Lesson 33

ALS-XZ

The rule

Two almost-locked sets linked by a restricted common candidate force another shared candidate into at least one of them, so that candidate can be removed from any cell outside the two sets that sees every cell with that candidate across both sets.

Step by step

1. Look at the first set . These 2 cells all lie in the same row and have 3 different candidates among them, one more than the number of cells. This is called an Almost Locked Set (ALS).
2. Now look at the second set . These 3 cells all lie in the same row and have 4 different candidates among them, one more than the number of cells, so they also form an ALS. The two sets share candidate 3 as a restricted common candidate (RCC): every cell with candidate 3 in one set sees every such cell in the other, so the digit 3 can be placed in at most one of the two sets, never in both.
3. Both sets contain 5 as a candidate. Since the digit 3 can be placed in at most one set, at least one set will not use 3. A set that does not use 3 has as many distinct candidates left as cells, so it must place each of them, including 5, somewhere inside it. So 5 is placed in at least one of the two sets, and we can remove the candidate 5 from any cell outside the two sets that sees every cell with candidate 5 across both sets. That is where the name comes from: X is 3, the candidate the two sets share, and Z is 5, the candidate removed.