Almost Locked Sets

Level 11 · Red Belt

Strategy:

Almost Locked Sets

Requires:

Naked Pair

Learn after:

ALS-XZSue de Coq

Overview

An Almost Locked Set (ALS) is a group of N cells containing N+1 candidates. If one candidate is removed, the remaining N candidates are locked into the N cells.

How It Works

  1. Find a group of N cells containing exactly N+1 different candidates.
  2. All cells must see each other (share a house).
  3. If any candidate is removed from outside, the remaining N candidates lock.
  4. Use this to chain eliminations.

Example

Starting position

Look for Almost Locked Sets.

1

Two ALSs: r4c4, r4c5, r4c6 and r4c9 and r5c7, r5c8, r6c8 and r6c9

Find two Almost Locked Sets (ALS): r4c4, r4c5, r4c6 and r4c9 and r5c7, r5c8, r6c8 and r6c9.

2

What an Almost Locked Set is

An ALS has N cells with N+1 candidates. If one candidate is removed, the remaining candidates become locked into the set.

3

Restricted common candidate 3

These ALSs share restricted common candidate 3, whose instances all see each other.

4

These cells cannot keep 6

One ALS must contain the shared candidate 6, so these cells cannot keep it: r5c5.

5

Remove 6 from r5c5

One ALS must contain the shared candidate 6, so remove 6 from r5c5.

6

Result

Result after applying the technique.

Tips & Patterns

  • ALS is a building block for advanced chains and techniques.
  • Start by identifying ALS groups, then look for how they interact.
  • Common: two cells with 3 candidates, three cells with 4 candidates.