SuuudokuuuBox Line Reduction Sudoku Technique
Updated
Box line reduction happens when a digit can only go in cells of one row or column that all belong to the same box, which forces the digit into that box segment and removes it from the rest of the box.
When box line reduction applies
A row and a box overlap in exactly three cells. Box line reduction is the deduction that runs through that overlap in the line-to-box direction. Every row must contain the digit once. If the only cells on the row that can still take it are inside a single box, then the digit is somewhere in that three-cell overlap, and the other six cells of the box cannot hold it.
Compare that with a pointing pair, which runs the other way: there the digit is confined to a line inside a box, and the line outside the box is cleared. Both are called locked candidates, and it is worth practising them as a pair so the direction of the elimination never gets muddled.
Box line reduction is the harder of the two to see by eye, because you have to notice an absence along a whole line rather than a cluster inside a box. Solvers who keep full pencil marks find it easily; solvers who cross-hatch tend to miss it.
Worked example
Column 1 still has three empty cells: r1c1, r2c1 and r5c1. The digit 5 is possible in r1c1 and r2c1 but not in r5c1, whose row already carries a 5. Both surviving cells sit in the top-left box, so that box receives its 5 from column 1.
The top-left box has one further blank away from column 1, namely r3c2, and it still listed 5 among its candidates. That is now impossible and the mark comes off, leaving r3c2 with 7 and 9. As always with an intersection, no digit is placed; the value of the move is the smaller candidate list it leaves behind.
How to spot box line reduction
- Work along a line, not a boxPick a row or column that still needs a particular digit and list the cells on it where the digit is still possible.
- Check whether the survivors share a boxTwo or three survivors that all fall inside the same 3×3 box is the pattern. Survivors spread over two boxes prove nothing.
- Erase the digit from the rest of that boxRemove the candidate from the six box cells that are not on the line. This is the opposite direction from a pointing pair.
- Rescan the box for singlesThe cleared cells often collapse to one candidate, and the box frequently gains a hidden single for an unrelated digit.
Common mistakes
- Running the elimination backwards and clearing the line instead of the box. That is a pointing pair, and here it is wrong.
- Missing the pattern because the line still has several blanks. What matters is where the digit can go, not how empty the line looks.
- Forgetting that the three overlap cells keep the candidate. The deduction never says which of them takes the digit.
- Only checking rows. Columns produce box line reductions just as often, and a stuck puzzle frequently hides one in a column.
Box line reduction FAQ
Is box line reduction the same as a claiming candidate?
Yes. “Claiming”, “locked candidate type 2” and “line-box interaction” all describe this deduction. The line claims the digit and the box gives up its other cells.
How is it different from a pointing pair?
A pointing pair reasons from the box and eliminates along the line. Box line reduction reasons from the line and eliminates inside the box. They use the same three-cell intersection in opposite directions.
Can it involve three cells rather than two?
Yes. If all three cells of the overlap are the only homes for the digit on the line, the same elimination applies. Two or three survivors work identically.
Why do I keep missing this pattern?
Because it is defined by what is absent from the rest of the line, and absences are harder to see than clusters. Keeping complete pencil marks, or scanning digit by digit along each line, makes it much easier to catch.