Degenerate XWings

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Degenerate XWings

Postby Yogi » Wed Feb 06, 2019 2:02 am

.2456179..914372....68294.1958.4......29785......5.9...85.14..916.2958.4..9.86...

6FebPost.png
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Here, r68c3 & r8c8 are all (3,7). Or should that be (3-7) or (3=7)? Anyway, those three cells are all limited to candidates 3 and 7
and they form three corners of an XWing. What can we infer from that in Box6?
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Re: Degenerate XWings

Postby Leren » Wed Feb 06, 2019 3:39 am

Not much. The reason is that r6c3 and r8c8 have the same parity ie they are both 3 or both 7. If they are both 7 you can't say anything directly about Box 6. Instead there is a Sashimi finned Jellyfish in 3's that resolves their position as follows.

Code: Select all
*-----------------------------------------------*
| *38    2     4  | 5  6 1  | 7    9      *38   |
| 58     9     1  | 4  3 7  | 2    568     568  |
|*357   *37    6  | 8  2 9  | 4   *35      1    |
|-----------------+---------+-------------------|
| 9      5     8  | 16 4 23 | 136  12367   2367 |
|*346   *134   2  | 9  7 8  | 5   *1346   *36   |
| 3467   1347  37 | 16 5 23 | 9    123468  2368 |
|-----------------+---------+-------------------|
| 27-3   8     5  | 37 1 4  | 36   2367    9    |
| 1      6    F37 | 2  9 5  | 8   *37      4    |
| 247-3  47-3  9  | 37 8 6  | 13   12357   2357 |
*-----------------------------------------------*

It doesn't solve the whole puzzle but you resolve your cell values of interest.

Code: Select all
*-----------------------------------------*
| 38  2    4 | 5  6 1  | 7    9      38   |
| 58  9    1 | 4  3 7  | 2    568    568  |
| 357 37   6 | 8  2 9  | 4    35     1    |
|------------+---------+------------------|
| 9   5    8 | 16 4 23 | 136  1236   7    |
| 346 134  2 | 9  7 8  | 5    1346   36   |
| 346 134 #7 | 16 5 23 | 9    123468 2368 |
|------------+---------+------------------|
| 27  8    5 | 37 1 4  | 36   236    9    |
| 1   6   #3 | 2  9 5  | 8   #7      4    |
| 247 47   9 | 37 8 6  | 13   1235   235  |
*-----------------------------------------*

Leren
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Re: Degenerate XWings

Postby SpAce » Wed Feb 06, 2019 5:14 am

Leren is right that the (37)-pattern itself doesn't produce anything useful (not even UR potential here, because the corners are in four boxes). Then again, catching a Finned Sashimi Jellyfish doesn't seem like a very realistic option for most manual solvers either (certainly not for me). There's a much simpler X-Chain of 3s that does the same trick, though:

Code: Select all
.------------------.------------.---------------------.
| 38    2      4   | 5   6   1  |   7    9       38   |
| 58    9      1   | 4   3   7  |   2    568     568  |
| 357   37     6   | 8   2   9  |   4    35      1    |
:------------------+------------+---------------------:
| 9     5      8   | 16  4  b23 |  c136  12367   2367 |
| 346   134    2   | 9   7   8  |   5    1346    36   |
| 3467  1347  a37  | 16  5  b23 |   9    123468  2368 |
:------------------+------------+---------------------:
| 237   8      5   | 37  1   4  | c(3)6  2367    9    |
| 1     6    a(3)7 | 2   9   5  |   8    7-3     4    |
| 2347  347    9   | 37  8   6  | c(3)1  12357   2357 |
'------------------'------------'---------------------'

Extended Grouped Skyscraper:

(3)r[8=6]c3 - r[6=4)c6 - (3)r[4=79]c7 => -3 r8c8

Standard Eureka: Show
(3)r8c3 = r6c3 - r6c6 = r4c6 - r4c7 = (3)r79c7 => -3 r8c8

Incidentally that pattern is also a Finned Sashimi Swordfish (with the same elimination), but I only noticed that fact afterwards (apparently having more aptitude for being a chain-ganger than a fisherman):

