## The UHC Solvers on the Shye Fireworks

As announced last post, a series on Sysudoku Basic is postponed for another look at fireworks. In recent posts, we have been reviewing examples from forum commentator shye’s introduction of fireworks, and proposing a more limited, but  better defined form of firework, the elbow. Another look is prompted by my discovery that both the available DIY oriented solvers used here for recent reviews, known here as Sudokuwiki and Beeby, have quickly added firework options.  First off, let’s see how well they reveal the fireworks of shye’s examples.

My first post on fireworks was December 28, 2021. It’s been revised to show that in an elbow, a candidate of the elbow value in either the neck cell or at least one of the cuff cells is true.

Shye’s first example illustrates how three supermposed elbows of three values creates a 3-set, a form of hidden triple not confined to one house. Shye’s example actually is two superimposed elbows and a slink in the third value including the intersection, which has the same result. You know that the solution places the 3 values in these three cells, but that’s all. But what generally happens is that the follow up on the removals of extra candidates pins down these placements and more.

After Basics,  when the Fireworks button is pressed Beeby announces :

“Fireworks triple of 123 at r1c9, r1c1 and r9c9, eliminating: -8 r1c9; -9 r1c9; -6 r1c1; -7 r1c1; -9 r1c1; -4 r9c9; -7 r9c9;   Solved!”

That’s appropriate timing for fireworks.

Another success occurs in shye’s second example, in which two matched pairs of elbows frame a rectangle, with neck cells on opposite corners. This makes a 4-set quad of four corner cells. Candidates of 5, 6, 8 and 9 are removed because the 4 corner cells must contain 1 and 2 of one elbow and 3 and 4 of the other elbow. Values of one elbow are barred from the neck of the other elbow, because the two elbows share the same cuff cells. 1r4c6 forces 3 and 4 into the two cuffs, leaving one elbow of the 1,2 pair without its value.

Both solvers spot the 4-set elbow firework. Sudokuwiki’s note can be misinterpreted. It says r9c1 must be 1 or 2, and r4c6 must be 3 or 4, but that is not true generally of matched pairs of elbows. It’s true only in the context of the quad 4-set formation.

Shye’s examples 3 and 4 combine two matched elbows with matching bv that could be included in solvers’  repertoire, but are not as yet.

Shye’s example 5 is closest to the notion of combined fireworks exploding into far reaching removals. Five fireworks, four of them elbows, share a single cell as an row/column intersection. The problem for solver coding is that only one of the five has a true neck candidate, and there is no programmable fireworks rule establishing which one it is, other than trying each firework.

Each solver had full opportunity to find this firework. For Beeby, it meant calling for it after each move. For Sudokuwiki, it meant following its path until  several techniques past its difficulty list had been tried. Shye’s example 6 is based on a simple trial of an elbow’s intersection candidate, and should not be included.

In notes on Beeby’s fireworks option, Philip Beeby cites the Catherine Wheel, another shye fireworks quad example from the forum thread. Like the second example above, Beeby sets up the four fireworks elbows and makes corresponding removals. This time it’s not an immediate collapse, but the analysis is worth the effort. Full story next time.