Cross-Hatching

Cross-Hatching is a simple method by which players can find Hidden Singles in a Sudoku puzzle. It is one of the few methods that does not depend on the presence of pencilmarks.

The primary target of Cross-Hatching are the boxes, but the method will also work with rows and columns.

How it Works

The player selects a digit that has already been placed several times in the grid, but not all (9) instances have been placed. The player then focuses on a single box or line, drawing imaginary lines from the cells outside this box or line which contain this digit. The lines mark the invalid positions for this digit. Cells already containing another digit are also excluded.

An example:

.-------.-------.-------.
| 1-----|-------|-+-----|
| . . . | . . . | | 2 3 |
| . . . | . . . | | . 4 |
:-------+-------+-------:
| . . . | . . . | | . . |
| . . . | . . . | | . . |
| . . . | . . . | 1 . . |
'-------'-------'-------'

We are inspecting digit 1, box 3. The placement in r1c1 eliminates the candidates from row 1. The placement in r6c7 eliminates the candidates from column 7. Of the remaining 4 cells, 3 already contain another digit. We can now place digit 1 in r3c8, because all other candidates in box 3 are eliminated.