Finned Sashimi Swordfish: (3)c367\r468 f:r79c7 => -3 r8c8

Either that or the X-Chain should be easier to see than the Jellyfish variant. (Unfortunately it's not a very effective move here no matter which way you spot it).
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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Re: Degenerate XWings

Postby Yogi » Wed Feb 06, 2019 9:04 pm

I think I’m more into chaining than Jellying also, although 2Fish seem routine to me. That’s why I’m examining these variations of XWings.
I notice that nominating 3r6c3 quickly leads to 3r58c8, proving 7r6c3, with more singles flowing on, although the puzzle remains difficult.
This does seem to be related to SpAce’s suggestion, although it joins the chain at a different point. An ordinary Skyscraper is easy enough to describe as two parallel CPs in the same candidate with their ends occupying four boxes arranged rectangularly, with one end cell of each of the CPs being in the same row or column, but their other ends NOT being in the same row or column. Maybe you can help me see this pattern here as an ‘Extended Skyscraper’.
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Re: Degenerate XWings

Postby SpAce » Thu Feb 07, 2019 12:05 am

Yogi wrote:An ordinary Skyscraper is easy enough to describe as two parallel CPs in the same candidate with their ends occupying four boxes arranged rectangularly, with one end cell of each of the CPs being in the same row or column, but their other ends NOT being in the same row or column. Maybe you can help me see this pattern here as an ‘Extended Skyscraper’.

An Extended Grouped Skyscraper. It has thus two separate complications when compared to a regular Skyscraper: one is the grouping (one end-point is a group instead of a single candidate, in this case 3r79c7) and the other is the extension (the chain has an extra linking pair, in this case 3r46c6). Otherwise it works just like a Skyscraper (or any other chain) by proving that at least one of the end-points must be true, which causes the eliminations. (Note: using the "Extended" keyword here is probably non-standard or at least non-common).

  1. Skyscraper:

    Code: Select all
    .------------------.------------.---------------------.
    |                  |            |                     |
    |                  |            |                     |
    |                  |            |                     |
    :------------------+------------+---------------------:
    |                  |            |                     |
    |                  |            |                     |
    |               3  |            |  3                  |
    :------------------+------------+---------------------:
    |                  |            |                     |
    |              (3) |            |          x       x  |
    |  x      x        |            | (3)                 |
    '------------------'------------'---------------------'

  2. Grouped Skyscraper

    Code: Select all
    .------------------.------------.---------------------.
    |                  |            |                     |
    |                  |            |                     |
    |                  |            |                     |
    :------------------+------------+---------------------:
    |                  |            |                     |
    |                  |            |                     |
    |               3  |            |  3                  |
    :------------------+------------+---------------------:
    |                  |            | (3)                 |
    |              (3) |            |          x       x  |
    |                  |            | (3)                 |
    '------------------'------------'---------------------'

  3. Extended Skyscraper

    Code: Select all
    .------------------.------------.---------------------.
    |                  |            |                     |
    |                  |            |                     |
    |                  |            |                     |
    :------------------+------------+---------------------:
    |                  |          3 |  3                  |
    |                  |            |                     |
    |               3  |          3 |                     |
    :------------------+------------+---------------------:
    |                  |            |                     |
    |              (3) |            |          x       x  |
    |  x      x        |            | (3)                 |
    '------------------'------------'---------------------'

  4. Extended Grouped Skyscraper

    Code: Select all
    .------------------.------------.---------------------.
    |                  |            |                     |
    |                  |            |                     |
    |                  |            |                     |
    :------------------+------------+---------------------:
    |                  |          3 |  3                  |
    |                  |            |                     |
    |               3  |          3 |                     |
    :------------------+------------+---------------------:
    |                  |            | (3)                 |
    |              (3) |            |          x       x  |
    |                  |            | (3)                 |
    '------------------'------------'---------------------'


    Legend: Show
    x: possible elimination (of a candidate 3)
    (3): chain end point
    (note: all marked candidate 3s are the only ones in their columns)

