Today we illustrate the full blown Death Blossom with ALS petals. Earlier I noted Death Blossom Lite as a removal technique in the bv scan. Completion of a DB Lite with a closing ALS is also relatively easy to find. As we enumerate and test ALS, we can also look at them as possible Death Blossom petals. The post ends with a rollicking checkpoint on the SOB fate of the Maestro ALS-XZ demo puzzle, with no help from ALS or Death Blossom toxic sets.
In this schematic of a death blossom, each candidate of a cell, the stem, sees all matching candidates in an ALS (including bv). The matching ALS, the petals, have at least one number in common among them. The ALS candidates of the common number form a toxic set.
The reason is, one of the petals must give up a candidate to the stem, and is locked. One of its common number candidates must therefore be true. The petal candidates of any common number therefore form a toxic set. Any outside candidate that sees all candidates of the common number sees the candidates of the locked ALS, and therefore, the true candidate of that number.
While ALS-XZ and the Death Blossom both depend on two or more ALS, search filtering for them are quite different. For the ALS-XZ, you favor a stretching the ALS out to reach a number of a single candidate. Then you look for a partner ALS with and RC and that candidate. In the Death Blossom scan, you favor bv or triple number stem cells, and look for RC partners for all stem numbers. Of course, ALZ-XZ should come first, unless a Death Blossom steps up and slaps you in the face. The odds are much better.
Death Blossoms were not illustrated in the demo section of my Sudoku Maestro magazine, but a cute one was lurking in there, appearing right after the first ALS-XZ was found in the scan of the last post.
The blossom is bv 35 in r5c2. The petals are the bv 15r7c2 and c8 ALS136. The common number is 1. Victim 1r7c4 gets run over after looking both ways on r7 street, but not before dragging three friends under the bus by supporting their ER vision.
For another, more typical example, I like Andrew Stuart’s first in his Death Blossom chapter of The Logic of Sudoku. In Sysudoku notation, it shows two ALS partners, carefully selected in their respective units to have an RC with the stem bv 28r8c9, and a common number 1. The row/column trap is something to keep in mind in a DB scan.
Now as to your homework on the fate of the Maestro 8-9 demo of Fall 2009 under the SSOB microscope.
Starting after line marking, a single alternate Sue de Coq shows up first. SASdC Wr4 = 9(3+5)(1+2) + 291 is indecisive, the trial of 291 stalling. It is put on the trial list, but I know it would have led to the solution, since Wr1 =291 turns out to match the solution found later. Another interesting SASdC occurs near the end of the scan, SASdC SEr8 = 5(3+4)(1+6) + 354 +453. In this trial, the naked pair in SEr8 forces all 1’s from r8, and the classic Sue de Coq remains, in which r8c9 must supply (1+6).
My bv map uncovers no XYZ wing, but the XY railroad produces a nice nice loop, with three toxic set removals. One of them creates a boxline removing three more, and another, the naked pair r3np37, creates the same results as the 2r3c6 removal above.
We leave the nice loop in place, for possible extensions and coloring, as…
We invade computer code territory again with our next blog subject, the pattern overlay method, or POM for short.
This allows a second nice loop, and the two share the number 3, allowing them to be tied together (red wink) with direction colors coordinated into one cluster. Three traps extend the cluster, to a point where green is wrapped as it forces two green 6’s in the S box. Blue is true.
You can work it out, but needless to say, that’s all she wrote.
We invade new territory with the next post. It’s the land of POM, or Pattern Overlay Method. The Sysudoku human scale version will be called LPO, for Limited Pattern Overlay.