Sudoku Pointing Pairs and Box/Line Reduction

A pointing pair is a digit whose places in a box all lie in one row or column. Whichever cell it ends up in, that row or column gets its digit from this box, so you can rule the digit out of the rest of the row or column. Box/line reduction is the same idea the other way round: if a digit’s places in a row or column all lie in one box, rule it out of the rest of that box.

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This is the third of the Sudoku techniques, and the first that rules digits out instead of placing them. The how to solve page calls them pointing and claiming.

The rule: pointing

Pick a box and a digit it’s missing.
Find every cell in the box where the digit could go.
If they’re all in one row (or one column), cross the digit out of that row (or column) everywhere outside the box.

The top-middle box’s 1 can only go in column 4, so the 1s in rows 7 and 8 of column 4 go.

A pointing pair places nothing by itself. Its value is what it leaves behind: here, with the 1s gone from rows 7 and 8, row 7 has only one place left for its 1.

In a real puzzle

In the Hard puzzle every technique page follows, the hidden singles run out after five moves. The next three moves are all pointing, in a row:

The top-middle box’s 6 is somewhere in column 6, rows 1 to 3, so row 7, column 6 can’t be 6.

The top-middle box’s 6s all lie in column 6 (this one uses three cells), which rules out the 6 in row 7, column 6.
The same box’s 7s are in column 6 too, which rules out the 7s in rows 7 and 8.
The centre box’s 4s all lie in column 4, which rules out the 4s in rows 7 and 9.

That last one leaves row 9, column 4 with only 9 in its notes, a naked single. Pointing comes back twice more later in the solve.

The reverse: box/line reduction

Pick a row or column and a digit it’s missing.
Find every cell in the line where the digit could go.
If they’re all inside one box, cross the digit out of the rest of that box.

Row 1’s 9 is in the top-left box, so the box’s other 9s go.

The Hard puzzle uses it straight after the naked single. Row 9’s 3 can only go in columns 8 and 9, both in the bottom-right box. So the box’s 3 is in row 9, and the 3s in rows 7 and 8 of the box are ruled out.

Row 9’s 3s are both in the bottom-right box, so four 3s in rows 7 and 8 go.

One of those 3s, in row 7, column 9, sits in the column where the next step happens: a naked pair.

How often you’ll need them

On PeerPuzzles, pointing is needed in 45 of the 50 Hard levels and 10 of the 50 Medium ones, and box/line reduction in 12 Hard and 3 Medium. Most Medium levels never need notes at all. Pointing is the first note technique to learn, and on Hard levels it’s the most common one.

How to find them fast

One digit at a time. You don’t need full notes. Pick a digit and, box by box, see whether its places line up.
Use Snyder notes. A digit pencilled into exactly two cells of a box that share a row or column is a pointing pair, ready to use. See tip 6.
Check what it opens. After ruling digits out, look along the row or column you just changed for a hidden single, and at any cell left with one note.

Next steps

Play Sudoku →
Read next: Sudoku Naked Pairs: Two Cells, Two Digits
More on Sudoku Techniques

Questions

What are locked candidates?

Another name for the same two techniques. Pointing is sometimes called locked candidates type 1, and box/line reduction (also called claiming) type 2. The digit is “locked” into the cells where a box and a line overlap.

Does it have to be a pair?

No. Two or three cells work the same way, as long as all of the digit’s places in the box are in one row or column. Three in a line is sometimes called a pointing triple.

Do I need full notes to use it?

No. It’s about one digit at a time, so you can check one digit’s places in a box without writing anything else. Snyder notes, which mark a digit when it has two places in a box, show pointing pairs at a glance.