Solving Patterns within Broken Wing and Sister Patterns

Advanced methods and approaches for solving Sudoku puzzles

Solving Patterns within Broken Wing and Sister Patterns

Postby Bud » Thu Sep 04, 2008 9:13 am

A few months ago I became a contributing member of Sudopedia because I had gotten a lot of help from this site and I thought some of my personal solving techniques might be useful to others. I have always been fascinated by the broken wing and its sister 7, 9, etc. cell patterns. Although I have encountered these patterns many times, I never found a case where the guardian technique could be used. Therefore I began classifying different types of the broken wing patterns based on the number of strong and weak links and how they are arranged. For example a broken wing pattern with only one weak link is always a color wrap and the wrap always occurs in the cells in the weak link. In fact every color wrap is also either a broken wing or sister pattern. This is because every color wrap must be an X-chain loop with an odd number of cells. I now identify color wraps by pattern. I'm not going to cover 2 other solving patterns I found here since these are are covered in an article I wrote on the broken wing page at Sudopedia. I am in the process of editing this article to add additional information. My problem is this. One of the classifictions I made is an AIC broken wing pattern which contains an AIC sub pattern with 2 strong links separated by a weak link. The 2 additional weak links in the broken wing pattern are not part of this AIC subpattern. The AIC subpattern contains 4 of the 5 cells in the broken wing pattern. The AIC subpattern can be present as either of three visually distinct patterns. But it doesn't matter which since the cell elimination in the broken wing pattern is always the single cell which is not part of the AIC subpattern. If the diagonal link is also the weak link in the AIC subpattern is a 2-string kite. If the diagonal link is strong, the AIC subpattern is an ER. If the diagonal link is weak but is not part of the strong link-weak-link strong-link pattern the AIC subpattern is a color wing, but since all of these patterns are based on the same multicolor logic, I called all 3 an AIC broken wing pattern. If it is considered as ! pattern, then there are 4 solving patterns in the broken wing pattern. Otherwise there are 6.

Let me clear up one misconception that someone made me aware of in a private message. I have tried to clear this up by editing my original post and using the term AIC subpattern.
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Joined: 24 August 2008

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