{"id":676,"date":"2016-12-31T11:17:25","date_gmt":"2016-12-31T10:17:25","guid":{"rendered":"http:\/\/www.saueregger.at\/?p=676"},"modified":"2017-01-15T09:25:12","modified_gmt":"2017-01-15T08:25:12","slug":"sudoku-using-wing-pincers-as-a-link-in-a-skyscraper-or-kite","status":"publish","type":"post","link":"http:\/\/www.saueregger.at\/?p=676","title":{"rendered":"Sudoku: Using Wing Pincers as a Link in a Skyscraper or Kite"},"content":{"rendered":"

For years now, some of us (Marty, Keith, and Helmut, et al) have been using \u201cuseless\u201d or \u201cflightless\u201d wings as a link to make eliminations in more difficult puzzles.\u00a0 We have all remarked on how useful and powerful the technique might be.<\/p>\n

More recently, Helmut Saueregger (Nataraj) engaged me in a new discussion on this, and he has extended his Helmut\u2019s Sudoku Helper (HSH) to find these things.\u00a0 HSH is here:<\/p>\n

http:\/\/www.saueregger.at\/sudoku\/HSH\/HSH.htm<\/a> (Note 1)<\/p>\n

You should be looking at HSH V4.1 or greater.<\/p>\n

For the following, we will use XY-wings as the example.\u00a0 However, the same logic applies to W- and M-wings.<\/p>\n

There are two requirements:<\/p>\n

1. You know how to find Kites and Skyscrapers, which are collectively known as Turbot Fish (Note 2).<\/p>\n

2. You know how to find an XY-wing.<\/p>\n

(We also imply that you use pencil and paper to solve Sudoku for personal enjoyment. If you see Sudoku solving as a contest in computer software, please do not read further.)<\/p>\n

The simple point here is that the pincers of a Wing can be one link of the two links that make up a Turbot pattern.<\/p>\n

