Cross-Hatching is a visual scanning technique used to find where a specific digit can be placed within a 3x3 box. It works by drawing imaginary lines through the box along the rows and columns that already contain the target digit elsewhere in the grid. These lines eliminate cells from consideration, and often only one cell remains — revealing where the digit must go.
To perform Cross-Hatching, choose a digit and a 3x3 box that does not yet contain it. Then look at each row that passes through the box: if that row already contains the digit somewhere outside the box, the entire row within the box is eliminated. Do the same for each column passing through the box. The cells that survive both the row and column eliminations are the only candidates for placing the digit. If exactly one cell survives, you have found the answer.
Cross-Hatching is essentially a visual and systematic way of performing Hidden Singles within boxes. Many experienced solvers use it as their primary scanning technique because it is fast and reliable. By practicing Cross-Hatching with each digit across all nine boxes, you can quickly identify placements without needing to write down candidates. This technique is particularly effective at the start of a puzzle when many digits are already given and their row-column lines eliminate most cells in neighboring boxes.
Try It Yourself
Walk through each step of the cross-hatching technique on a real puzzle. Follow the instructions and try entering the correct value when prompted.
Let us find where digit 7 goes in the top-left 3x3 box (rows 0-2, columns 0-2). First, identify which rows already contain the digit 7 outside this box.
Step-by-Step Guide
Pick a digit from 1 to 9 that you want to place.
Find a 3x3 box that does not yet contain that digit.
Check each of the three rows passing through the box — if a row contains the digit elsewhere, eliminate all cells in that row within the box.
Check each of the three columns passing through the box — if a column contains the digit elsewhere, eliminate all cells in that column within the box.
Also eliminate any cells in the box that are already filled with other digits.
Count the remaining candidate cells in the box.
If only one cell remains, place the digit there.
Picture shining a laser across every row and column that already has your target digit. The beams block off cells in the box you are examining, and the one cell the lasers cannot reach is where the digit belongs.
Every cell in a Sudoku grid sits at the intersection of three constraints: its row, its column, and its box. If a digit already appears in a row, no other cell in that row can hold it; the same applies to columns. By projecting these row and column exclusions into a box that still needs the digit, you are simultaneously applying multiple constraints to reduce the candidate set. When only one cell in the box survives all exclusions, the box's own uniqueness constraint guarantees that digit must go there.
When to use: When you want to place a specific digit inside a 3x3 box, look at the rows and columns passing through that box. If other instances of the digit in those rows and columns leave only one cell unblocked, you have found it.
Common Mistakes to Avoid
Only checking rows but forgetting to also check columns, so you think two cells are valid when one is actually blocked.
Always cross-hatch in both directions — first eliminate cells by rows, then by columns. Both checks are required.
Skipping already-filled cells when scanning the box, accidentally thinking a filled cell is an open candidate.
Before looking for the target digit, first mark which cells in the box are already occupied. Only empty cells can be candidates.
Assuming the technique failed when two cells remain, instead of trying a different digit or box.
If more than one cell survives, move on to a different digit or box. Cross-Hatching only gives a definite answer when exactly one cell remains.
More Examples
See cross-hatching applied in different puzzle configurations to strengthen your pattern recognition.
Highlighted cells show the cross-hatching pattern
Practice Puzzles
Apply the cross-hatching technique on these mini challenges. Tap a highlighted cell and enter the correct digit.
Quick Reference
- Pattern:
- A digit is missing from a box, and row/column elimination leaves one cell
- Action:
- Place the digit in the only remaining valid cell in the box
- Look for:
- Boxes missing a digit where rows and columns eliminate most options