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.

- Yogi
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