Did that help?
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Re: Degenerate XWings

Postby eleven » Fri Feb 08, 2019 8:57 pm

This is a one-stepper, which i don't want to formulate in AIC, but i hope, Yogi would accept it.
Code: Select all
 *--------------------------------------------------------------*
 |  38     2      4    |  5    6  1    |  7     9       b38     |
 |  58     9      1    |  4    3  7    |  2    b568      568    |
 |  357    37     6    |  8    2  9    |  4    b35       1      |
 |---------------------+---------------+------------------------|
 |  9      5      8    |  16   4  23   |  136   12367    2367   |
 |  346    134    2    |  9    7  8    |  5     1346     36     |
 |  3467   1347   37   |  16   5  23   |  9     123468   2368   |
 |---------------------+---------------+------------------------|
 |  237    8      5    |  37   1  4    |  36   c2367     9      |
 |  1      6      37   |  2    9  5    |  8     37       4      |
 |  2347   347    9    |  37   8  6    |  13   a12357    35-27  |
 *--------------------------------------------------------------*

-5r9c9 => 5r9c9 => 386 r3c8,r1c9,r2c8 => 27r78c8
==> r9c9<>27
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Re: Degenerate XWings

Postby SpAce » Fri Feb 08, 2019 11:01 pm

eleven wrote:This is a one-stepper, which i don't want to formulate in AIC, but i hope, Yogi would accept it.

-5r9c9 => 5r9c8 => 386 r3c8,r1c9,r2c8 => 27r78c8
==> r9c9<>27

Nice solution! I'd write it like this, though it's not necessarily standard Eureka:

Code: Select all
.----------------.-----------.------------------------.
| 38    2     4  | 5   6  1  | 7     9       b38      |
| 58    9     1  | 4   3  7  | 2    b568     b568     |
| 357   37    6  | 8   2  9  | 4    b35       1       |
:----------------+-----------+------------------------:
| 9     5     8  | 16  4  23 | 136   12367    2367    |
| 346   134   2  | 9   7  8  | 5     1346     36      |
| 3467  1347  37 | 16  5  23 | 9     123468   2368    |
:----------------+-----------+------------------------:
| 237   8     5  | 37  1  4  | 36  c(27)36    9       |
| 1     6     37 | 2   9  5  | 8   c(7)3      4       |
| 2347  347   9  | 37  8  6  | 13    12357   a3(5)-27 |
'----------------'-----------'------------------------'

(5)r9c9 = (5,6,8,3)b3p6538 - (6|3=27)r78c8 => -27 r9c9; stte
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Degenerate XWings

Postby Yogi » Tue Feb 12, 2019 5:29 am

Thanx to SpAce for that explanation. I see it works just like a Sashimi or Finned XWing with the Either or Neither reasoning in Box 9:

1) If Either of the two fins r79c7 are 3, then -3r8c8 => 3r8c3
||
2) If Neither of r79c7 are 3, then 3r4c7 => => 3r8c3

The 23Locked Pair r46c6 connects r4c7 to r6c3 beautifully to keep the forcing chain going in that direction.

However, it is true that there is still another step required to finally solve the puzzle.
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Re: Degenerate XWings

Postby SpAce » Tue Feb 12, 2019 6:21 am

Yogi wrote:Thanx to SpAce for that explanation. I see it works just like a Sashimi or Finned XWing with the Either or Neither reasoning in Box 9:

1) If Either of the two fins r79c7 are 3, then -3r8c8 => 3r8c3
||
2) If Neither of r79c7 are 3, then 3r4c7 => => 3r8c3

Exactly.

The 23Locked Pair r46c6 connects r4c7 to r6c3 beautifully to keep the forcing chain going in that direction.

That's one way to see it, but it's more complicated because then it's no longer a single-digit technique. You don't actually need the locked pair for anything because you have a conjugate pair of 3s in that column, which is enough for the linking action. It would work just as well if there were many other digits in those two cells -- it's just a coincidence that it's also a locked pair.
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