Almost Locked Sets: one digit short of a locked set

Count distinct digits once

A basic ALS here has N cells in one unit and N+1 distinct candidates between them. A naked subset instead reserves N digits in N cells. An ALS therefore does not immediately remove all its digits from outside cells; another condition or connection is needed.

HoDoKu — Almost Locked Sets · SudokuWiki — Almost Locked Sets

Our two cells and three digits

Let D1={2,5} and D4={5,8}. Their union is {2,5,8}: three digits for two cells in row D. Count 5 once even though it appears in both notes.

D7 can still have 2 or 8 under these partial conditions. D1/D4 could use 5/8 or 2/5 respectively, leaving the other digit outside. Treating the ALS like a naked pair would lose valid possibilities.

Add a justified restriction

If a separate proof removes 8 from D4, then D4=5 and D1=2. The cells now genuinely reserve {2,5}, removing those digits elsewhere in row D. The additional deduction did the work; the label ALS alone did not.

Connect two sets with ALS-XZ

Take two disjoint ALSs. Choose a shared digit X whose every position in one set sees every position in the other: both sets cannot contain X at once. For another shared digit Z, an outside cell seeing every Z position in both sets cannot be Z. Otherwise both ALSs lose Z, lock their remaining digits and require X simultaneously.

HoDoKu — Almost Locked Sets · SudokuWiki — Almost Locked Sets

Walk through our own example

Set one is A1={2,5}, A4={5,8}; set two is B1={2,6}, B7={6,8}. Each has two cells and three digits. X=2 at A1/B1 is mutually visible. Z=8 is at A4/B7, both visible from B4, so remove 8 from B4 if present.

Check it backwards: B4=8 forces A4=5 then A1=2, and B7=6 then B1=2. Those two 2s clash. This original partial scenario assumes complete candidates in the four source cells; it is not a full puzzle.

What the scanner covers

The scanner checks disjoint ALS-XZ pairs with at most three cells per set and a bounded number of combinations. It does not cover every ALS form. Finding nothing does not prove that your board has no ALS deduction.

In Classic 9×9, use Scan to scan the current entries, inspect justified eliminations and open this lesson. Chain and ALS searches are bounded; UR Type 1 and BUG+1 require verified uniqueness. Reading this lesson never changes your saved game.

Try before looking

References and further reading

Read the source explanations and compare them with our examples. Links are references, not endorsements or claims of affiliation.

• HoDoKu — Almost Locked Sets
• SudokuWiki — Almost Locked Sets