Cross Hatching

Cross Hatching uses values already placed in the puzzle to identify locations in a box, row or column for a new value.

Generally, cross hatching is done on boxes first but does not have to be.

In the Cross Hatching example in Figure 1 the highlighted cell in box 4 shows the only place the value 2 can be placed in box 4.

The value 2 cannot be placed in rows 4 or 5, or column 2 because there is already a value 2 in these units. The only empty cell in box 4 that is not in rows 4 or 5, or column 2 is the highlighted cell.

Scanning each box one value at a time will usually identify the most cross hatching opportunities.

You are really looking for a single cell in a unit that contains a particular candidate. When there is only one cell in a unit that contains a particular candidate, that candidate can be inserted as the solution for that cell.

Cross Hatching can also be applied to rows or columns. In the example in Figure 2, the value 4 can only be placed in the highlighted cell in column 7. All other empty cells in column 7 cannot be the value 4 because of the value 4 already in rows 1,7 and 8 and/or the value 4 in box 9.

In this case, either the value 4 in row 7 or the value 4 in box 9 can be used to remove the cell in row 7 column 7 as a possible location for the value 4. Similarly, the value 4 in row 8 or the value 4 in box 9 can be used to remove the cell in row 8 column 7 as a possible location for the value 4.