This closing post adds two examples of a fierce looking line marking being de-fanged by hidden dublex on the over abundant X values

A double line exclusion, or dublex, is one of the primary moves of Basic sudoku, in which the intersection of two parallel lines through a box cannot contain a candidate of the dublex value, forcing a third line chute to contain a true candidate of the value.

When each of the intersecting lines only contain candidates of the value, then each contains a true candidate.  We just don’t know which line remainder contains which true candidate. We call that a hidden dublex, or in trace language, an hdx.

The hidden dublex is a frequent move in the bypass and follow up, but is especially useful when an over abundant value needs weeding. Scroll down for the givens of Extreme Hard 1503, with one 7-candidate and no sign of the 8 value.

The bypass leaves 4 3-fills, each with an 8 candidate to be placed.

On the 7 value of box marking, columns 4 and 6 contain true 7 candidates outside of the C box, for a 7-slink, and soon after SW7m generates the second slink W7m for a 7-wing, another form of hidden dublex.

The 7-wing’s E7m slink is trimmed to clue E7 by the second hdx in c79, squeezing c8 to the naked pair 18, for a 1-wing keeping 1 out of r5c9. But the real damage is done in the 8 camp as C8m starts a collapse.

The collapse trace:

 I have one more Extreme Hard example of the hidden dublex avoiding a tough line marking. It’s 1506.

At the 9 value in box marking, note the hdx on r8 which creates slink W9m. The  hdx chain continues with a c2hdx forcing NW9!

The immediate collapse is typical of unbalanced puzzles tripped up when headed for a cluttered line marking.

To illustrate, here is the line marked grid when the hidden dublex chain is ignored. The 8 and 9 candidates are everywhere.

Weekly posts pause now, awaiting reader requests. Next week, expect the home page, where update announcements and comments will continue. The pause will allow the pages and over 500 posts to be brought to the level of graphics and instruction realized my 12 years of Sysudoku blogging.