Here is an example (from Helmut):<\/p>\n

+-------+-------+-------+\r\n| 2 8 . | 1 . . | . . . |\r\n| . 1 5 | 7 4 . | 6 8 . |\r\n| . . . | . . . | 9 . . |\r\n+-------+-------+-------+\r\n| 5 . . | . 9 . | . . 8 |\r\n| . . . | 4 . 2 | . . . |\r\n| 1 . . | . 8 . | . . 4 |\r\n+-------+-------+-------+\r\n| . . 7 | . . . | . . . |\r\n| . 9 2 | . 3 6 | 7 5 . |\r\n| . . . | . . 4 | . 6 9 |\r\n+-------+-------+-------+<\/pre>\n
After basics:<\/p>\n
+-------------------+-------------------+-------------------+\r\n| 2\u00a0\u00a0\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 69\u00a0\u00a0\u00a0 | 1\u00a0\u00a0\u00a0\u00a0 56\u00a0\u00a0\u00a0 59\u00a0\u00a0\u00a0 | 34\u00a0\u00a0\u00a0 34\u00a0\u00a0\u00a0 7\u00a0\u00a0\u00a0\u00a0 |\r\n| 39\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0 | 7\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0 39\u00a0\u00a0\u00a0 | 6\u00a0\u00a0\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0 |\r\n| 367\u00a0\u00a0 3467\u00a0 346\u00a0\u00a0 | 23\u00a0\u00a0\u00a0 26\u00a0\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 | 9\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0 |\r\n+-------------------+-------------------+-------------------+\r\n| 5\u00a0\u00a0\u00a0\u00a0 23467 346\u00a0\u00a0 | 36\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0 137\u00a0\u00a0 | 123\u00a0\u00a0 237\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 |\r\n| 379\u00a0\u00a0 37\u00a0\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 | 4\u00a0\u00a0\u00a0\u00a0 15\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0 | 15\u00a0\u00a0\u00a0 379\u00a0\u00a0 6\u00a0\u00a0\u00a0\u00a0 |\r\n| 1\u00a0\u00a0\u00a0\u00a0 2367\u00a0 369\u00a0\u00a0 | 356\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 357\u00a0\u00a0 | 235\u00a0\u00a0 2379\u00a0 4\u00a0\u00a0\u00a0\u00a0 |\r\n+-------------------+-------------------+-------------------+\r\n| 68\u00a0\u00a0\u00a0 56\u00a0\u00a0\u00a0 7\u00a0\u00a0\u00a0\u00a0 | 9\u00a0\u00a0\u00a0\u00a0 125\u00a0\u00a0 15\u00a0\u00a0\u00a0 | 248\u00a0\u00a0 24\u00a0\u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0 |\r\n| 4\u00a0\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0 | 8\u00a0\u00a0\u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0 6\u00a0\u00a0\u00a0\u00a0 | 7\u00a0\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 |\r\n| 38\u00a0\u00a0\u00a0 35\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 | 25\u00a0\u00a0 \u00a07\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0 | 28\u00a0\u00a0\u00a0 6\u00a0\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0 |\r\n+-------------------+-------------------+-------------------+<\/pre>\n
There is an XY-wing 2-35 in R9C4.\u00a0 After that:<\/p>\n
+-------------------+-------------------+-------------------+\r\n| 2\u00a0\u00a0\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 69\u00a0\u00a0\u00a0 | 1\u00a0\u00a0\u00a0\u00a0 56\u00a0\u00a0\u00a0 59\u00a0\u00a0\u00a0 | 34\u00a0\u00a0\u00a0 34\u00a0\u00a0\u00a0 7\u00a0\u00a0\u00a0\u00a0 |\r\n| 39#\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0 | 7\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0 39#\u00a0\u00a0 | 6\u00a0\u00a0\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0 |\r\n| 367\u00a0\u00a0 467\u00a0\u00a0 346\u00a0\u00a0 | 23@\u00a0\u00a0 26\u00a0\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 | 9\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0 |\r\n+-------------------+-------------------+-------------------+\r\n| 5\u00a0\u00a0\u00a0\u00a0 23467 346\u00a0\u00a0 | 36\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0 137\u00a0\u00a0 | 123\u00a0\u00a0 237\u00a0 \u00a08\u00a0\u00a0\u00a0\u00a0 |\r\n| 379\u00a0\u00a0 37\u00a0\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 | 4\u00a0\u00a0\u00a0\u00a0 15\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0 | 15\u00a0\u00a0\u00a0 379\u00a0\u00a0 6\u00a0\u00a0\u00a0\u00a0 |\r\n| 1\u00a0\u00a0\u00a0\u00a0 2367\u00a0 369\u00a0\u00a0 | 356\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 357\u00a0\u00a0 | 235\u00a0\u00a0 2379\u00a0 4\u00a0\u00a0\u00a0\u00a0 |\r\n+-------------------+-------------------+-------------------+\r\n| 68\u00a0\u00a0\u00a0 56\u00a0\u00a0\u00a0 7\u00a0\u00a0\u00a0\u00a0 | 9\u00a0\u00a0\u00a0\u00a0 125\u00a0\u00a0 15\u00a0\u00a0\u00a0 | 248\u00a0\u00a0 24\u00a0\u00a0\u00a0 3\u00a0\u00a0 \u00a0\u00a0|\r\n| 4\u00a0\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0 | 8\u00a0\u00a0\u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0 6\u00a0\u00a0\u00a0\u00a0 | 7\u00a0\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 |\r\n|-38\u00a0\u00a0\u00a0 35@\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 | 25\u00a0\u00a0\u00a0 7\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0 | 28\u00a0\u00a0\u00a0 6\u00a0\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0 |\r\n+-------------------+-------------------+-------------------+<\/pre>\n
It seems you now have to join the chain gang (Note 3). But, let\u2019s look closer:
\n@@ are the Wing pincers.\u00a0 One or both is 3.
\n## is a strong link on 3.\u00a0 Together @@ and ## make a sort of Kite.
\nR9C1 is not 3, puzzle solved!
\nNote that there is also a flightless XY-wing 23-6 in R3C4 that takes out 6 in R4C3:<\/p>\n
