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
