## Almost X-wing?

Advanced methods and approaches for solving Sudoku puzzles

### Almost X-wing?

I am not sure if this is something new (well it won't be), but maybe it's worth considering.

In this puzzle (#1384/ 1465) and at that point Simple Sudoku has no further hints.

If you filter on 6 it is obvious that R59C18 would form an X-wing if there was not the candidate 6 in R7C8. If R7C8 <> 6 then the X-wing would kill the 6s in R5C27 and - more important for my point - in R9C4. That would leave a single in in block 8 (R8C4) so that the 6 in R8C7 can be eliminated safely (if R7C8=6, the 6 in R R8C7 can be eliminated anyway). It does not solve the puzzle directly but (due to some single 8s) it leads a big step forward.

I am sure it's not a classical fillet-o-fish/X-wing, but what is it?

Code: Select all
` *-----------* |...|2..|7.6| |...|..6|14.| |4..|..8|.2.| |---+---+---| |38.|...|.9.| |..5|3.1|...| |...|.6.|...| |---+---+---| |5..|9.2|3..| |2..|...|.7.| |.79|...|...| *-----------*   *--------------------------------------------------------------------------------------* | 189      1359     138      | 2        13459    3459     | 7        358      6        | | 789      2359     2378     | 57       359      6        | 1        4        3589     | | 4        13569    1367     | 157      1359     8        | 59       2        359      | |----------------------------+----------------------------+----------------------------| | 3        8        12467    | 45       245      457      | 2456     9        12457    | | 679      2469     5        | 3        2489     1        | 2468     68       2478     | | 179      1249     1247     | 458      6        4579     | 2458     1358     1234578  | |----------------------------+----------------------------+----------------------------| | 5        146      1468     | 9        7        2        | 3        168      148      | | 2        1346     13468    | 14568    1458     45       | 45689    7        14589    | | 168      7        9        | 14568    13458    345      | 2458     1568     12458    | *--------------------------------------------------------------------------------------*`
Neunmalneun

Posts: 52
Joined: 22 December 2005

To me it seems like a finned swordfish that eliminates 6 from r5c8, and thus also from r8c7 through locked candidates:

Code: Select all
` . . . . . . . . . . . . . . . . . . . 6 6 . . . . . . . . 6 . . .#6 . .*6 6 . . . .*6-6 . . . . . . . . . . . 6 6 . . . . 6 . . 6 6*6 . .*6 . .*6 . .*6 . . . 6 .`

Nice catch!

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

Or see it as grouped coloring with x-wing:

r8c7=6 => r7c8<>6 => x-wing for 6 in r59c18 => r9c4<>6 => r8c4=6 => r8c7<>6

See another nice sample by Daj Triple Implication Chain Forces X-Wings, where both implication chains use an x-wing and 4 numbers can be eliminated.

Dont know, if all these deductions should get an own name (though they can be found by seeing almost x-wings).
ravel

Posts: 998
Joined: 21 February 2006

Ok, another example (#1205 from 1465)

Code: Select all
` *-----------* |...|53.|.91| |...|64.|...| |...|..9|.2.| |---+---+---| |..4|36.|...| |7..|...|..6| |.93|..5|1..| |---+---+---| |38.|4..|.57| |..2|.5.|...| |..9|...|...| *-----------*  *-----------------------------------------------------------------------------* | 248     246     678     | 5       3       278     | 4678    9       1       | | 9       1235    1578    | 6       4       1278    | 3578    378     358     | | 148     13456   5678    | 178     178     9       | 345678  2       3458    | |-------------------------+-------------------------+-------------------------| | 1258    125     4       | 3       6       18      | 25789   78      2589    | | 7       125     158     | 1289    1289    4       | 2358    38      6       | | 6       9       3       | 278     278     5       | 1       4       28      | |-------------------------+-------------------------+-------------------------| | 3       8       16      | 4       29      16      | 29      5       7       | | 14      1467    2       | 1789    5       13678   | 3489    16      3489    | | 145     14567   9       | 1278    1278    13678   | 2348    16      2348    | *-----------------------------------------------------------------------------*If R2C2 <> 1 the X-Wing in R27C36 kills the 1 in R4C6 which eliminates candidate 1 in R5C2. So R5C2 <> 1.`
Neunmalneun

