# 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:

**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