I was closing down the weekly posts with a set of scroll down basic level puzzles, when I got another collection book , 3000 more “very hard to extreme “, for Adult puzzles. I did a few from the extreme section, and found them to be generally bordering on advanced level. Many Extreme Hard puzzles start with a value or two missing from the givens, and consequently, will have at least one very poorly restricted value on the line marked grid. It’s a situation calling for boxlines and X-wings to attack those over abundant candidates. 

In the Guide, a boxline is explained as a feature of the bent region, an intersection of a box and a crossing line. The cells in the box, but outside the line, is the box remainder. The cells in the line, cut outside the box, is the line remainder.

This picture makes the boxline rule simple to state: if a candidate value is absent from one remainder, it must be absent in the other remainder. That’s because there has to be a true candidate of that value in the intersection, which I sometimes call the chute.

Boxlines work in both directions, and you could have a series of boxlines alternating box and line remainders absent a value. When the chute contains more than one candidate of the boxline value, the boxline becomes a slink or aligned triple pointer. Extreme Hard illustrates both of these. Scroll down for the citation and starting grid for your discovery of this. You’re 18 or older, right?

In the bypass and box marking, values 4 gets no action, and is destined to cover the line marked grid in candidates. In the 3-fills, the 4-candidates are already showing up.

Here is the box marked grid. Missing value 4 is the threat, with almost missing value 3 a potential problem as well.

In 1505, the Wr5 boxline effect  is        

E3 => ( 3absent in r5 remainder) slink W3m.

The NWc1 boxline effect is

W3m (absent W remainder => (absent NW remainder NW3m.

The NW3m slink leaves a hidden single N3 in r1, and a naked pair in N.

As line marking begins, N3 has dismissed the only 4 in r1 outside of NW, leaving NW4m and a naked triple in c1.

The rest is follow up.

Next week, let’s see what you do with a second Extreme Hard, 1503, with one 7 and no 8 candidates. There are 7-wings to help avoid a burdensome line marking.