Posts: 52
Joined: 22 December 2005

Code: Select all
`*-----------------------------------------------------------------------------------*| 189      1359     138     | 2        13459    3459    | 7        358      6       || 789      2359     2378    | 57       359      6       | 1        4        3589    || 4        13569    1367    | 157      1359     8       | 59       2        359     ||---------------------------+---------------------------+---------------------------|| 3        8        12467   | 45       245      457     |#2456     9        12457   ||*679      2469     5       | 3        2489     1       |*2468    -68       2478    || 179      1249     1247    | 458      6        4579    | 2458     1358     1234578 ||---------------------------+---------------------------+---------------------------|| 5        146      1468    | 9        7        2       | 3        168      148     || 2        1346     13468   |*14568    1458     45      |*45689    7        14589   ||*168      7        9       |*14568    13458    345     | 2458     1568     12458   |*-----------------------------------------------------------------------------------**-----------------------------------------------------------------------------------*| 189      1359     138     | 2        13459    3459    | 7        358      6       || 789      2359     2378    | 57       359      6       | 1        4        3589    || 4       *13569   *1367    | 157      1359     8       | 59      *2        359     ||---------------------------+---------------------------+---------------------------|| 3       *8       *12467   | 45       245      457     |#2456    *9        12457   || 679      2469     5       | 3        2489     1       | 2468    -68       2478    || 179      1249     1247    | 458      6        4579    | 2458     1358     1234578 ||---------------------------+---------------------------+---------------------------|| 5       *146     *1468    | 9        7        2       | 3       *168      148     || 2        1346     13468   | 14568    1458     45      | 45689    7        14589   || 168      7        9       | 14568    13458    345     | 2458     1568     12458   |*-----------------------------------------------------------------------------------*Eliminating 6 From r5c8 (Finned Swordfish in Columns 147 with fin in r4c7,or by constructing a Sashimi Swordfish in rows 347 with fin in r4c7)`

Code: Select all
`*--------------------------------------------------------------------------*| 248     246     678    | 5       3       278    | 4678    9       1      || 9       1235    1578   | 6       4       1278   | 3578    378     358    || 148     13456   5678   | 178     178     9      | 345678  2       3458   ||------------------------+------------------------+------------------------||#1258   #125    *4      | 3       6      *18     | 25789   78      2589   || 7       125    -158    | 1289    1289    4      | 2358    38      6      || 6       9       3      | 278     278     5      | 1       4       28     ||------------------------+------------------------+------------------------|| 3       8      *16     | 4       29     *16     | 29      5       7      || 14      1467    2      | 1789    5       13678  | 3489    16      3489   || 145     14567   9      | 1278    1278    13678  | 2348    16      2348   |*--------------------------------------------------------------------------*Eliminating 1 From r5c3 (Sashimi XWing in Rows 47 with fin in r4c12)`

tarek

tarek

Posts: 2699
Joined: 05 January 2006

Neunmalneun wrote:Ok, another example (#1205 from 1465)(...) If R2C2 <> 1 the X-Wing in R27C36 kills the 1 in R4C6 which eliminates candidate 1 in R5C2. So R5C2 <> 1.

Tarek wrote:Eliminating 1 From r5c3 (Sashimi XWing in Rows 47 with fin in r4c12)

We could do better than that:

Code: Select all
` *----------------------------------------------------------------------* | 248     246     678   | 5       3       278   | 4678    9       1    | | 9       1235    1578  | 6       4       1278  | 3578    378     358  | | 1458    13456   15678 | 178     178     9     | 345678  2       3458 | |-----------------------+-----------------------+----------------------| | 1258    125     4     | 3       6       18    | 25789   78      2589 | | 7       125     158   | 1289    1289    4     | 2358    38      6    | | 6       9       3     | 278     278     5     | 1       4       28   | |-----------------------+-----------------------+----------------------| | 3       8       16    | 4       29      16    | 29      5       7    | | 14      1467    2     | 1789    5       13678 | 3489    16      3489 | | 145     14567   9     | 1278    1278    13678 | 2348    16      2348 | *----------------------------------------------------------------------*`

1. [r4c6]-1-[r5c45|r2c6]=1=[X-Wing:r25c23]-1-[r7c3]=1=[r7c6]-1-[r4c6],
and so r4c6 cannot be "1".

2. After that we have, for example:

r2c6=7 or r8c6=7. But [r2c6]=1=[r2c3]-1-[r3c1]-4-[r23c9]-3-[r2c7]-7-
-[r2c6]. So, r8c6=7 and the puzzle is solved.

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

Tarek: Why don't you eliminate the 1 in R5C2 as well ?
Neunmalneun

Posts: 52
Joined: 22 December 2005

Carcul wrote:1. [r4c6]-1-[r5c45|r2c6]=1=[X-Wing:r25c23]-1-[r7c3]=1=[r7c6]-1-[r4c6],
and so r4c6 cannot be "1".

From a pattern POV, that's a finned swordfish.
Code: Select all
` 248    246    678    | 5      3      278    | 4678   9      1 9     *1235  *1578   | 6      4     *1278   | 3578   378    358 1458   13456  5678   | 178    178    9      | 345678 2      3458----------------------+----------------------+--------------------- 1258   125    4      | 3      6     -18     | 25789  78     2589 7     *125   *158    |#1289  #1289   4      | 2358   38     6 6      9      3      | 278    278    5      | 1      4      28----------------------+----------------------+--------------------- 3      8     *16     | 4      29    *16     | 29     5      7 14     1467   2      | 1789   5      13678  | 3489   16     3489 145    14567  9      | 1278   1278   13678  | 2348   16     2348`

If both fin cells r5c45<>1, then the row swordfish in r257c236 causes r4c6<>1. Either r5c4=1 or r5c5=1 does the same.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Neunmalneun wrote:Tarek: Why don't you eliminate the 1 in R5C2 as well ?

