Whatever happened to Strong Wings?

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Whatever happened to Strong Wings?

Postby Yogi » Tue Jan 02, 2018 8:21 pm

34857..1617.4.6.585.6.81.749572648316817..4254..815697765..814.8.415.76.21.64758.
This puzzle can be solved with a fairly long chain which shows that 3r8c2 => 3r8c6.
9r8c2 then quickly reduces to a BUG+1 @ r7c5, but is there a simpler more obvious way?
RCB Solver set r3c4 at 3 through a different process:
Strong Wing on candidate 3 at (3)r2c5=r3c4 - (3)r3c4=r7c4 - (9)r7c4=r7c5 - (2)r7c5=r2c5
3a. Setting candidate: 3 at r3c4
Has this term ‘Strong Wing’ fallen out of favour, or is it now regarded as just part of something else?
For those interested, this was a 17-clue puzzle which started as 3.......6.......58.....1....5.26......1...4.....8.....7.....14.....5.7.....6.....
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Re: Whatever happened to Strong Wings?

Postby Leren » Tue Jan 02, 2018 9:40 pm

Yogi wrote : but is there a simpler more obvious way?

Depends what you mean by that. I just plugged your position into Hodoku. It used a Skyscraper, two W Wings and the BUG +1. Isn't that simple and obvious enough ?

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Re: Whatever happened to Strong Wings?

Postby eleven » Tue Jan 02, 2018 9:56 pm

The "Strong wing" chain is weird. It is not possible at all to prove 3r3c4 from these cells.
You can use the skyscraper (finned x-wing) for 9 in columns 2,4 and also an xy-wing then to get to the BUG.
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Re: Whatever happened to Strong Wings?

Postby Yogi » Fri Jan 12, 2018 10:56 pm

Thanx. I went on to the lengthy chain because I did not find much that I could use with the skyscraper, which simply confined 9 to Row7 in Box8.
I presume you were refering to the XY Chain r1c6(9/2) - r8c6(2/3) - r7c4(3/9) which shows that
2r1c6 => 3r8c6 => 9r7c4 => r3c4 <> 9
OR 9r1c6 => r3c4 <> 9, therefore r3c3 = 3 In English this could be stated as 'All available options in r1c6 exclude 9 from r3c4, so r3c4 = 3.'
This leads on to a wider question of how the Pen & Paper Solver would spot such an animal?
Is is really that simple:
1) 2 in r1c6 sees 2 in r8c6
2) Alternative candidate 3 in r8c6 sees 3 in r7c4
3) Alternative candidate 9 in r7c4 sees 9 in r3c4, which can also see the starting cell, thus closing the loop.
It doesn't work the same going back the other way:
1) 9 in r1c6 sees 9 in r3c4
2) Alternative candidate 3 in r3c4 sees 3 in r7c4, but then
3) Alternative candidate 9 in r7c4 would need a different path and more jumps to get back to r1c6.
Does it need to work around the same path in both directions, or is one way alone enough to get a result in these cases?
After all, the above elimination did work.

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Re: Whatever happened to Strong Wings?

Postby eleven » Sat Jan 13, 2018 5:43 pm

Code: Select all
+----------------+----------------+----------------+
| 3    4    8    | 5    7   @29   | 29   1    6    |
| 1    7    29   | 4    239  6    | 239  5    8    |
| 5    29   6    | 3-9  8    1    | 239  7    4    |
+----------------+----------------+----------------+
| 9    5    7    | 2    6    4    | 8    3    1    |
| 6    8    1    | 7    39   39   | 4    2    5    |
| 4    23   23   | 8    1    5    | 6    9    7    |
+----------------+----------------+----------------+
| 7    6    5    |@39   239  8    | 1    4    239  |
| 8    39   4    | 1    5   #23   | 7    6    239  |
| 2    1    39   | 6    4    7    | 5    8    39   |
+----------------+----------------+----------------+

This is an xy-wing. The pivot is the cell r8c6 with candidates 23.
If it is 2, r1c6=9.
If it is 3, r7c4=9.
So one of r1c6 and r7c4 must be 9. The cell r3c4 sees both, thus the 9 there can be eliminated.

