Peak Sudoku

ALS Chain

Links built from almost-locked sets – N cells sharing N+1 candidates.
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Overview

Tier 4
Fish, wings, chains & uniqueness
Typical difficulty
Peak Score 80–95
Also known as
Almost Locked Sets, ALS-XZ, ALS-XY-Wing

An Almost Locked Set (ALS) is a set of N cells in a house sharing N+1 candidates. When connected through restricted common candidates, they form extraordinarily powerful elimination chains.

An Almost Locked Set (ALS) is an N-cell group in a house that contains N+1 candidates. A single bivalue cell is the simplest ALS (1 cell, 2 candidates); two cells sharing three candidates is another (2 cells, 3 candidates). Because N cells can only hold N numbers, exactly one candidate is the 'odd one out'. If you eliminate even one candidate from an ALS, the remaining N candidates become a locked Naked Subset! By linking almost-locked sets together via restricted common candidates, solvers can make eliminations that no fish, wing, or simple bivalue chain can ever reach.

Worked examples

1 / 5
Reading the exampleCells forming the patternCells losing candidatesEliminated candidates

Almost-locked sets do the work here. A set holding just one more candidate than it has cells must place all but one of those digits, so ruling a digit out of the set pins the rest inside it.

Suppose R6C7 is not 8.

  1. Then R5C8 is 3, since without 8, R5C8 and R6C7 (two cells holding only 3, 4 and 8) must hold both 3 and 4.
  2. So R5C8 is not 4, since a cell holds just one digit.
  3. So 8 sits in R1C8 or R2C8, since without 4, R1C8, R2C8 and R5C8 (three cells holding only 3, 4, 8 and 9) must hold all of 3, 8 and 9.

Either R6C7 is 8 or 8 sits in R1C8 or R2C8, so 8 can be removed from any cell that sees both.

Removes: 8 from R3C7, R1C7

How to apply it

Spotting the pattern and making the deduction, in order.

  1. Identify two 'almost-locked sets' in different houses (groups of cells that have just one more candidate than cells, such as 2 cells with 3 candidates).
  2. Find a shared candidate digit that connects the two sets, where all instances in the first set see all instances in the second set.
  3. Because that connecting digit cannot be true in both sets at once, at least one set will not contain it.
  4. Whichever set loses the connecting digit instantly locks down its remaining candidates like a naked subset.
  5. Find a second candidate number shared between both sets.
  6. Eliminate that second candidate from any cell in the grid that has line of sight to all occurrences of that digit in both sets.

Common mistakes

  • Failing to verify that the connecting candidate is truly restricted (all instances in set A must see all instances in set B).
  • Eliminating the candidate from cells that only see the digits in one of the two sets.
  • Miscounting the candidate total: an ALS of size N must have exactly N+1 candidates.

Frequently asked questions

What is an ALS-XZ rule?
ALS-XZ is the fundamental two-ALS rule. One restricted candidate connects the two sets, and a second common candidate is eliminated from intersecting external cells.
Why are ALS techniques considered so advanced?
Because nodes in an ALS chain are entire sets of cells rather than individual digits or bivalue cells, allowing eliminations across complex multi-digit relationships.
Peak Score 75–90Nice Loop (AIC)An alternating chain of strong and weak links – open or closed.Peak Score 70–85XY-ChainA chain of bivalue cells that forces a digit at both endpoints.Peak Score 90–100Forcing ChainBoth branches from a bivalue cell reach the same conclusion.

Put ALS Chain into practice

Try a puzzle from the Extreme tier (Peak Score 81–90).

Play a Extreme puzzleAll 25 techniques