The sashimi xwing is formed in rows 4,7 & columns 3,4......The fin is in row 4......

the elimination cells are cells in Columns 3,4 that can "see" the fin. r5c2 is not in columns 3 or 4....

Construct the fish (N rows * N columns).......
if the fin is in the row then you eliminate in cells of the columns that can see the fin & vice versa

tarek

tarek

Posts: 2699
Joined: 05 January 2006

So you just used another technique with another result. As there is no contradiction it seems we're both right (about different topics).
Neunmalneun

Posts: 52
Joined: 22 December 2005

I'm sure there will be a way to do both or even better eliminations (as ronk & carcul demonstrated)........but with that specific sashimi x-wing...only r5c3 is affected.

tarek

tarek

Posts: 2699
Joined: 05 January 2006

### Re: Almost X-wing?

Neunmalneun wrote:I am not sure if this is something new (well it won't be), but maybe it's worth considering.

In this puzzle (#1384/ 1465) and at that point Simple Sudoku has no further hints.

If you filter on 6 it is obvious that R59C18 would form an X-wing if there was not the candidate 6 in R7C8. If R7C8 <> 6 then the X-wing would kill the 6s in R5C27 and - more important for my point - in R9C4. That would leave a single in in block 8 (R8C4) so that the 6 in R8C7 can be eliminated safely (if R7C8=6, the 6 in R R8C7 can be eliminated anyway). It does not solve the puzzle directly but (due to some single 8s) it leads a big step forward.

I am sure it's not a classical fillet-o-fish/X-wing, but what is it?

Forgive me for backing up to your first post, but everyone took a tangent on your puzzle and I'd like to review your logic. You are describing an X-Wing with a single fin cell. In this case, either the X-Wing is true or else the fin cell is true. You need to look for an overlap in eliminations from the X-Wing and [r7c8]=6. I don't think you'll find it; at least, not without some complex relationships on <6>. This is probably why everyone presented their interpretations of your puzzle.

Your second example is again based on inequality (<>) in the fin cell instead of equality (=) and looking for an overlap. Each time, you just get lucky that the fin cell isn't true.

ravel: Thanks for referencing my TIC Forces X-Wings!
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Daj95376, thanks for your reply. I agree that in my first example either the fin cell (R7C8)=6 or the X-wing (R59C18) =6. But I don't agree that there is no overlap in both eliminations. If the X-wing is right R9C4<>6 leaving a single 6 in block 8 (in the cell R8C4) which kills the 6 in R8C7. If the fin cell (R7C8) = 6, the 6 in R8C7 is eliminated too. So in my opinion the elimination of 6 in R8C7 is a logic deduction and no lucky guess. The same is right for my second example: no matter if the fin cell is right or wrong R5C2 cannot be 1.

In regard with my second example I am a little bit disappointed. I asked if you agree that the "almost x-wing" (by the way I agree to ravel that it is not important to give all kinds of deductions an own name) in R27C36 kills the 1 in R5C2. One answer pointed out that it is a sashimi X-wing eliminating 1 from R5C3, the other showed that there is a monster chain eliminating 1 from R4C6. Don't get me wrong: both alternative steps are totally logic and correct and I admit they are more sophisticated than my own observation. But both are not exactly answers to my questions.They are just two different steps on the same digit in the same grid.
Neunmalneun

Posts: 52
Joined: 22 December 2005

Neunmalneun wrote:I asked if you agree that the "almost x-wing" (...) But both are not exactly answers to my questions.

Yes, your Almost X-Wing is correct, but I don't know why you are asking that, since you finded a correct deduction by your own. Anyway, I see your conclusion in this way:

[r5c2]-1-[r2c2]=1=[X-Wing: r27c36]-1-[r4c6]=1=[r4c12]-1-[r5c2],

which is equivalent to your words.

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

Neunmalneun, both of your examples are of almost X-wings which have been discussed most recently in this thread. Reiterating what you've said, r8c7 is linked to r9c18 by strong link between r8c4 and r9c4 (r8c7-6-r8c4=6=r9c4-6-r9c18). Then because of the direct link between r8c7 and r7c8, the covering set is reduced to r5 and thus r8c7<>6. I don't see any other eliminations with this fish. The grouped strong link between r4c12 and r4c6 serves the same purpose in your second example where the covering set is reduced to c3 and thus r5c2<>1.
Mike Barker

Posts: 458
Joined: 22 January 2006

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