There would be another xy-wing with r8c2 instaed of r7c4, but the only cell, which sees both r1c6 and r8c2 is r1c2, which has no 9 to eliminate.

As a chain: (9=2)r1c6-(2=3)r8c6-(3=9)r7c4
Either r1c6 is 9
or it is 2 then r8c6=3 and r7c4=9
Again r1c6 or r7c4 must be 9.

Using a contradiction:
If r3c4=9, then r1c6=2, r8c6=3 and r7c4=9. But 9 cannot be both in r3c4 and r7c4
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Re: Whatever happened to Strong Wings?

Postby Yogi » Sat Jan 20, 2018 12:13 am

Thanx for that. Plenty to think about there.
However, no-one has yet answered the original question about why the term Strong Wing seems to not be currently used.
Tso posted 'Strong Wing vs XY Wing' in 2006, but I haven't seen it used more recently.

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Re: Whatever happened to Strong Wings?

Postby eleven » Sun Jan 21, 2018 11:08 pm

Can you provide a link ? The sample in your opening post was just weird.

Ah, i found it here. This is a small loop. I think, people call it ring now (?) Note that tso says, that Strong wings and xy-wings can't coexist.
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Re: Whatever happened to Strong Wings?

Postby StrmCkr » Tue Jan 23, 2018 8:07 am

http://forum.enjoysudoku.com/post22386.html?hilit=strong%20wing#p22386
examples:
[url]post22267.html?hilit=strong%20wing#p22267[/url]

these where noted to be AiC, Nice loops {continuous/discontinuous} and where never really used by anyone else on here except Tso by the reference of strong-wing
Some do, some teach, the rest look it up.
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Re: Whatever happened to Strong Wings?

Postby SpAce » Tue Jan 23, 2018 1:20 pm

I'd use the obvious Skyscraper first:

(9)r8c2 = r3c2 - r3c4 = (9)r7c4 => -9 r8c6

and then (after the pointing pair elimination) one or the other XY-Wing:

(3=9)r4c3 - (9=2)r1c6 - (2=3)r8c6 => -3 r7c4

or:

(9=3)r7c4 - (3=2)r8c6 - (2=9)r1c6 => -9 r3c4

to get to the BUG+1 @r8c9.

Easy enough for a pencil-and-paper solver, don't you think?

Alternatively you could replace the XY-Wing with an AIC Type 2:

Code: Select all
+--------------+------------------+-------------+
| 3   4   8    |  5     7   d2(9) | 29  1   6   |
| 1   7   29   |  4     239  6    | 239 5   8   |
| 5   29  6    | a(3)-9 8    1    | 239 7   4   |
+--------------+------------------+-------------+
| 9   5   7    |  2     6    4    | 8   3   1   |
| 6   8   1    |  7     39   39   | 4   2   5   |
| 4   23  23   |  8     1    5    | 6   9   7   |
+--------------+------------------+-------------+
| 7   6   5    | b39    239  8    | 1   4   23  |
| 8   39  4    |  1     5   c23   | 7   6   239 |
| 2   1   39   |  6     4    7    | 5   8   39  |
+--------------+------------------+-------------+


(3)r3c4 = r7c4 - (3=2)r8c6 - (2=9)r1c6 => -9 r3c4

...which you can see as a Discontinuous Nice Loop Type 2 that proves 3r3c4:

(3)r3c4 = r7c4 - (3=2)r8c6 - (2=9)r1c6 - (9=3)r3c4 => 3r3c4

That's the closest resemblance to a "strong wing" I can see here, but it's not it. (Edit: See below for a possibly closer attempt.)
Last edited by SpAce on Tue Jan 23, 2018 3:34 pm, edited 1 time in total.
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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Re: Whatever happened to Strong Wings?

