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ALS-XY-Chain

An ALS-XY-Chain is a XY-Chain whose nodes are Almost Locked Sets. It is a generalization of the usual XY-Chain (whose nodes are bivalue cells), since each bivalue cell is itself an Almost Locked Set.

The ALS-XZ rule is an ALS-XY-Chain of length two, while the ALS-XY-Wing is an ALS-XY-Chain of length three.

Contents 1 Example 2 Nice Loop Notation 3 Eureka Notation 4 See also

Example

The following example comes from a Eureka! forum post.

 .    A46    .    | .     .     .    |D25   D258   .
 .     .     .    | .     .     .    | .     .     .
 .     27-4  .    |C13    .     .    | .    D1258 D1248
------------------+------------------+------------------
 .     .     .    | .     .     .    | .     .     .
 .     .    B26   |C367   .     .    | .     .     .
 .    A269   .    | .     .     .    | .     .     .
------------------+------------------+------------------
 .    A469   .    | .     .     .    | .     .     .
 .     .     .    |C37    .     .    | .     .     .
 .     .     .    | .     .     .    | .     .     .

There are four Almost Locked Sets, labeled A, B, C and D in the diagram. These Almost Locked Sets form a ALS-XY-Chain with the following links:

• A and B has a restricted common 2.
• B and C has a restricted common 6.
• C and D has a restricted common 1.

Since all cells in A and D with candidate 4 see the cell r3c2, we conclude that 4 can be eliminated from r3c2.

Nice Loop Notation

r3c2 -4- ALS:r167c2 -2- r5c3 -6- ALS:r358c4 -1- ALS:[r1c78,r3c89] -4- r3c2 => r3c2 <> 4

Eureka Notation

(4=692)ALS:r167c2 - (2=6)r5c3 - (6=371)ALS:r358c4 - (1258=4)ALS:r1c78,r3c89 => r3c2 <> 4

See also

• XY-Chain
• Almost Locked Set
• ALS-XZ
• ALS-XY-Wing

This page was last modified 03:38, 28 March 2009.  

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