The intuition
Pointing Pair reasons box-to-line: a box restricts a digit to one line. Box/Line Reduction reasons line-to-box: a line restricts a digit to one box. Both are 'locked candidates' — the digit's legal positions have collapsed to the intersection of a row (or column) and a box, and whichever unit is doing the restricting, the digit is guaranteed to come from that intersection. Everything outside the intersection, but still inside the restricted unit, can be eliminated.
When you'll use it
Box/Line Reduction shows up alongside Pointing Pair in Hard puzzles, and the two together usually break most stalls before X-Wing becomes necessary. Learn them as a pair — once one clicks, the other is a five-minute add-on.
How to spot a Box/Line Reduction
- Pick a row (or column) and a digit.
- Mark every empty cell in that row where the digit is still a candidate.
- If those candidates all sit inside a single 3×3 box, the digit is locked to that box on that row.
- Eliminate the digit from the rest of that box — the cells not on the original row.
Why the Box/Line Reduction logic works
Every row must contain each digit exactly once. If digit 5's only remaining candidates on row 4 both happen to sit inside box 4, then row 4's copy of digit 5 is going to come from box 4 — there's nowhere else on the row for it. But box 4 also needs exactly one 5, and it's already guaranteed to get one from row 4. So any other cell in box 4 — on row 5 or row 6 — can safely drop 5 as a candidate; the box's quota is already spoken for.
A worked Box/Line Reduction example
Row 4's only candidates for digit 5 are R4C1 and R4C2, both inside box 4 (a given 5 elsewhere in column 3 has already ruled out R4C3). Since box 4 will get its 5 from row 4, eliminate 5 from every other cell of box 4: R5C1, R5C2, R5C3, R6C1, R6C2 and R6C3.
Walkthrough
Row 4 is filled solid from C4 through C9 with other digits, so the only cells left open on row 4 are C1, C2 and C3 — all three inside box 4.
A 5 already placed at R2C3 rules out C3 for digit 5 on row 4 (same column). That leaves R4C1 and R4C2 as the only candidates for row 4's 5, and both happen to sit inside box 4.
Because row 4 must contain a 5 somewhere, and its only remaining options are inside box 4, box 4's 5 is guaranteed to land on row 4. That's the 'locked' part — the digit is locked to the row-and-box intersection.
Box 4 still has empty cells on rows 5 and 6 (R5C1–C3, R6C1–C3). None of them can be 5 any more, because box 4's single 5 is already accounted for by row 4. Erase 5 from all six of those cells.
How to drill this technique
Open a Hard puzzle and pencil-mark fully. Pick any row that has three or fewer empty cells left. For each digit still missing from that row, check whether its candidates are confined to one box. If so, sweep that box for eliminations before moving to the next row.
Common mistakes
- Confusing the direction with Pointing Pair. Box/Line Reduction eliminates inside a box, using a line as the restriction. Pointing Pair eliminates along a line, using a box as the restriction. Getting the direction backwards erases the wrong cells.
- Applying the technique when the digit's candidates on the line span more than one box — the restriction only works when all of them fall inside a single box.
- Forgetting that Box/Line Reduction works for columns exactly the same way it works for rows.
FAQ
Is Box/Line Reduction the same as 'Claiming'?
Yes — Claiming and Locked Candidates Type 2 are the same technique. A line 'claims' a digit for one box, and every other cell in that box loses the digit as a candidate.
How is Box/Line Reduction different from Pointing Pair?
They're opposite directions of the same locked-candidates idea. Pointing Pair starts from a box and eliminates along a line. Box/Line Reduction starts from a line and eliminates inside a box. If you can do one, the other is just running the same logic backwards.
Can Box/Line Reduction involve three cells instead of two?
Yes. If a digit's candidates on a line span three cells and all three fall in the same box, the elimination works exactly the same way — remove the digit from the rest of the box.
What comes after Box/Line Reduction in the learning path?
X-Wing. Locked candidates (Pointing Pair and Box/Line Reduction) work within a box-and-line intersection; X-Wing is the first technique that reasons across the whole grid using two full rows or columns instead of a single box.
What to learn next
Once Box/Line Reduction feels natural, move on to X-Wing — it builds directly on the candidate-tracking habits you've just developed. Or revisit the full Sudoku techniques library to see the full progression from beginner to advanced.