The Death Blossom

So far we’ve looked at three ways to exploit almost locked sets to eliminate candidates. In the Sue de Coq, ALS in the remainders of a chute reveal the chute contents to be a simple logical form, eliminating candidates inconsistent with that form. Then there’s the Aligned Pair Exclusion (APE), and its multiple line cousin, the Unaligned Pair Exclusion (UPE) in which ALS limit possible pairings of candidate values in a pair of cells. Then we saw how two ALS can be selected and connected to create toxic sets, eliminating any candidate that sees them all. In an easier spotted and especially effective ALS toxic set pair, the ALS_XZ, one ALS is a bv cell.

Death Blossom is a fourth way. The idea comes directly from the ALS property that an ALS can give up only one value in the placement of a solution, an ALS value being a group of one or more candidates of the same number.

The central feature of a Death Blossom is its stem cell, marked in Sysudoku grids by a four-point star. The stem cell of three or more candidates is not an ALS, but each of its candidates “sees” a value group in a different ALS. These are the petals of the blossom.  If there is a common value among all the petals, the combined groups of that value is a toxic set. One of them contains the true candidate of the common value. This is because one of the petals must give up a value to the stem, and its remaining value groups all contain true candidates.

The Death Blossom is relatively new, and most of the widely shared examples are still around. After a look at several of them, we’ll know better what to look for. One principle is clear from the diagram: the fewer the stem cell candidates, the better. Indeed, most stem cells are bv, and a 3 value death blossom is very rare. Four or five candidates? Forget it.

Here is the simple, but typical example 3 of five from SudokuOne.  The common z = 8 values are seen by two victims.

Note the grouped wink within the North box. The stem candidate sees all of the 2-group.

The rectangular shape of the Death Blossom is typical, allowing victims to see two value groups. Groups of one are easiest to see.

Clearly, the prime candidates for common values are singles, but this example from Andrew Stuarts Wikipedia strategies shows how leaving a candidate out of the ALS can create a Death Blossom fatality.

 

 

 

 

An ALS within a box can also can be combined with a line ALS to form the required rectangular form.  The second Stuart strategies example here is repeated on several sites.

As suggested, the Death Blossom is available right out of line marking.

The three examples above could be constructed following this prescription:

You can easily modify the construction to cover a stem of 3 or more candidates, but keep your expectations low. Victims are scarce.  It doesn’t work to attach two petals to a stem of 3 candidates. The unattached candidate could be the true one, with both petals retaining all values.

So what do you make of this legitimate three stem example, from Hodoku?  Don’t believe what I read somewhere that petal overlap is prohibited.

 

Notice the careful drawing of ALS boundaries that select the proper ingredients for each.This flexibility aids construction, but produces hordes of ALS, overwhelming the searcher.

Seeing candidates in more than one value group, you might wonder if there can be more than one common value among petals. SudokuOne’s example 4 addresses that question.

 

 

How about a Death Blossom that fails, but succeeds?

 

This example comes from the Sudoku Coach Taupier’s site. With a finned swordfish and an ALS ANL, you reach the coach’s grid, but this earlier one is what you would confront in the bv scan.

No outside candidate can see both value 7 groups. But the 7-groups see each other. At the stem, if 3 is true, the blue ALS  loses the 3 value, and if 9, then the green ALS loses 9, keeping 7, so the blue ALS loses the 7 value. Either way, the blue 4 and 5 groups have true candidates. It is another example of the internal slink between the value groups of an ALS.

There is a symmetry here. If stem 3 is true, blue loses 3 and keeps 7 and green loses 7. If 9 is true green loses 9. Therefore 2 is locked in the green ALS.

The coach’s version misses the elimination of 2’s because his green ALS has been reduced to a bv. But more importantly, Taupier’s link by link explanation misses the fact that his Death Blossom example is a special case in which the common value groups in the two ALS see each other. His players are unprepared for the typical DB.

Here is the final example, currently the Hodoku Ex. 1 of Death Blossom. It’s a tight one, and I’ve left on the toxic set markers.

Remembering the internal ALS slinks between value groups, note how the death blossom is converted into a nice loop below. Nobody sees the internal slink, of course, but the death blossom winks now become aligned nice loop winks and imply eliminations.

 

Looking back, I think that the Death Blossom is underrepresented in the Sysudoku collection reviews. If you find more, tell me where to look. I’ll update posts, or add new ones to put yours in and credit your find.

Death Blossom is last method in the Order of Battle not supplemented by an extracted map. It is followed in SSOB by the XYZ/WXYZ scan, using the XYZ Map. That is followed by chaining methods, leading off with the simplest, the XY-chain, aided by the XY Railway on the bv map.

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