June 3, 2026 · 8 min read · By Arnaldo Lima

Pointing Pairs and Box/Line Reduction

Pointing pairs and box/line reduction are the two intersection techniques — sometimes filed together as "locked candidates." Both exploit the same fact: every 3×3 box overlaps three rows and three columns, so a digit confined within one of those units tells you something about the other. Learn both together, because they are the same insight read from opposite ends.

Unlike the subset techniques, which work inside a single unit, these look at the three cells where a box and a line cross. That overlap is the whole mechanism. If a digit is stuck inside the overlap, whichever unit did the confining, the other unit loses that candidate everywhere outside it.

Pointing pairs and triples

A pointing pair (or pointing triple) is an interaction between a box and a line. When a digit's only possible cells inside a box all sit in the same row or column, that digit must end up in the box somewhere along that line — so it can be eliminated from the rest of that row or column outside the box. It's one of the most common intermediate eliminations and a staple of hard-puzzle solving.

The technique is sometimes called "locked candidates, type 1." The candidates are locked because, although you don't yet know which cell of the box holds the digit, you know it lies on one particular line. That's enough to clear that line elsewhere.

• the unit in focus
• the pattern
• a placement
• an elimination

Inside the top-middle box, the digit 3 can only go in two cells (amber) — and both lie in the same row. We don't know which of the two will be the 3, but we know the box's 3 is somewhere on that row. Since that row can contain only one 3 in total, no cell elsewhere in the row can be a 3. The candidate is removed from the cell to the left, outside the box (red).

If the digit had been confined to two cells sharing a column instead, the same logic would point down the column. Three confined cells in a line make a pointing triple; the effect is identical.

How to spot it

For each box, take a digit it still needs and look at which of the box's empty cells can hold it. If all of those cells fall in a single row, or a single column, you have a pointing pattern. Then follow that line out of the box and erase the digit from every cell it touches.

The cue to watch for is a digit whose candidates within a box are squeezed onto one line. This happens constantly on medium and hard boards, so it pays to check after every few placements.

Box/line reduction (claiming)

Box/line reduction — also called claiming or "locked candidates, type 2" — is the reverse of a pointing pair. When a digit's only possible cells in a row or column all fall inside a single 3×3 box, that digit is claimed by the line and can be eliminated from the rest of that box.

The name captures the logic: the line "claims" the digit. You don't know which cell of the line will hold it, but you know it sits inside one particular box — so the other cells of that box can't.

• the unit in focus
• the pattern
• a placement
• an elimination

Look at the highlighted row. The digit 1 can only go in two of its cells (amber), and both of those cells happen to lie inside the same box. The row must contain a 1, so the 1 is somewhere in those two cells — which means it's definitely inside that box, on that row. Therefore no other cell in the box can be a 1, and the candidate is removed from the cell above (red), elsewhere in the same box.

The elimination lands inside the box, not along the line — that's the difference from a pointing pair, where the elimination runs out along the line.

Spotting the pattern

Work line by line. For a row or column, pick a digit it still needs and find every cell on that line that can hold it. If all of those cells sit within one box, you have a box/line reduction. Then clear that digit from the box's other cells — the ones not on the original line.

It helps to scan with pencil marks in place: you're hunting for a digit that appears as a candidate two or three times on a line, with all those appearances clustered in one box.

Telling the two apart

This is the most common mix-up at the intermediate level, so it's worth a clear rule. Ask: which unit confines the digit?

• If a box confines the digit to one line, it's a pointing pair, and you eliminate along the line, outside the box.
• If a line confines the digit to one box, it's box/line reduction, and you eliminate inside the box, off the line.

A useful way to hold it in your head: the elimination always happens in the unit that did not do the confining, and always outside the overlap. The three cells where the box and the line cross are never touched — they're the cells you've just proven the digit lives in.

Both rely on the same overlap between a box and a line; they just read it from opposite ends. If you find yourself unsure which one you're looking at, name the unit you counted the candidates in. That unit is the one doing the confining, and the elimination goes in the other.

Scanning for both in one pass

Because the two techniques share a mechanism, it's efficient to hunt for them together rather than in separate sweeps. Pick a digit — say the 4 — and work through the board once with only that digit in mind:

1. For each box still missing a 4, check whether its candidate cells share a row or a column. If so, clear the 4 from the rest of that line.
2. For each row and column still missing a 4, check whether its candidate cells all sit in one box. If so, clear the 4 from the rest of that box.
3. Move to the next digit.

One digit at a time is the key. Trying to watch all nine at once is what makes these techniques feel hard; restricting your attention to a single digit turns them into a mechanical check that takes seconds per box.

The same overlap, read both ways

It helps to see the two techniques on one piece of board. Take the top-left box and the top row of the grid. They share exactly three cells — call them the overlap — and each unit has six cells of its own outside it.

Now suppose you are chasing the digit 7. Two different observations are possible, and they lead in opposite directions:

• You count the 7s inside the box and find that every cell able to hold one lies in the overlap. The box's 7 is therefore on the top row. The box is satisfied either way, so nothing changes inside it — but the row now has its 7 accounted for, and you clear the candidate from the row's six other cells. That's a pointing pair.
• You count the 7s along the row and find that every cell able to hold one lies in the overlap. The row's 7 is therefore inside the top-left box. The row is satisfied either way — but the box now has its 7 accounted for, and you clear the candidate from the box's six other cells. That's box/line reduction.

Same three cells, same digit, two completely different eliminations. What decides which one you get is simply which unit you counted in and found the digit confined. Nothing about the overlap itself tells you; the answer is in the six cells you looked at outside it.

The mistake to avoid

The error almost everyone makes at least once is eliminating in the wrong direction — spotting a pointing pair and then clearing candidates inside the box rather than along the line. It produces a contradiction several moves later, by which point the cause is hard to trace.

The guard against it is to say the deduction out loud before you erase anything: "the box's 7 is on this row, so the row's other cells lose it." If the sentence doesn't end with the unit you're about to erase from, stop and re-read the pattern. Both halves of the sentence matter, and getting them the right way round is the entire technique.

Why intersections matter

Intersection eliminations rarely solve a cell directly. What they do is thin out a line or a box just enough to reveal a hidden single, or to set up a naked pair that clears more candidates in turn. On hard boards, a couple of well-spotted pointing pairs are often the difference between flow and frustration.

They also mark the ceiling of intermediate play. Combined with the subset techniques, pointing and claiming resolve a large share of hard puzzles before you ever need advanced patterns like the X-Wing — which, when you get there, is recognisably the same idea stretched across two rows and two columns at once. For the full picture of how all eight techniques fit together, head back to the Sudoku strategies guide.