Death Blossom Sudoku Technique

Death Blossom attaches one Almost Locked Set to every candidate of a single cell and reads what the whole flower has in common. The cell is the stem, the sets are the petals, and if every petal contains the same digit, that digit is forced into one of them no matter what the stem turns out to be.

What the pattern is

An Almost Locked Set is a group of n cells in one unit carrying n + 1 candidates. Remove one of its digits and it locks: the remaining cells must use every remaining digit.

A Death Blossom needs three things:

• A stem cell with k candidates, usually two or three.
• One petal per stem candidate — an Almost Locked Set containing that digit, where every copy of that digit inside the petal sees the stem.
• A digit z, not a stem candidate, present in all of the petals.

Set the stem to any of its values. That value is knocked out of the matching petal, the petal locks, and it is forced to place z. Every value of the stem leads to some petal holding z, so z cannot live in a cell that sees all of the z candidates across all petals.

When to look for it

Look once you are comfortable spotting Almost Locked Sets and a Legendary grid still refuses to move. Bivalue stems are the practical case: two petals, two branches, quick to verify. The stem itself is often an ordinary pair you have already stared at for ten minutes.

How to apply it, step by step

1. Pick a cell with two or three candidates as the stem.
2. For each stem candidate, find a nearby Almost Locked Set containing that digit where every copy of it sees the stem.
3. List the digits each petal holds besides the stem digit.
4. Take a digit that appears in every petal and is not a stem candidate. That is z.
5. Mark every z candidate in every petal.
6. Remove z from any cell outside the stem and petals that sees all of those marks.

A worked example

stem      r5c5 {6,7}

petal A   r5c1 {4,6}   r5c2 {6,9}    2 cells, digits {4,6,9}, shares row 5 with the stem
petal B   r1c5 {4,7}   r2c5 {7,8}    2 cells, digits {4,7,8}, shares column 5 with the stem

shared digit z = 4      in A only at r5c1,  in B only at r1c5

If the stem is 6, both cells of petal A lose their 6, so r5c1 = 4 and r5c2 = 9. If the stem is 7, both cells of petal B lose their 7, so r1c5 = 4 and r2c5 = 8. Either way a 4 lands on r5c1 or r1c5. The one cell that sees both is r1c1 — row 1 for r1c5, column 1 for r5c1 — so r1c1 loses its 4.

Common mistakes

• Using a petal that does not contain the stem digit it is supposed to answer. Each petal must cover exactly one branch.
• Choosing z from the stem's own candidates. It has to be independent of the stem's value.
• Letting a petal overlap the stem cell or another petal.
• Eliminating from cells that see the z marks of only one petal.

Where you meet it

Death Blossom is an extreme-tier tool and appears mainly in Legendary puzzles. It behaves like a very short forcing structure with the branching hidden inside the petals, which is why solvers who are fluent with XY-Chains usually find it easier than they expect.