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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.

## 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:

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