Special X-chains

The “Special X-chains”  of the title are the names assigned to particular X-chains, like “skyscraper” and “2-string kite”.  You might think that it’s of value to look for them, but I disagree.  They just pop out at you when you go through your normal sysudoku x-chain analysis.  So let’s debunk special x-chains,  just as we have debunked keypad pencil marks, number scanning for candidate discovery, and XY or Y-wings aside from XY-chains.

Post 7-panelBut first, I owe you a marked up 7-Panel on a Washington Post 6-star:

Below is the full grid documenting this step. You can see by tracking a few slinks through the bv that the removal is going to wreck this 6-star.

Wonder  how this puzzle fared with the bv methods, seeing the sea of them?  Not so well.  The same removal is found, and a  less decisive one, by XY-chains.

I only knew about the 7-chain because I went through it back when longer XY chains seemed humanly impossible to manage. I had them way back in the order of battle.

If you’d like to try your XY-chaining prowess,  you have until next week’s post, where I will print the hellish XY-net that this many bv generate.  What is amazing is how easy this monster  is to construct, and how easy it is to find  the removals.  I hope you’ll have reason to agree.

Now on to our topic.

The puzzle  is from the www.sudopedia.com  presentation on the 2-string kite. We’ve replaced the keypad marking with slink marking (see Slink Marking post of 10/04/11).  The 2-string kite is an X-chain of three links.

The 5-panel below shows how this chain and removal would appear.

Placing an x in the victim cell records that a number was there, while enabling the panel  to be used for further solving.  Here the middle link is drawn as a slink, a holdover from using the panel as a tool for finding  alternating winks  among the slinks. When you have put in the slinks, it’s hard to miss.


The 5-panel at right is from Sudopedia’s accompanying diagram, where it is explained that when one of the kite strings falls within a box, the pattern is not a 2-string kite, but is instead a box/line reduction removing the victim.

Presumably you were directed earlier to the next post on boxlines, and you see that the c2 slink does imply a NWc2 boxline removing 5r1c3, which confirms 5r1c6. It does indeed hit the same victim.

But any concern about whether an X-chain qualifies as a kite, or anything else, is misplaced. As a treasured sysudoku blog reader, you can also savor the point that, boxline or not, 5r1c3 has the misfortune of seeing both ends of a slink, and is toast.


A “skyscraper” is another three link X-chain, with strong links parallel, and aligned on one end,  and the opposite ends  not aligned, but in aligned boxes.  As in the 5-panel  here, definitions typically show the cells in which matching candidates are removed.  This looks impressive, but just note that “x” patterns can be drawn for any toxic set. The concept of “seeing” toxic chain ends covers it.

In an update of this post, I’m adding another “Not Wanted” poster to the “a.k.a X-chain” gallery. How about the “Turbot Fish”? In a chapter of this title, the Peter Gordon’s Mensa Guide issues a reader challenge to find one on his grid, describing the structure this way:

“It requires five cells that are arranged so that two pairs of cells are in the same rows, two pairs are in the same columns, and two cells are in the same box. If three or four of the pairs are the only places where a particular number can go, you have a turbo fish. If there are only two such pairs, then it still works, as long as those two pairs don’t share a cell. “

Now what am I looking for again? Look ahead to my post of 1/13/15 to find the challenge grid, and my directions to sketch the above description out (use scrap paper), only to discover it has to be an almost nice loop with two winks together (eliminating) or two winks apart (confirming). You’ll never find one based on the quoted description, but if you just routinely link up slinks on X-panels, someday you’ll find that you’ve made one. Peter’s challenge grid has two intertwined eliminating Turbo Fish and a spare 3- link, eliminating X-chain that avoids being a either a two string kite, or a skyscraper.  Wow!


About Sudent

My real name is John Welch. I'm a happily married, retired professor (computer engineering), timeshare traveling, marathon running father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. The blog is about Sudoku solving. It covers how to start, basic solving to find candidates efficiently, and advanced solving methods in an efficient order of battle. It is about human solving methods, not computer solving.
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2 Responses to Special X-chains

  1. Dave says:

    Do you realize that the people who are smart enough to understand you, would be smart enough not to need your help.

    • Sudent says:

      Dave, you’re right on, but was that a question? I need to work harder on being more clear. But if the smart people need no help, why aren’t they doing what I enjoy so much. If they are, how are they managing to keep it all to themselves?

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