Rooted: Created page with "The '''Death Blossom''' technique involves a ''stem'' cell of N candidates that sees N ''petals'', each an Almost Locked Set. It is developed by extending the..."

2020-06-04T01:11:05Z

Created page with "The '''Death Blossom''' technique involves a ''stem'' cell of N candidates that sees N ''petals'', each an Almost Locked Set. It is developed by extending the..."

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The '''Death Blossom''' [[technique]] involves a ''stem'' [[cell]] of N [[candidate]]s that sees N ''petals'', each an [[Almost Locked Set]].

It is developed by extending the [[Aligned Pair Exclusion]] technique into an arbitrary sized set of non-aligned cells (see [[Subset Exclusion]]), with most of the cells belonging to [[Almost Locked Set]]s.

== How it works ==
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[[Image:DeathBlossom.png]]
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A Death Blossom consists of a "stem" cell and an Almost Locked Set (or ALS) for each of the stem cell's candidates. The ALS associated with a particular candidate of the stem cell has that number as one of its own candidates, and within the ALS, every cell that has the number as a candidate can see the stem cell. The ALSes can't overlap; i.e., no cell can belong to more than one ALS. Also, there must be at least one number that is a candidate of every ALS, but is not a candidate of the stem cell.

Once we've found a Death Blossom, if an outside cell that doesn't belong to one of the ALSes (and isn't the stem cell) can see every cell in each ALS that has a particular number as a candidate, and the number isn't a candidate of the stem cell, then the number can't be a candidate of the outside cell.

The workings of the Death Blossom is best explained via an example. This example is a [[scramble]]d version of the example at [http://www.scanraid.com/AdvanStrategies.htm#DB Andrew Stuart's Advanced Sudoku Strategies] page.

We have a stem cell at '''r1c9''' with two candidates 1 and 8. Observe that '''r1c9''' sees all the 1s in the blue ALS, and '''r1c9''' sees all the 8s in the yellow ALS. These two ALSes are the petals. Now, by a proof by cases:
* If '''r1c9=1''', then the blue ALS gets reduced to a [[Naked Triple]] of 3, 5 and 6 and so '''r6c5<>5'''.
* If '''r1c9=8''', then '''r5c9=7''', and the remainder of the yellow ALS gets reduced to a [[Naked Pair]] of 1 and 5 and so '''r6c5<>5'''.

Therefore, we can eliminate 5 from '''r6c5'''.

Observe how this is an extension of [[Aligned Pair Exclusion]], whose cells consist of the '''r6c5''', the blue ALS and the yellow ALS. If '''r6c5=5''', then '''r1c5=1''' is forced by the blue ALS, and also '''r5c9=8''' is forced by the yellow ALS, and so '''r1c9''' has no candidates remaining. The Death Blossom technique is derived by working forwards from '''r1c9'''.
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== Note ==
If the stem cell has exactly two candidates, like the example above, then the same eliminations can be replicated using a [[ALS-XY-Wing]] move.

== External links ==
* [http://www.scanraid.com/AdvanStrategies.htm#DB Advanced Sudoku Strategies]
* [http://www.sudoku.com/forums/viewtopic.php?t=4755 APE - Further extendable?]

== See also ==
* [[Almost Locked Set]]
* [[ALS-XZ]]
* [[ALS-XY-Wing]]

[[Category:Solving Techniques]]
[[Category:Chains and Loops]]

Death Blossom - Revision history

Rooted: Created page with "The '''Death Blossom''' technique involves a ''stem'' cell of N candidates that sees N ''petals'', each an Almost Locked Set. It is developed by extending the..."