Almost locked sets: ALS-XZ

A worked example

This position comes from SudokuByte’s lesson on the Almost locked sets: ALS-XZ. Gold cells hold the evidence; green cells are the pattern’s ends.

1. Where to look

   Count N cells and N+1 digits. Verify that every X in one set sees every X in the other.

   An ALS has one more candidate digit than cells. Connect two such sets with a restricted common digit X; a shared Z is then guaranteed somewhere across them.

2. Read the evidence in this position

   Set A is r3c4: 1 cells, with 2 digits (2, 3). Set B is r3c5: 1 cells, with 2 digits (2, 3).

3. Why the deduction must follow

   Every 2 in set A sees every 2 in set B, so both sets cannot use 2. One set must do without it. That set then has exactly as many available digits as cells and must use all those digits, including 3. Thus 3 occurs somewhere in A or B. Here, target means a pencil mark we are considering erasing. A target cell must share a row, column, or box with every cell in A or B that still has a candidate 3. Then wherever that 3 goes, it rules out the target.

   In ordinary words: at least one of these two groups has to contain 3. We do not know where. We can still erase 3 from a cell that would conflict with every possible location. "3 locations" means locations for the digit 3, not 3 different cells.

4. Apply the result

   Erase 3 from r3c6, r3c7, r3c9, r1c6. The pattern may remove candidates without immediately solving a cell.