

as there conjugated strong links by row,column, or box if you consider the way they are possitioned.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 841
Joined: 05 September 2006

Look at it this way. You want [r6c6]<>1 through some fish/pattern in the after 'a' grid. This would imply that [r6c6]=1 disrupts some fish/pattern in this grid. However, [r6c6]=1 leaves a perfectly stable grid after it's performed. No disruption!
daj95376
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Joined: 15 May 2006

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