## The Elbow n-set of shye’s Roman Candle

This post is about the sixth example of forum commentator shye’s introductory post on fireworks, his name for elimination methods based on the restriction of candidate values in row/box/column combinations. Our series of posts on fireworks defines a particular form of firework, the elbow, with single candidates in the intersecting row and column outside the box. This post accounts for a 7-set, an extended naked set selected by shye, to solve his Roman Candle puzzle.  This post shows how the 7-set can be derived from an elbow, and resolved for an immediate collapse of the Roman Candle.

Here is the basic trace of the Roman Candle.

The Candle gives up nothing in the first stage bypass, which derives clues and subsets from clues and subsets.  The second stage produces slinks (strong links) in each box., and the last stage fills in candidates in every row and column, with bv and line slinks marked.

The candidates grid, with line marking fill strings attached

In looking for fireworks,  we start with the elbows, marked on an X-panel .

About this panel, shye’s report  says, “seven cells for the following placements: a firework on 1s in r5c5b5 along with positions of 3r1, 4c5, 6c1, 7c9, 8r9, 9r5. all other candidates removed.”

What? The seven cells are necks and cuff cells selected from one elbow and four arms from other elbows, and cells containing 4 from c5 and 9 from r5. The 7 cells form a 7-set, 7 cells solving to 7 values, but shye doesn’t say how they are selected.

A clue to that mystery is that the selected elbow arms are slinks. Place them on the grid and what shye is doing becomes clear. He is assuming that 1r5c5, in the neck cell of the single 1-elbow, is true, removing 1’s in its cuff cells. That adds two more bv to the 7-set.

With 4 and 9 removed from r5c5, two connecting slinks are added and the selected bv form an XY nice loop. Sysudoku readers know that nice loop candidates form a coloring cluster. Along with 1r5c5, either the the blue or the green candidates are true.

Taking the blue candidates to be true, here is the collapse trace, and the solution.

Did this extraordinary example tell us anything about DIY fireworks analysis? No. Looking for an elbow with XY chains forming a closed loop is not a practical DIY trial strategy.

This is a cascaded trial. It starts on the guess without evidence that 1r5c5 is true, then constructs the nice loop for a trial of blue vs. green candidates. Was this guess in fact the basis for composing the puzzle? That would explain a lot.

Concluding this post review, how typical are the elbow panels of shey’s six fireworks examples for hard puzzles? My survey of the 12 ultrahardcore right page puzzles of the Stefan Heine review was not encouraging. No elbow matches, no productive cooperation with coloring, and no enhancement of AIC building. It bears out the impression from shye’s forum posts that it takes extensive computer search to find impressive firework shortcuts comparable to his examples.

I had planned to move on to an update of Sysudoku Basic, by means of recent Dave Green Conceptis 5-stars. But that’s on hold. I just discovered that both of my DIY oriented solvers, Andrew Stuart’s Sudokuwiki, and Philip Beeby’s PhilsFolly, have added a Fireworks component, and have their own interpretation of what Fireworks actually are. So naturally, I have to find out, what’s the take of these two expert programmers on this blog’s particular firework, the elbow. Next Tuesday’s post will be on that.