ALS-XZ Rule

The ALS-XZ rule is the doorway to Almost Locked Set logic - the family of techniques behind Sue de Coq and the Death Blossom. An almost locked set is a group of cells holding just one more candidate than it has cells: a bi-value cell is the smallest example, and any near-naked pair or triple qualifies. Link two of them cleverly and you can eliminate a digit neither could touch alone.

The idea

Take two almost locked sets, A and B, that share two digits, called X and Z. The digit X must be the restricted common: every cell holding X in A can see every cell holding X in B, so X can be true in only one of the two sets. That restriction locks the sets together - whichever one gives up X becomes fully locked. The consequence falls on the other shared digit, Z: no matter which way X resolves, one of the two sets is forced to contain Z. Therefore any cell outside both sets that can see every Z in A and every Z in B cannot itself be Z, and you remove it.

A worked example

Let set A be the bi-value cell r1c1 = {3,6} - one cell, two candidates, so almost locked. Let set B be two cells, r1c4 = {3,9} and r2c4 = {6,9}, holding {3,6,9} between them: two cells, three candidates, also almost locked. The shared digits are 3 and 6. The only 3 in A (r1c1) sees the only 3 in B (r1c4) along row 1, so 3 is the restricted common X and 6 becomes Z. Whichever set gives up its 3 locks and must supply the 6 - so a cell that sees both 6s, r2c1 (column 1 to r1c1, row 2 to r2c4), cannot be 6. From two small, harmless-looking sets, a clean elimination appears.

Set A (blue) = {3,6}; set B (green) = {3,9} and {6,9}. The 3s see each other along row 1 (dashed) - 3 is the restricted common. So one set must hold the 6, and r2c1, seeing both 6s, loses its 6.

Step by step

Find two almost locked sets - each with one more candidate than cells.
Identify two shared digits, X and Z.
Confirm X is restricted - every X in one set sees every X in the other.
Eliminate Z from cells outside both sets that see all copies of Z in each.

Common mistakes

X not truly restricted. If a single X in one set cannot see an X in the other, the lock fails and no elimination follows.
Removing Z inside a set. The eliminations are on outside cells only - cells within A or B are part of the argument, not its target.
Miscounting the set. An almost locked set has exactly one spare candidate; two spares is not the same pattern.

Which Sudoku types is this best for?

The same logic applies across variants, but it pays off more in some than others.

Works Classic Sudoku A versatile advanced tool that resolves grids beyond the reach of chains and fish. → Works Killer Sudoku Killer cages naturally form almost locked sets, so ALS logic is at home here. → Works Sudoku X The diagonals create extra almost locked sets to pair up. → Limited Samurai Sudoku Rarely worth the bookkeeping across five grids. →

Where to practise this

This technique starts paying off at Evil, which is where puzzles first stop yielding to anything simpler. Reading about a pattern and spotting it on a live grid are different skills - the second one only comes from playing.

Play Evil Sudoku About Evil Sudoku

Related techniques

Sue de Coq - Advanced Sudoku Technique Cells at a box-and-line intersection, plus almost-locked sets in the box and line, force eliminations in both. Death Blossom - Almost Locked Set Sudoku Technique A stem cell whose every candidate links to an almost locked set; a digit common to all the petals can be eliminated from cells seeing it in each. ALS-XY-Wing - Almost Locked Set Sudoku Technique Three almost locked sets - a pivot joined to two others by restricted commons - force a digit shared by the outer two out of cells seeing it in both. Jellyfish - the Order-4 Sudoku Fish One digit confined to the same four columns across four rows (or vice versa) - eliminate it from the rest of those columns.