Pointing pairs and box/line reduction

1 September 2026 · 7 min read

Every box overlaps three rows and three columns, three cells at a time. Those overlaps — called intersections — carry information that neither the box nor the line reveals on its own, and squeezing it out is called locked candidates.

There are exactly two directions to squeeze, and they are easy to mix up:

• Pointing — a digit is confined, within a box, to cells on a single line. Eliminate it from the rest of that line.
• Box/line reduction (also called claiming) — a digit is confined, within a line, to cells inside a single box. Eliminate it from the rest of that box.

Same intersection, opposite reasoning. Both are shown below on one board, which happens to contain both at once.

Pointing pairs

A box has to contain every digit somewhere. So if a digit’s only possible cells in that box all sit on one row, then that row is where the box’s copy of the digit goes — wherever exactly it lands.

In the bottom-left box below, the digit 1 can only go in two cells, and both are on row 8:

Box 7 needs a 1. It has to be one of those two cells. Either way, row 8 gets its 1 from box 7 — so no cell in row 8 outside that box can hold a 1:

Two cells is the common case, hence the name. But it works with three as well — a pointing triple is the same argument and the same eliminations. Do not skip a three-cell instance because it is not a pair.

Box/line reduction

Now reverse it. A row also has to contain every digit somewhere. So if a digit’s only possible cells in that row all sit inside one box, the box is where the row’s copy goes — and the rest of the box is clear.

On the same board, look at row 1 and the digit 9. It can only go in two cells, both inside the top-left box:

Row 1 needs a 9, and it is coming from one of those two cells — both of which are in box 1. So box 1’s 9 is already spoken for by row 1, and the rest of the box cannot have one:

Telling the two apart

The reliable test is which unit you counted in:

• Counted the digit’s options inside a box and found them all on one line? That is pointing. Eliminate along the line, outside the box.
• Counted the digit’s options along a line and found them all in one box? That is box/line reduction. Eliminate inside the box, off the line.

Both eliminate from the part of the unit you were not counting in. If you find yourself eliminating from the unit you just counted, something has gone wrong — you would be removing the digit from the very cells you proved it must occupy.

Where to look

Locked candidates are the best value technique in Sudoku, because you can hunt them without full pencil marks. You need to know where one digit can go in one box, which is a quick visual check, not a marked-up grid. That makes them the natural next step after singles.

Practical routine:

1. Pick a digit already placed five or six times. It constrains the most lines, so its remaining homes are the most confined.
2. For each box missing it, see where it could go. Two or three cells on one line is a pointing instance.
3. Then do the same by line: for each row and column missing the digit, check whether its options huddle inside one box.

Boxes with two of their three bands already filled are the richest ground — two filled rows leave the digit only the third row to sit on, which is a pointing instance by construction.

How this connects to the rest

Locked candidates sit in a clear place in the hierarchy. Above singles, roughly alongside naked pairs, and below the X-wing — which is the same idea again, stretched across two boxes instead of contained in one.

This site’s Explain next step teaches pointing pairs as the fourth and hardest of the techniques it covers, and its Hard difficulty is defined as puzzles that genuinely require either a naked pair or a pointing pair to finish. Why difficulty is measured that way rather than by counting clues.

Every diagram on this page is a real position from a generated puzzle, and every elimination shown is checked against that puzzle’s unique solution as part of the test suite. Want a move explained on your own board? Play a puzzle.