Death Blossom
The Death Blossom is a striking Almost Locked Set pattern that builds on the ALS-XZ rule. It centres on one cell — the stem — and attaches an almost locked set to each of the stem's candidates, like petals on a flower. When the petals share a digit, that digit can be eliminated somewhere on the grid no matter which way the stem falls.
The idea
Pick a stem cell with, say, three candidates. For each candidate, find an almost locked set — a petal — such that placing that candidate in the stem would fully lock the petal (the stem cell sees, and so removes, that digit from the petal). Now suppose some digit Z appears in every petal. Whichever value the stem finally takes, exactly one petal locks, and that petal is forced to place Z. So Z must be true in one of the petals regardless of the stem — and any cell outside them all that can see Z in every petal cannot be Z itself.
A worked example
Take a stem cell r5c5 = {1,4,7} with three petals down column 5. Petal r1c5 = {1,9}: if the stem is 1 it removes the 1 from r1c5, locking it to 9. Petal r2c5 = {4,9} locks to 9 when the stem is 4; petal r7c5 = {7,9} locks to 9 when the stem is 7. Whichever value the stem finally takes, exactly one petal is forced to 9, so a 9 is guaranteed among the petals — all of which share column 5. Any other cell of column 5, such as r9c5, therefore cannot be 9. The stem never has to be resolved for the elimination to hold.
Stem r5c5 = {1,4,7} (purple); each stem digit locks a petal (green) to 9 — {1,9}, {4,9}, {7,9}. One petal is always forced to 9, so column 5 holds a 9 among them and r9c5 loses its own 9.
Step by step
- Choose a stem cell with two or more candidates.
- Attach a petal — an almost locked set — to each candidate, locked by the stem.
- Find a shared digit Z present in every petal.
- Eliminate Z from any cell that sees Z in all the petals.
Common mistakes
- A petal the stem can't lock. Each petal must be fully locked when its stem candidate is placed, or the guarantee collapses.
- Z missing from a petal. The shared digit has to appear in every petal, not most of them.
- Diving in early. Death Blossoms are expert-level — try singles, chains and the ALS-XZ rule first.
Which Sudoku types is this best for?
The same logic applies across variants, but it pays off more in some than others.