Box-line reduction: sudoku technique

Within a line, a number is confined to one box, so the rest of that box can't use it.

How it works

This is the mirror image of a pointing pair. Pick a row and a number. If every place that number can go in the row falls within one box, then that box's copy of the number must be in this row.

So you can erase the number from the other cells of that box, in the rows that aren't this one. It works the same way for columns.

Worked example

This example comes from a real puzzle in our collection, at the exact moment the technique applies.

Here is the board at that moment, with the candidates still open in each empty cell. Earlier steps may already have ruled some out.
135
35
9
7
4
6
2
15
8
7
568
2
15
18
9
3
4
56
156
568
4
125
3
28
7
156
9
9
2
8
13
16
5
4
7
36
4
356
35
9
2
7
1
8
356
356
1
7
34
68
48
9
56
2
8
9
1
24
5
24
6
3
7
35
7
35
6
9
1
8
2
4
2
4
6
8
7
3
5
9
1
Along this line, the candidate only appears inside one box. The cells that matter are highlighted.
135
35
9
7
4
6
2
15
8
7
568
2
15
18
9
3
4
56
156
568
4
125
3
28
7
156
9
9
2
8
13
16
5
4
7
36
4
356
35
9
2
7
1
8
356
356
1
7
34
68
48
9
56
2
8
9
1
24
5
24
6
3
7
35
7
35
6
9
1
8
2
4
2
4
6
8
7
3
5
9
1
The result: one candidate goes. 1 leaves row 3, column 4.
135
35
9
7
4
6
2
15
8
7
568
2
15
18
9
3
4
56
156
568
4
125
3
28
7
156
9
9
2
8
13
16
5
4
7
36
4
356
35
9
2
7
1
8
356
356
1
7
34
68
48
9
56
2
8
9
1
24
5
24
6
3
7
35
7
35
6
9
1
8
2
4
2
4
6
8
7
3
5
9
1

Where you'll need it

Box-line reductions appear on hard boards. They are easiest to find when you scan one number at a time.

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Practice on a hard sudoku