+-------------------+-------------------+-------------------+\r\n| 2\u00a0\u00a0\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 69#\u00a0\u00a0 | 1\u00a0\u00a0\u00a0\u00a0 56#\u00a0\u00a0 59\u00a0\u00a0\u00a0 | 34\u00a0\u00a0\u00a0 34\u00a0\u00a0\u00a0 7\u00a0\u00a0\u00a0\u00a0 |\r\n| 39\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0 | 7\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0 39\u00a0\u00a0\u00a0 | 6\u00a0\u00a0\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0 |\r\n| 367\u00a0\u00a0 467\u00a0\u00a0 346\u00a0\u00a0 | 23\u00a0\u00a0\u00a0 26@\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 | 9\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0 |\r\n+-------------------+-------------------+-------------------+\r\n| 5\u00a0\u00a0\u00a0\u00a0 23467 34-6\u00a0 | 36@\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0 137\u00a0\u00a0 | 123\u00a0\u00a0 237\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 |\r\n| 379\u00a0\u00a0 37\u00a0\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 | 4\u00a0\u00a0\u00a0\u00a0 15\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0 | 15\u00a0\u00a0\u00a0 379\u00a0\u00a0 6\u00a0\u00a0\u00a0\u00a0 |\r\n| 1\u00a0\u00a0\u00a0\u00a0 2367\u00a0 369\u00a0\u00a0 | 356\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0 357\u00a0\u00a0 | 235\u00a0\u00a0 2379\u00a0 4\u00a0\u00a0\u00a0\u00a0 |\r\n+-------------------+-------------------+-------------------+\r\n| 68\u00a0\u00a0\u00a0 56\u00a0\u00a0\u00a0 7\u00a0\u00a0\u00a0\u00a0 | 9\u00a0\u00a0\u00a0\u00a0 125\u00a0\u00a0 15\u00a0\u00a0\u00a0 | 248\u00a0\u00a0 24\u00a0\u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0 |\r\n| 4\u00a0\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0 | 8\u00a0\u00a0\u00a0\u00a0 3\u00a0\u00a0\u00a0\u00a0 6\u00a0\u00a0\u00a0\u00a0 | 7\u00a0\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 |\r\n| 38\u00a0\u00a0\u00a0 35\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0 | 25\u00a0\u00a0\u00a0 7\u00a0\u00a0\u00a0\u00a0 4\u00a0\u00a0\u00a0\u00a0 | 28\u00a0\u00a0\u00a0 6\u00a0\u00a0\u00a0\u00a0 9\u00a0\u00a0\u00a0\u00a0 |\r\n+-------------------+-------------------+-------------------+<\/pre>\n
How difficult is this?\u00a0 I think it is quite easy.
\nPersonally, after doing the basics, I check for strong links to find single-digit eliminations (usually Turbots, which are Skyscrapers and Kites). That is explained here:
\nhttp:\/\/forum.enjoysudoku.com\/post247168.html#p247168<\/a>
\nAs a side benefit, this Turbot search is a check that you have done the basics correctly.
\nAfter that, I look for XY-, W- and M-wings (note 4). Even if these wings do not make eliminations by themselves (they are \u201cflightless\u201d), I now have all the information to find the \u201cTurbot Wings\u201d described here (Note 5).
\nSo, I think this is not a very \u201cadvanced\u201d technique. Actually, I think it simplifies the issue, by taking links found by multi-digit techniques back into the single-digit world.<\/p>\n
Keith<\/p>\n
    \n
  1. Notes:
    \nHelmut\u2019s Sudoku Helper (HSH) is an interesting tool that allows you to explore paths through puzzles. It is not a Sudoku solver per se.<\/li>\n
  2. If this is new to you, start with Havard\u2019s excellent explanation: http:\/\/forum.enjoysudoku.com\/strong-links-for-beginners-t3326.html<\/a><\/li>\n
  3. See also http:\/\/hodoku.sourceforge.net\/en\/tech_sdp.php<\/a> for more on Skyscrapers, Kites, and Turbots.<\/li>\n
  4. https:\/\/www.youtube.com\/watch?v=zBn5aIfZElE<\/a>
    \nFor more on M- and W-wings see:     http:\/\/www.dailysudoku.co.uk\/sudoku\/forums\/viewtopic.php?t=2143<\/a><\/li>\n
  5. Names are an aid to communication, and I think the name \u201cTurbot Wing\u201d is appropriately descriptive of a Turbot where one of the two links comes from a Wing.<\/li>\n<\/ol>\n
     <\/p>\n","protected":false},"excerpt":{"rendered":"
    For years now, some of us (Marty, Keith, and Helmut, et al) have been using \u201cuseless\u201d or \u201cflightless\u201d wings as a link to make eliminations in more difficult puzzles.\u00a0 We have all remarked on how useful and powerful the technique might be. More recently, Helmut Saueregger (Nataraj) engaged me in a new discussion on this, … „Sudoku: Using Wing Pincers as a Link in a Skyscraper or Kite“ <\/span>weiterlesen<\/a><\/p>\n","protected":false},"author":461,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[14],"tags":[],"_links":{"self":[{"href":"http:\/\/www.saueregger.at\/index.php?rest_route=\/wp\/v2\/posts\/676"}],"collection":[{"href":"http:\/\/www.saueregger.at\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.saueregger.at\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.saueregger.at\/index.php?rest_route=\/wp\/v2\/users\/461"}],"replies":[{"embeddable":true,"href":"http:\/\/www.saueregger.at\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=676"}],"version-history":[{"count":5,"href":"http:\/\/www.saueregger.at\/index.php?rest_route=\/wp\/v2\/posts\/676\/revisions"}],"predecessor-version":[{"id":687,"href":"http:\/\/www.saueregger.at\/index.php?rest_route=\/wp\/v2\/posts\/676\/revisions\/687"}],"wp:attachment":[{"href":"http:\/\/www.saueregger.at\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=676"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.saueregger.at\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=676"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.saueregger.at\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=676"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}