ALS-XZ

Level 11 · Red Belt

Strategy:

Almost Locked Sets

Requires:

Almost Locked Sets

Learn after:

Overview

ALS-XZ is the simplest ALS chain technique. Two Almost Locked Sets share a restricted common candidate (X), allowing elimination of any other common candidate (Z) from cells seeing all Z's in both sets.

How It Works

Find two ALS (groups of N cells with N+1 candidates).
Find a restricted common candidate X (all X's in ALS1 see all X's in ALS2).
Find another common candidate Z that appears in both ALS.
Eliminate Z from cells that see all Z's in both ALS.

Example

Starting position

Look for ALS-XZ.

Sudoku grid showing the initial puzzle state for Look for ALS-XZ.

1

Find two Almost Locked Sets

Find two Almost Locked Sets (ALS) - each has N cells with N+1 candidates.

Sudoku grid illustrating step 1: Find two Almost Locked Sets — Find two Almost Locked Sets (ALS) - each has N cells with N+1 candidates.

2

Restricted common candidate 5

These ALSs share restricted common candidate 5: every 5 in one ALS sees every 5 in the other.

3

Only one ALS can hold the shared digit

The restricted common candidate can be true in only one ALS. If it is true in one, the other ALS becomes a locked set.

Sudoku grid illustrating step 3: Only one ALS can hold the shared digit — The restricted common candidate can be true in only one ALS. If it is true in one, the other ALS becomes a locked set.

4

Cells that see every 6 in both ALSs

Both ALSs contain candidate 6. Cells that see every 6 in both ALSs cannot keep it: r5c5.

Sudoku grid illustrating step 4: Cells that see every 6 in both ALSs — Both ALSs contain candidate 6. Cells that see every 6 in both ALSs cannot keep it: r5c5.

5

Remove 6 from cells seeing both ALSs

Both ALSs contain candidate 6. One ALS must contain 6, so remove 6 from cells seeing both: r5c5.

Sudoku grid illustrating step 5: Remove 6 from cells seeing both ALSs — Both ALSs contain candidate 6. One ALS must contain 6, so remove 6 from cells seeing both: r5c5.

6

Result

Result after applying the technique.

Sudoku grid showing the result after applying the technique

Tips & Patterns

The restricted common X can only be true in one ALS.
This forces Z to be locked in at least one ALS.
Any cell seeing all Z's in both sets can never be Z.