Advanced Boxlines

Advanced Boxlines

Boxline Exclusions, or boxlines in Sysudoku posts, are described in a page of that title in the Sysudoku Basic pyramid of the Guide.  For reference, here is a quote:

“In the intersection of a box and a line, let’s call the section of line outside of the box the line remainder and the section of box outside of the line, the box remainder.

Now that we are all introduced, here is:

The reason is, the absence from a remainder guarantees a placement of the value in the intersection, which sweeps the other remainder. Simply elegant.”

Basic solving examples are included in Sysudoku Basic/Box Line Exclusion, arising mostly in the discovery of missing values as boxes and lines are marked. The role of boxlines in follow up marking of candidate removals is also noted.

This page continues with advanced boxline examples from the collection reviews.  Boxlines react to the removal of candidates, so the examples are ordered according to the methods that generate the triggering removal. The advanced methods are ordered by Sysudoku Order of Battle, so that readers can return to the page to progress through them as they go through the advanced solving pages.

Unique Rectangle

UR’s are signaled early by naked pairs. The Type 1 UR only requires spotting candidates that remove the last barrier to a solution rectangle of interchangeable values. In this one from Manuel Castillo’s Only Extreme 304, posted 5/07/19, either of the victim 6’s would remove 6r6c2. But also, either would place 6 in r9c1, removing the only 3 from the SE7 box remainder. Consistent with other multiple effects, 3 is marked for removal as a boxline victim of the UR 1.

XY Almost Nice Loop

The XY ANL is the easiest AIC to find in quantity, when bv are plentiful. Here in James Forest’s Classic 72, p0sted 3/12/19, the 6r1c4 removal clears the line remainder or NEr1, and thereby, the NE box remainder.

The naked triple is a bonus.

 

 

X-chain and Coloring

Moving to the X-panel, here is a simple X-chain triggering a  boxline, from J.B. Nakamoto Extreme 143, posted 4/07/20p. The inner victim markers show the 3-chain removing 3r7c3 to empty the SWc8 box remainder, deleting 3r4c2 from its line remainder.

The outer victim markers are for the coloring victim 2r4c2 departing the SWc2 line remainder to remove 3r7c3 from the box remainder.

Striking, but not extreme.

For that, how about

Paired AIC Boomerangs

Nakamoto Extreme 43, posted 2/11/20, puts on a parade of boomerangs, One from 8r1c4 and another from 6r1c6 share an AIC path and together, clear the Nr1 box remainder to boxline 2r3c2. The next boomer in the parade, from 1r2c8, clears the NWr2 line remainder for NWbxl9m.

Instead of three removals, boxlines make it six.

Boxlines occur everywhere. A boxline is a type of link, in which false => false.