Proven Sudoku

Techniques / Locked candidates

Locked candidates: pointing and claiming

A digit trapped in the overlap between a box and a line.

3 techniques in this family, introduced at tier 2, 3 with a worked example from a real board. How to read a sudoku grid explains the notation used below.

What these have in common

A box and a row meet in three cells. If everything you know about a digit forces it into those three cells, then you know something about both the box and the row, even though you cannot yet place anything. Locked candidates is the whole of that idea.

Why the logic holds

Take a digit and a box. If every cell in the box that could still hold that digit lies in one row, the digit is somewhere in that row, because it must be somewhere in the box. So it cannot be anywhere else in that row, and it comes out of the other six cells. Run the same argument starting from the row instead of the box and you get the other direction.

When to reach for it

The moment singles dry up. It is the cheapest thing to check after them, it needs no pencil marks beyond one digit at a time, and on a medium puzzle it usually restarts the cascade on its own.

How the members differ

Pointing runs from the box outward to the line. Claiming runs from the line inward to the box. Type 1 and Type 2 in the literature are those two directions, and the general form is the observation that they are one rule about an intersection, stated twice because people find it easier to scan in one direction at a time.

The mistake to avoid

Expecting it to place a digit. It never does. Locked candidates only ever removes candidates, and on a grid without pencil marks the removal is invisible, so it is the first technique where writing your notes down stops being optional.

Start with Locked Candidates Type 1 (Pointing). Inside one box, every spot left for a digit sits in the same row or column.

Every technique in this family