Locked Candidates

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An intersection is the set of cells shared by a row or column and a box. Locked Candidates eliminates candidates by examining the positions of a single candidate digit in the two houses that form an intersection.

How to spot it

• For each candidate x from 1 to 9, examine its positions in each house. You can start with rows (or columns) or with boxes, according to your preference. The following two checks can be made in either order.
• If, within a row or column, candidate x can appear only in its intersection with a box, eliminate x from the other cells in that box.

• If, within a box, candidate x can appear only in its intersection with a row or column, eliminate x from the other cells in that row or column.

How it works

If, within a house (row, column, or box), a candidate can appear only inside one intersection, it is said to be locked in that intersection. No matter which cell in the intersection finally contains the digit, the digit must also belong to the other house that forms the same intersection. Therefore, in that other house, the candidate cannot appear outside the intersection, and those candidates can be eliminated.

Examples

Depending on where the locking is found and where the elimination is made, Locked Candidates can be divided into four cases:

• Case 1: A candidate is locked in the intersection of a box and a row, discovered from the box. Therefore, the candidate can be eliminated from other cells in the row.
• Case 2: A candidate is locked in the intersection of a box and a column, discovered from the box. Therefore, the candidate can be eliminated from other cells in the column.
• Case 3: A candidate is locked in the intersection of a row and a box, discovered from the row. Therefore, the candidate can be eliminated from other cells in the box.
• Case 4: A candidate is locked in the intersection of a column and a box, discovered from the column. Therefore, the candidate can be eliminated from other cells in the box.

For example:

Case 1 (Box ⇒ Row): On the board below, candidate 5 in box 3 can appear only in the intersection of box 3 and row 3. Therefore, no other cell in row 3 can contain 5; if any do, those candidates can be eliminated.

Case 2 (Box ⇒ Column): On the board below, candidate 7 in box 4 can appear only in the intersection of box 4 and column 3. Therefore, no other cell in column 3 can contain 7; if any do, those candidates can be eliminated.

Case 3 (Row ⇒ Box): On the board below, candidate 8 in row 9 can appear only in the intersection of row 9 and box 9. Therefore, no other cell in box 9 can contain 8; if any do, those candidates can be eliminated.

Case 4 (Column ⇒ Box): On the board below, candidate 5 in column 8 can appear only in the intersection of column 8 and box 9. Therefore, no other cell in box 9 can contain 5; if any do, those candidates can be eliminated.