Death Blossom

A stem cell whose candidates each link to an almost-locked set.

Death Blossom is one of the most advanced almost-locked-set patterns in Sudoku. It is built around a single "stem" cell whose every candidate links out to its own almost-locked "petal" set. When one digit happens to appear in every petal, that digit becomes trapped: whichever value the stem finally settles on closes off one petal-link and forces that petal to place the shared digit. The Death Blossom sudoku technique then lets you erase that digit from any cell that can see all of the petals at once, since one of them is guaranteed to hold it.

Worked example

Stem R1C1={1,2,3}; each candidate links to a petal that also holds 9 — R1C2={1,9}, R1C3={2,9}, R1C4={3,9}. Whatever the stem becomes its petal must be 9, so 9 is trapped in the petals and R1C9 loses it.12319293989
Stem R1C1={1,2,3}; each candidate links to a petal that also holds 9 — R1C2={1,9}, R1C3={2,9}, R1C4={3,9}. Whatever the stem becomes its petal must be 9, so 9 is trapped in the petals and R1C9 loses it.

Here the stem is R1C1={1,2,3}, and each of its candidates owns a petal that also contains 9: R1C2={1,9} for the 1, R1C3={2,9} for the 2, and R1C4={3,9} for the 3. If the stem resolves to 1, R1C2 loses its 1 and must become 9; if it is 2, R1C3 becomes 9; if it is 3, R1C4 becomes 9. So a 9 is guaranteed to land in one of the three petals no matter which value the stem takes. R1C9={8,9} sees all three petals, so it can never be that 9 — the 9 is eliminated from R1C9, forcing it to 8.

When to use it

Save Death Blossom for expert grids where singles, subsets, fish and the simpler chains have all stalled. Scan for a multi-candidate cell you can treat as a stem, then try to attach an almost-locked set — in the easiest case a single bivalue cell — to each of its candidates. If those petals all share one digit and some cell sees every petal, that digit comes out. In this grid R1C1's three petals each held a 9, which is exactly what sealed the elimination at R1C9.

How to use it

  1. Pick a stem and its petals. Choose a stem cell with three or more candidates. For each candidate, find a petal almost-locked set that holds that digit and is seen by the stem on it.
  2. Find the shared digit Z. The petals must all share another candidate Z that is not one of the stem candidates. Whatever the stem turns out to be, its petal collapses and is forced to place Z.
  3. Eliminate Z across the petals. Because Z must land in one of the petals, remove Z from any cell outside the flower that sees every Z candidate across all petals.
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Frequently asked questions

What is a Death Blossom in Sudoku?

A Death Blossom is a stem cell plus one almost-locked petal set for each of the stem's candidates. If a single digit appears in every petal, it is forced to show up among them, so it can be removed from any cell that sees all the petals. In the example the stem R1C1={1,2,3} has three bivalue petals — R1C2, R1C3 and R1C4 — that each contain a 9, which traps the 9 and clears it from R1C9.

How do I spot the stem and petals on the grid?

The stem is the central multi-candidate cell, and each petal is an almost-locked set tied to one stem candidate by a restricted common. Start from a cell like R1C1={1,2,3}, then find a petal for every candidate — R1C2={1,9} covers the 1, R1C3={2,9} the 2, and R1C4={3,9} the 3. Once all the petals share a digit (9 here), look for a cell such as R1C9 that sees every one of them; that is where the shared digit can be eliminated.

How is Death Blossom related to ALS-XZ?

It is a multi-petal extension of the same almost-locked-set logic. ALS-XZ pairs two sets across a single restricted common, whereas Death Blossom branches out from one stem cell to several petals at once. The shared digit that must appear among the petals — 9 in this grid — plays the same trapping role that the Z digit does in ALS-XZ.