Solving techniques

Box-line reduction

Box-line reduction is the reverse of pointing pairs. You start from a line and clear the box.

The logic

A row needs one of each digit. If a digit has only two possible cells in the row and both are in the same box, then the digit in that row sits in that box. The box needs only one such digit, so the rest of the box cannot hold it.

How to find it

1. Choose a row or column and one digit.
2. List the cells in that line where the digit can go.
3. If they all fall in one box, remove the digit from the other cells of that box.

Pointing pair or box-line reduction?

In a pointing pair you start from a box and clear a line. In box-line reduction you start from a line and clear the box. Many solvers check both in the same pass.

Common mistakes

• Removing the digit from the line itself instead of from the box.
• Forgetting that the cells in the line must all be inside the same box.
• Skipping the check because the digit seems to have many options. Count carefully.