Postby SpAce » Tue Jan 23, 2018 2:58 pm

Yogi wrote:This puzzle can be solved with a fairly long chain which shows that 3r8c2 => 3r8c6.


Can you show that chain? Are you sure you're talking about a chain and not a net? I can see a forcing net that empties r8c6 if 3r8c2:

Code: Select all
r8c2=3 -> r8c6<>3
       -> r6c2=2 -> r3c2=9 -> r3c4=3 -> r7c4=9 -> r8c6<>9
                           -> r2c3=2 -> r2c5<>2 -> r1c6=2 -> r8c6<>2
-> r8c6 <> 2,3,9 => r8c2 <> 3


Or as an AIC net:

(9=3)r8c2 - (3=2)r6c2 - (2=9)r3c2 - [[(9=2)r2c3 - r2c5 = r7c5 - r8c6] | [(9=3)r3c4 - (3=9)r7c4 - r8c6]] = (3)r8c6 => -3 r8c2

It works, but it's a very complicated way to solve this puzzle, especially since it's not even a one-step solution (still requires a BUG or an XY-Wing after that).

RCB Solver set r3c4 at 3 through a different process:
Strong Wing on candidate 3 at (3)r2c5=r3c4 - (3)r3c4=r7c4 - (9)r7c4=r7c5 - (2)r7c5=r2c5
3a. Setting candidate: 3 at r3c4


That chain makes no sense as written. Can you clarify how it's supposed to work and how it's related to the "strong wing" concept?

I can see something like this but I'm still not sure if it's a strong wing (and it's only possible after the Skyscraper elimination):

Code: Select all
+--------------+--------------------+-------------+
| 3   4   8    |  5      7      29  | 29  1   6   |
| 1   7   29   |  4     d(2)9-3 6   | 239 5   8   |
| 5   29  6    | a(3)9   8      1   | 239 7   4   |
+--------------+--------------------+-------------+
| 9   5   7    |  2      6      4   | 8   3   1   |
| 6   8   1    |  7      39     39  | 4   2   5   |
| 4   23  23   |  8      1      5   | 6   9   7   |
+--------------+--------------------+-------------+
| 7   6   5    | b39    c239    8   | 1   4   23  |
| 8   39  4    |  1      5      23  | 7   6   239 |
| 2   1   39   |  6      4      7   | 5   8   39  |
+--------------+--------------------+-------------+


As an AIC: (3)r3c4 = (3-9)r7c4 = (9-2)r7c5 = (2)r2c5 => -3 r2c5

or as a Discontinuous Nice Loop: (3)r3c4 = (3-9)r7c4 = (9-2)r7c5 = (2-3)r2c5 = (3)r3c4 => 3r3c4

Added: one more way to do it (but still no strong wing, I guess):

Code: Select all
+--------------+---------------------+-------------+
| 3   4   8    | 5      7       b29  | 29  1   6   |
| 1   7   29   | 4     a(2)9-3   6   | 239 5   8   |
| 5   29  6    | 39     8        1   | 239 7   4   |
+--------------+---------------------+-------------+
| 9   5   7    | 2      6        4   | 8   3   1   |
| 6   8   1    | 7     d(3)9    c39  | 4   2   5   |
| 4   23  23   | 8      1        5   | 6   9   7   |
+--------------+---------------------+-------------+
| 7   6   5    | 39     239      8   | 1   4   23  |
| 8   39  4    | 1      5        23  | 7   6   239 |
| 2   1   39   | 6      4        7   | 5   8   39  |
+--------------+---------------------+-------------+

AIC: (2)r2c5 = (2-9)r1c6 = (9-3)r5c6 = (3)r5c5 => -3 r2c5

DNL: (3)r3c4 = (3-2)r2c5 = (2-9)r1c6 = (9-3)r5c6 = r5c5 - r2c5 = (3)r3c4 => 3r3c4
Code: Select all
   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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