The New Sudoku Players' Forum

[Hud]

I ran across this Suboku puzzle last week and I found an xyzw wing in it. This was the only time I've used this technique.I used it and it worked out to solve the puzzle. Was there an easier way to do it, or was I just lucky?

| x 8 x | 9 4 2 | x x x |
| 6 x x | x 7 x | x x x |
| x 4 9 | 8 x x | x x x |

| 3 x x | 1 x x | x x x |
| 8 1 x | x x x | x 3 7 |
| x x x | x x 3 | x x 8 |

| x x x | x x 8 | 5 2 x |
| x x x | x 3 x | x x 6 |
| x x x | 2 6 7 | x 4 x |

[Shazbot]

Well, unless I'm some kind of subconscious genius and found your xyzw wing without realising it (which I highly doubt - what IS that?), I'm sorry to say the puzzle wasn't as complex as you thought. The hardest thing I needed to use was a naked quad (or a hidden pair if you're better at spotting those - I'm not much good at either). The rest was just naked pairs and singles, hidden singles and locked candidates.

Sorry to burst your bubble. At least it's always fun to know you've used a more advanced technique to solve a puzzle - even if there IS an easier way.

[sweetbix]

Hud, can you show me the wxyz wing. Thanks.

[Hud]

sweetbix, sorry so long in replying. I'll try to reconstruct the scene of the crime. I had a feeling there was an easier solution, but it was fun trying a new technique.

[Hud]

OK, here's a quick and dirty representation of where I was when I performed the unnecessary wxyz wing. Several months back I saw it discussed on a thread here named "interesting pattern" I didn't try to simplify the candidates so it would show better.

+----------------------+------------+--------------------+
| 157—-8-----3-------| 9 4---2----| 167---1567---15-- |
| 6------25----125----| 3 7---15---| 489---89-----49-- |
| 157—-4-----9-------| 8 15—6----| 1237--157—-1235 |
+----------------------+------------+----------------------+
| 3-----25679-24567-| 1 8---459-| 2469—569---2459 |
| 8-----1-------245---| 6 259 459-| 249---3------7--- |
| 2459 2569 2456---| 7 259 3----| 12469 1569- 8--- |
+------------------+------------+-----------------+
| 179—-367---167---| 4 19—-8---| 5-----2----139--|
| 1249 29----1248---| 5 3---19---| 1789--1789-6----|
| 159- 359---158----| 2 6---7-----| 1389--4----139--|
+---------------------+-------------+-------------------+

Please forgive the bad grid but I'm trying.
r2c2 is xy x=2 y=5
r8c2 is xz z=9
r2c6 is yw w=1
r8c6 is zw

According to the thread, x is eliminated from all other places in c2
y r2
z r8
w c6

[ronk]

Code: Select all

 *--------------------------------------------------------------------*
 | 157    8      3      | 9      4      2      | 167    1567   15     |
 | 6      25     12     | 3      7      15     | 489    89     49     |
 | 157    4      9      | 8      15     6      | 1237   157    1235   |
 |----------------------+----------------------+----------------------|
 | 3      5679   24567  | 1      8      459    | 2469   569    2459   |
 | 8      1      245    | 6      259    459    | 249    3      7      |
 | 2459   569    2456   | 7      259    3      | 12469  1569   8      |
 |----------------------+----------------------+----------------------|
 | 179    367    167    | 4      19     8      | 5      2      139    |
 | 124    29     1248   | 5      3      19     | 178    178    6      |
 | 159    359    158    | 2      6      7      | 1389   4      139    |
 *--------------------------------------------------------------------*

r2c2 is xy x=2 y=5
r8c2 is xz z=9
r2c6 is yw w=1
r8c6 is zw

According to the thread, x is eliminated from all other places in c2
y r2
z r8
w c6

Those eliminations are certainly valid, but I've never seen any write-ups about such a pattern. I tried to find the thread you mentioned, but there doesn't seem to be a way to search thread titles. If you can find a link to the thread, I would appreciate it.

The wxyz-wing name I'm familiar is for a pattern that has all four values in one cell referred to as the 'pilot' cell.

[Hud]

ronk, I wasn't sure what to call it, but that seemed all inclusive. The thread in question appeared on Oct 27, 05, and tso, bennys, and Lummox JR were involved. I guess a search of tso and his post #363 would find it. I'll also try to find it.

[Hud]

OK, I found it again. It was authored by bennys and was named "Interesting Pattern". I'm not sure about the capitalization so maybe the search didn't take that into consideration? Bennys post is what I copied for later use and Shazam (not Shazbot), I thought it had paid off lol.

[Bob Hanson]

This is the shortest possible Y-cycle. I don't think it's in the class of
an xy-wing or xyz-wing. But it's a nice one to spot:

Code: Select all

     
    (T)   (F)
     5..*..5
    /       \
(F)2         1(T)
   .         .
   .         .
   *         *
   .         .
   .         .
(T)2         1(F)
    \       /
  (F)9..*..9(T)


The idea here is that a FALSE at the the top end of this chain implies a
TRUE at the other end, and vice-versa, so either way we disallow any
other 2 in that column. There may be "easier" ways of seeing this, but
it's very nice -- and it applies to any of the numbers in the set, not just 2,
because of the symmetry.


you can find all sorts of things like this if you look at, say, the top95
puzzles with
http://www.stolaf.edu/people/hansonr/sudoku?&YCYCLESONLY&LOAD=top95
Examples include:
#4 #5 #17 #41

[ronk]

OK, I found it again. It was authored by bennys and was named "Interesting Pattern".

The link is http://forum.enjoysudoku.com/viewtopic.php?t=2022

Thanks, Ron

[Jeff]

Hi, Ronk, Hud and Bob

Hope this information is helpful. Actually, this pattern had been discussed in a few occasions in this forum under the headings of:

non-repetitive xy-chain
Is the 4 cell non-repetitive path common?
interesting pattern

Like an xy-wing, this pattern is also an xy-chain of length 4 but has a continuous propagation. It was referred to as an xy-ring in previous discussion. Whereas an elimination is made inside the chain for an xy-wing, multiple eliminations are possible for an xy-ring outside the chain.

This should not be confused with an wxyz-wing which is an extension of an xyz-wing.

[Hud]

Jeff, thanks for posting the other links to chains. Whenever it has been discussed, it has seemed like some foreign language but I see how it works now. I'll store that for future use when I get a bit more proficient at very hard Pappocoms. Later, I might like to access some puzzles requiring more advance techniques.

[Bob Hanson]

Here are some hard ones:

http://www.stolaf.edu/people/hansonr/sudoku?LOAD=top95

originally at http://magictour.free.fr/top95

These will keep you busy!