Locked Candidates: Pointing and Claiming

You will need notes for this one. If you don't use them yet, start with our guide to pencil marks. Rows are numbered 1 to 9 from the top, columns 1 to 9 from the left, and boxes 1 to 9 reading like a book.

The idea in one sentence

Every box, row and column must contain every digit once. So if a digit's only possible squares in one unit all fall inside a second unit, that digit is "locked" into the overlap, and the second unit can't have it anywhere else.

A box and a row (or column) overlap in three squares. That overlap gives two versions of the technique, depending on which unit you start from.

Pointing: from the box to the line

Look at one box and one digit. If all the squares in that box where the digit could go lie in the same row, the digit must end up in that row, inside this box. So the rest of the row, outside the box, can't have it. The candidates "point" along the row and clear it. The same works with a column.

Here is a real example. The diagram shows full notes after every simpler step has been used.

Highlighted: 7 the pattern · struck through: 7 removed

In box 1, the digit 3 is only possible in row 1, column 2 and row 1, column 3. Both are in row 1. Wherever the 3 ends up in box 1, it will be in row 1, and a row can only hold one 3. So 3 can be removed from row 1, column 8, the only other square in row 1 that still had it as a candidate.

Notice that we haven't placed the 3 yet. We don't know which of the two squares it goes in. We only know which row it is in, and that is enough.

Claiming: from the line to the box

Now start from the line instead. If all the squares in a row (or column) where a digit could go lie inside the same box, the digit must be in that box, inside this row. So the rest of the box can't have it. The row "claims" the digit for its part of the box. You will also see this called box-line reduction.

Highlighted: 7 the pattern · struck through: 7 removed

In column 3, the digit 3 is only possible in row 1, column 3, row 2, column 3 and row 3, column 3. All of them are inside box 1. The column must have a 3, so box 1's 3 has to be one of those squares. That means 3 can be removed from the rest of box 1: here, row 1, column 1.

Why it works, without the jargon

Think of the digit as one coin that must be hidden somewhere in a box. If you know the coin is in the top row of the box, you know it's not in the top row of the next box over, because that row can only hold one coin. Pointing and claiming are the same argument run in two directions.

How to scan for locked candidates

1. Go digit by digit. Pick a digit and look at each box that doesn't have it yet.
2. Look at the shape of its candidates. If they all sit in one row or one column of the box, you have pointing. Check whether that row or column has the digit as a candidate outside the box. If it does, cross it off.
3. Then do the lines. For each row and column, see whether the digit's candidates all fall inside one box. If they do and the box has the digit elsewhere, that's claiming.

Partial notes, where you only mark a digit in a box when it has two or three possible spots, make pointing very easy to see. Two marks side by side in a box are a pointing pair waiting to be used.

What happens next

A locked-candidate step usually leads somewhere quickly. Removing one candidate can leave a square with a single option, or a digit with a single spot in a unit. In the first example above, the next step our solver found was another case of pointing. Locked candidates often come in chains like that, so after each one, scan the same digit again.

Common mistakes

• Checking the box but not all of it. Pointing only works if every candidate for the digit in that box is in the one row or column. One stray candidate elsewhere in the box breaks it.
• Clearing the wrong unit. Pointing clears the line outside the box. Claiming clears the box outside the line. Mixing them up removes candidates that should stay.
• Using out-of-date notes. The technique is only as good as your candidates. If a square has lost a candidate you forgot to cross off, a pattern can look locked when it isn't. Our game tidies notes when you place a digit, but any other candidate you rule out, you have to remove yourself.

Practise

Locked candidates is one of the two techniques our hard puzzles are built around. The other is the naked pair, explained in our pairs guide. Every hard puzzle on the site needs at least one of them, and all of them can be finished with singles, locked candidates and naked pairs. If singles still give you trouble, our singles guide comes first.