The New Sudoku Players' Forum

[Yogi]

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.....
Yogi

[Leren]

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 ?

Leren

[eleven]

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.

[Yogi]

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.

Yogi

[eleven]

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

[Yogi]

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.

- Yogi

[eleven]

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.

[StrmCkr]

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

[SpAce]

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.)

[SpAce]

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

[StrmCkr]

after taking a long time away from what you where doing i finally figured it out.

at this stage of the puzzle

Code: Select all

.-----------.-------------.-------------.
| 3  4   8  | 5   7    29 | 29   1  6   |
| 1  7   29 | 4   239  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   39   39 | 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  |
'-----------'-------------'-------------'

a strong wing {from the links i provide in my above post }

Code: Select all

+-----------+--------------------+-------------+
| 3  4   8  | 5       7       29 | 29   1  6   |
| 1  7   29 | 4       9(23)   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  | -3(+9)  3(2-9)  8  | 1    4  23  |
| 8  39  4  | 1       5       23 | 7    6  239 |
| 2  1   39 | 6       4       7  | 5    8  39  |
+-----------+--------------------+-------------+


actually exists in this space.

[SpAce]

after taking a long time away from what you where doing i finally figured it out.

a strong wing {from the links i provide in my above post }

Code: Select all

+-----------+--------------------+-------------+
| 3  4   8  | 5       7       29 | 29   1  6   |
| 1  7   29 | 4       9(23)   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  | -3(+9)  3(2-9)  8  | 1    4  23  |
| 8  39  4  | 1       5       23 | 7    6  239 |
| 2  1   39 | 6       4       7  | 5    8  39  |
+-----------+--------------------+-------------+


actually exists in this space.

It seems so (and in this case it's not a loop so I don't mind the name so much!). You know what else it is? It's a dual L3-Wing (related to this on-going discussion)! That duality seems to be the defining characteristic of a "Strong Wing". Here's how I see those two possibilities:

Code: Select all

L3-Wing: (9)r7c4 = (9-2)r7c5 = (2-3)r2c5 = (3)r3c4 => -3 r7c4, -9 r3c4 (=> +3 r3c4, +9 r7c4)
L3-Wing: (9)r7c4 = (9-3)r3c4 = (3-2)r2c5 = (2)r7c5 => -9 r7c5          (=> +9 r7c4)

[ Because of the bivalues in r37c4 (coincidental, not required for the Strong Wing pattern), we also have:

Code: Select all

H2-Wing: (9=3)r7c4 - r3c4 = (3-2)r2c5 = (2)r7c5 => -9 r7c5 (=> +9 r7c4)
H2-Wing: (3=9)r3c4 - r7c4 = (9-2)r7c6 = (2)r2c5 => -3 r2c5 (=> +3 r3c4)

]

Of course you only need to use any one of those wings/chains to get the same results (+3 r3c4, +9 r7c4). Thus, my conclusion and answer to Yogi's original question is:

Has this term ‘Strong Wing’ fallen out of favour, or is it now regarded as just part of something else?

It sure seems so, and for a good reason. If the pattern exists, the same placement can be achieved with the more generalized L3-Wing (or as a short generic AIC if you don't bother to learn names). The "Strong Wing" pattern just happens to include two of those L3-Wings which doubles the chances of spotting one (and you only need one)! In this case it contains two H2-Wings as well, but that's not a defining feature.

So, it's a nice pattern if you find it because it gives you at least one immediate placement, but you don't actually need to know or recognize the full pattern to get the same results. Thus, it seems a bit redundant to me. "Nice to know" kind of stuff, but hardly necessary.