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Crosshatching is a focused Sudoku scanning method built around one digit and one box.
Existing copies of the target digit block cells along their rows and columns. If those crossing restrictions leave only one legal position inside the box, the digit is forced there.
The important distinction is:
- crosshatching is the search method;
- the forced placement it finds is normally a Hidden Single.
How crosshatching works
Suppose the center box still needs digit 6.
- Find solved 6s in rows that pass through the center box.
- Those rows cannot contain another 6, so corresponding cells inside the box are blocked.
- Find solved 6s in columns that pass through the box.
- Those columns block additional cells.
- Ignore cells already solved with other digits.
- If exactly one legal cell for 6 remains, place 6 there.
Crosshatching does not introduce a new Sudoku rule. It is a visual way to combine the existing row, column, and box constraints for one candidate digit.
The proof can be stated simply:
Every other cell in this box is impossible for 6, so this cell must contain 6.
Step-by-step example
Why crosshatching usually finds a Hidden Single
A Hidden Single exists when one digit has exactly one possible position in a row, column, or box.
Crosshatching is one way to expose that fact visually.
The target cell itself may still contain several legal candidates if you are using full notes. For example:
{2, 6, 9}
The cell is still solved as 6 if 6 has no other legal position in the box.
That is the key difference from a Naked Single. Crosshatching does not need the target cell to have only one candidate total; it needs the target digit to have only one position in the target house.
Why boxes are the natural crosshatching target
Classic crosshatching is usually taught box-first because a 3×3 box is intersected cleanly by three rows and three columns.
Solved copies of one digit outside the box can therefore remove whole horizontal or vertical strips of possible positions inside it.
A box also gives a compact visual target: only nine cells need to be considered at once, and several may already be solved.
The same logical principle can be described from rows or columns, but the box-centered presentation is the clearest and most common teaching model.
Crosshatching across horizontal bands
A band is a group of three horizontally aligned boxes.
Suppose two boxes in the same band already contain digit 4 in two different rows. Those rows are unavailable for 4 in the third box.
This can force 4 into the remaining row of that box.
If a column constraint then removes all but one cell on that row, the exact placement is solved.
Band scanning is efficient because the three boxes let you compare the same digit across neighbouring row restrictions quickly.
Crosshatching across vertical stacks
A stack is a group of three vertically aligned boxes.
The logic is the vertical mirror image of a band.
Solved copies of a digit in two columns can restrict the third box to a remaining column. Row constraints may then reduce that column segment to one exact cell.
Rows and columns exchange roles, but the proof is unchanged.
A two-stage way to think about crosshatching
Crosshatching is easier to reason about when you separate line restriction from exact placement.
Stage 1: Which row or column can contain the digit?
Use solved copies in neighbouring boxes to remove possible rows or columns inside the target box.
Sometimes this already leaves one line.
Stage 2: Which cell on that line is legal?
Use the crossing house and any solved cells to remove remaining positions.
If one cell survives, place the digit.
This two-stage view becomes especially useful when the first stage succeeds but the second does not — because that partial restriction can still matter.
Crosshatching does not always give an immediate placement
Suppose digit 5 is restricted to two cells inside a box, and both cells lie on the same row.
You cannot choose between those cells yet.
However, you have proved that 5 must appear somewhere on that row inside the box. Therefore 5 cannot appear elsewhere on the same row outside the box.
That is the logic behind Pointing / Locked Candidates.
So crosshatching is not only a beginner placement tool. It also teaches the box-line relationship that later becomes an elimination technique.
Crosshatching vs ordinary scanning
Scanning is the broad search habit: inspect useful houses, digits, cells, or changed areas systematically.
Crosshatching is one specific digit-first scanning routine:
one digit → one box → crossing row/column blockers.
You can scan without crosshatching, but crosshatching is one of the most useful structured scans for beginners because it turns a large grid into a small, repeatable task.
Crosshatching with and without pencil marks
Crosshatching does not require full candidate notation.
Without full candidates
Trace the target digit from existing solved copies and mentally exclude blocked cells. This is the classic visual use of the method.
With full candidates
Filter or inspect one candidate digit inside a box. If it occurs once, you have a Hidden Single. If it occurs two or three times on one line, you may have a Locked Candidates restriction.
The candidate display changes recognition, not the underlying logic.
A fast crosshatching routine
Pick one digit
Start with a digit that is already well represented in the grid. More solved copies usually create more blockers.
Move box by box
Identify boxes that do not yet contain the target digit.
Use visible blockers
Trace rows and columns from solved copies of the target digit.
Count the surviving positions
- one position → place the digit;
- two or more → do not guess;
- multiple positions on one line → remember the possible Locked Candidates restriction.
Re-scan after a placement
The newly placed digit becomes another blocker and can immediately create a new crosshatching opportunity in the same band or stack.
Change digit when the pass stops producing information
A systematic digit pass is more reliable than bouncing randomly around the board.
Common crosshatching mistakes
Blocking from the wrong digit
Crosshatching is performed for one target digit at a time. Other solved digits matter for general cell legality, but the horizontal and vertical lines you are tracing are created by existing copies of the target digit.
Treating two remaining cells as a guess
If two cells remain possible, the digit is not solved. Keep the restriction; do not choose between them.
Looking only inside the target box
The blocking information comes from solved copies in rows and columns that extend outside the box.
Assuming the final cell must have one candidate total
Crosshatching usually reveals Hidden Single logic. The target cell may still show several other candidates.
Forgetting solved cells inside the box
A cell already occupied by another digit is not a candidate position for the target digit, even if no same-digit blocker crosses it.
Drawing literal lines and losing the logic
The mental “crosshatch” is only a visual aid. The proof is still that the target digit cannot legally occupy the blocked positions.
FAQ
Is crosshatching the same as a Hidden Single?
No. A Hidden Single is the deduction: one digit has one possible position in a house. Crosshatching is a visual search method that often reveals that deduction.
Can crosshatching be used on rows and columns, not only boxes?
The same restriction logic can be described from any house, but the term is most commonly taught through rows and columns crossing a 3×3 box. This Guide uses that box-centered meaning consistently.
What if crosshatching leaves two cells?
Do not choose between them. If the remaining cells are aligned on one row or column inside the box, the restriction may support a Locked Candidates elimination outside the box.
Do I need candidates visible?
No. Crosshatching is especially useful before full candidate notation because it works directly from solved copies of the target digit.
Which digit should I crosshatch first?
Digits already placed several times are usually good targets because they create more row and column restrictions across the remaining boxes.
What to learn next
Continue to Hidden Singles to understand the deduction crosshatching usually reveals. Then learn Locked Candidates and Pointing Candidates to use the same box-line relationship when the target digit is restricted but not yet placeable.