Box/Line Reduction: learn the sudoku technique step by step at Sudokuen

See the technique in practice

Work through the examples step by step. Each step explains what you see in the puzzle and why the conclusion is valid.

Example:

We add candidate notes to every empty cell in the puzzle. Now we take a closer look at row 2 and box 3.
Look at digit 3 in row 2. It can only go in the highlighted cells, and they all lie inside box 3.
Digit 3 must go somewhere in row 2. Therefore, 3 is guaranteed to occupy one of the highlighted cells inside the box.
The box thus gets digit 3 from this line. Then no other cells in the box can contain 3, and we remove it from the notes in row 3, column 7.

We add candidate notes to every empty cell in the puzzle. Now we take a closer look at row 2 and box 2.
Look at digit 1 in row 2. It can only go in the highlighted cells, and they all lie inside box 2.
Digit 1 must go somewhere in row 2. Therefore, 1 is guaranteed to occupy one of the highlighted cells inside the box.
The box thus gets digit 1 from this line. Then no other cells in the box can contain 1, and we remove it from the notes in row 1, column 4.

We add candidate notes to every empty cell in the puzzle. Now we take a closer look at row 1 and box 1.
Look at digit 4 in row 1. It can only go in the highlighted cells, and they all lie inside box 1.
Digit 4 must go somewhere in row 1. Therefore, 4 is guaranteed to occupy one of the highlighted cells inside the box.
The box thus gets digit 4 from this line. Then no other cells in the box can contain 4, and we remove it from the notes in row 3, column 2 and row 3, column 3.

We add candidate notes to every empty cell in the puzzle. Now we take a closer look at row 5 and box 6.
Look at digit 3 in row 5. It can only go in the highlighted cells, and they all lie inside box 6.
Digit 3 must go somewhere in row 5. Therefore, 3 is guaranteed to occupy one of the highlighted cells inside the box.
The box thus gets digit 3 from this line. Then no other cells in the box can contain 3, and we remove it from the notes in row 4, column 7 and row 4, column 9.

We add candidate notes to every empty cell in the puzzle. Now we take a closer look at column 1 and box 4.
Look at digit 5 in column 1. It can only go in the highlighted cells, and they all lie inside box 4.
Digit 5 must go somewhere in column 1. Therefore, 5 is guaranteed to occupy one of the highlighted cells inside the box.
The box thus gets digit 5 from this line. Then no other cells in the box can contain 5, and we remove it from the notes in row 4, column 3 and row 5, column 3.

Box/Line Reduction is the Pointing Pair turned inside out. Here you look at a row or column and discover that a digit can only go in cells that belong to the same box. Then the digit must land in that box to fulfill the line, and the digit can be removed from the rest of the box.

Scan each line for digits whose candidates are all grouped within one box segment. The pattern is easy to miss because your eyes naturally follow the boxes, so deliberately switch your focus to rows and columns.

Choose a row or column and a digit that is missing from it.
Mark the cells in the line where the digit can go.
If all possibilities lie within the same box, the digit must go in that box.
Remove the digit from the box's remaining cells, that is, the ones not on the line.

Removing from the line instead of the box. The eliminations apply to the box's cells outside the line, while the candidates on the line remain untouched.
Missing a possibility in another box. One candidate outside the box is enough to invalidate the whole pattern.
Believing that the technique is the same as Pointing Pair. The direction is opposite, and that is what determines where you are allowed to remove from.

At the Hard level, you must consider several units together: digits that form rectangles across multiple rows, chains of linked cells and boxes that lock each other. These techniques still eliminate only candidates, but those eliminations are exactly what opens up the puzzle.

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Box/Line Reduction

See the technique in practice

How to recognize the pattern

Step-by-step procedure

Common mistakes

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