Sudoku Clan › Sudoku techniques › Box/line reduction
Box/line reduction in Sudoku
- Intermediate
- Needed from Expert puzzles
- 2 points in Duel
Also called claiming or locked candidates type 2.
When all the places a digit can go in a row or column fall inside one box, the line claims that digit, and it can be removed from the other cells of the box.
How it works
A row must contain each digit once. Suppose that in one row the digit 4 can only go in cells that all belong to the same box. Wherever the 4 ends up, it will be in that box and on that row. So the other cells of the box, the ones on its other two rows, cannot be 4.
It is the reverse of pointing pairs. Pointing starts from a box and clears a line. Box/line reduction starts from a line and clears a box. Together they are known as locked candidates.
- Choose a row or column and a digit that is not placed in it yet.
- Mark where that digit can go on the line.
- If every one of those cells is in the same box, remove the digit from the rest of that box.
- Look for the single that the removal reveals.
A real example
On the highlighted line the digit fits only in the blue cells, and those sit in one box. The red candidate elsewhere in that box is removed.
How to spot them
Box/line reductions hide better than pointing pairs because people scan boxes more naturally than lines. Look at rows and columns that are mostly filled, with two or three gaps that sit side by side in one box. For each missing digit of that line, ask whether it is confined to that box.
Common mistakes
- Clearing the line instead of the box. The line is where you found the pattern, the box is where you remove candidates.
- Missing a candidate. If the digit can go in even one cell of the line outside the box, there is nothing to remove.
Questions
What is box/line reduction in Sudoku?
When a digit can only go in one box along a row or column, it must be in that part of the box, so it is removed from the rest of the box. It is also called claiming.
What is the difference between pointing and claiming?
Pointing: the candidates in a box sit on one line, so the rest of the line is cleared. Claiming: the candidates on a line sit in one box, so the rest of the box is cleared.