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Medium

Box Line Reduction

Box Line Reduction is Pointing Pairs run in reverse. Instead of a box pointing out to a row or column, a row or column points inward to a single box: if all of a digit's remaining candidates in a row happen to sit inside one box, that digit can be eliminated from the rest of that box.

Why it works

The digit has to go somewhere in the row. If every cell it could go in also happens to sit in the same box, the box's other cells — the ones outside that row — can't be the answer, since the row has already claimed that digit for one of those shared cells.

Worked example

5
3
7
6
1
9
5
9
8
6
8
6
3
4
8
3
1
7
2
6
6
2
8
4
1
9
5
8
7
9
Step 1 of 3

Look at the line

In Row 1, 6 can only go in R1C4, R1C6.

5
3
7
6
1
9
5
9
8
6
8
6
3
4
8
3
1
7
2
6
6
2
8
4
1
9
5
8
7
9
Step 2 of 3

All in one box

Every one of those cells is in Box 2, so the 6 for Row 1 must be inside that box.

5
3
7
6
1
9
5
9
8
6
8
6
3
4
8
3
1
7
2
6
6
2
8
4
1
9
5
8
7
9
Step 3 of 3

Eliminate

The rest of Box 2 has no other 6 candidates, so nothing more is removed here.

Tips

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