When a candidate in a row or column is confined to a single box, it can be eliminated from all other cells in that box. The complement to Pointing Pairs.
Box-Line Reduction works by examining where a candidate number can go within a row or column. If all possible placements for a number in a particular row (or column) fall within the same 3x3 box, then that number is "claimed" by the row for that box. It must appear in the row-box intersection, so it can be eliminated from all other cells in the box that are not in that row.
For example, consider row 5. If the number 6 can only appear in cells R5C4 and R5C5 within that row, and both of these cells are in box 5, then 6 is claimed by row 5 within box 5. You can eliminate 6 from all other cells in box 5 - specifically R4C4, R4C5, R4C6, R6C4, R6C5, and R6C6 (if any contain 6 as a candidate).
This technique is the inverse of Pointing Pairs. While Pointing Pairs look outward from a box to a line, Box-Line Reduction looks inward from a line to a box. Both are equally important for intermediate solving. For terminology details, check our Sudoku glossary.
Box-Line Reduction is most valuable in medium and hard Sudoku puzzles when singles alone are insufficient. It works hand-in-hand with Pointing Pairs - always check both techniques together for maximum effectiveness.
Many experienced solvers make Box-Line Reduction part of their standard scanning routine, checking every box-line intersection after applying singles. This disciplined approach catches eliminations that would otherwise be missed. For a broader view of solving techniques, visit our strategies page, or learn the basics at how to play Sudoku.
Box-Line Reduction is classified as an intermediate-level technique. It sits alongside Pointing Pairs as one of the first intermediate methods to learn, bridging the gap between basic singles and more complex pair/triple strategies.
Not typically needed - singles cover easy puzzles
Commonly needed - a key technique for medium difficulty
Frequently used alongside other intermediate methods
Part of standard scanning routine for expert solvers
Box-Line Reduction occurs when a candidate number in a row or column is confined to cells within a single 3x3 box. Since the number must appear in that row/column within the box, it can be eliminated from all other cells in the same box that are not in that row or column.
They are complementary techniques. Pointing Pairs start with a box and eliminate from a row/column outside the box. Box-Line Reduction starts with a row/column and eliminates from a box. Both exploit the same box-line intersection but in opposite directions.
Yes. Box-Line Reduction is also commonly called "Claiming" or "Line-Box Interaction" in various Sudoku communities. The technique is the same regardless of the terminology used.
Look for Box-Line Reduction whenever you are checking for Pointing Pairs. The two techniques are best applied together as they cover the same type of intersection from both perspectives. Check after applying singles and before moving to pairs-based techniques.
Box-Line Reduction is highly effective for its complexity level. It is easier to learn than Naked Pairs or Hidden Pairs but can produce significant eliminations. Many medium puzzles that stall after singles can be broken open with a single Box-Line Reduction or Pointing Pair.
Track digit 5. Across the board, columns 4–9 already contain a 5. So in row 1, the digit 5 must come from columns 1, 2, or 3.
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