Pointing Pair
A Pointing Pair is a digit that within a box can only go in one row or one column. The box then points: the digit can be removed from the rest of the row or column outside the box.
Learn the techniqueBox/Line Reduction
Box/Line Reduction is the Pointing Pair turned inside out: when a digit within a row or column can only go in one box, the digit can be removed from the rest of that box.
See the technique in practice
Work through the examples step by step. Each step explains what you see on the puzzle and why the conclusion holds.
Example:
- We write candidate notes in all the empty cells on the puzzle. Now we look more closely at row 2 and at box 3.
- Look at digit 3 in row 2. It can only go in the highlighted cells, and they all lie inside box 3.
- Somewhere in row 2 digit 3 must go. Therefore it is guaranteed that 3 lands in 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.
How to recognize the pattern
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 line by line and look for digits where all the candidates bunch up in one box segment. The pattern is easy to miss because the eye naturally follows the boxes, so it pays to deliberately switch to reading rows and columns.
Step-by-step procedure
- 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.
Common mistakes
- 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.
When do you need the technique?
At Hard level you must see multiple units in context: digits that form rectangles across multiple rows, chains of linked cells and boxes that lock each other. The techniques still only remove candidates, but these are exactly the eliminations that open up the puzzle.
Try it on your own puzzle
Enter your puzzle in the Sudoku Solver and it will find the next step and explain the technique behind it.
Open Sudoku Solver