Crosshatching Technique in Sudoku
Quick Summary
Crosshatching is the most fundamental scanning technique in Sudoku. You pick a number and systematically check each 3x3 box to determine where that number must go, by eliminating positions using the rows and columns that already contain that number. It is the technique most solvers use first on every puzzle.
What is Crosshatching?
Crosshatching (also called cross-hatching or slicing and dicing) is a scanning technique where you focus on a single number at a time and determine where it must be placed within each 3x3 box. The name comes from the visual pattern you create: by "drawing" imaginary lines along the rows and columns that already contain your target number, you cross out positions in a box until only one valid cell remains.
Unlike techniques that analyze a single cell's candidates (like Naked Single), crosshatching takes a number-focused approach. Instead of asking "what can go in this cell?", you ask "where can this number go in this box?" This shift in perspective makes it much easier to spot placements, especially at the beginning of a solve when many cells are empty.
Crosshatching is closely related to the Hidden Single technique. When crosshatching narrows a number down to a single cell within a box, you've found a hidden single in that box. The difference is that crosshatching describes the process of scanning, while hidden single describes the result you find.
How Crosshatching Works: Step by Step
Follow these steps to apply crosshatching systematically. We'll walk through the process using a concrete example.
- 1Choose a target number
Pick a number to focus on. Start with the number that appears most frequently in the grid — it will have fewer remaining positions, making crosshatching easier and more likely to yield a result.
- 2Select a 3x3 box that doesn't contain the number
Look at each of the nine 3x3 boxes. Skip any box that already has your target number. Focus on one that's missing it.
- 3Eliminate rows that contain the number
Check the three rows that pass through this box. If a row already contains the target number (anywhere in its 9 cells), eliminate all cells in that row within the box — the number can't appear there again.
- 4Eliminate columns that contain the number
Similarly, check the three columns passing through the box. If a column already has the target number, eliminate all cells in that column within the box.
- 5Eliminate filled cells
Any cell within the box that already has a number is obviously unavailable. Remove those from consideration too.
- 6Check what's left
If only one empty cell remains in the box after all eliminations, place your target number there. If two or three cells remain, move on to the next box and try again later — more placements will eventually narrow it down.
Example: Finding Where 7 Goes
Let's say we're crosshatching for the number 7. Look at the grid below. We want to find where 7 goes in the top-right box (rows 1-3, columns 7-9).
Step-by-step reasoning:
- Row 1 already contains 7 (at column 5) — eliminate the entire first row of the box
- Column 8 already contains 7 (at row 9) — eliminate column 8 within the box
- Row 2, columns 7-8 are eliminated; Row 2, column 9 is empty but row 2 doesn't have a 7 yet... however column 9 has no 7
- Row 3, column 8 already has a 6 — eliminated
- Remaining candidates: Row 2 col 7, Row 2 col 9, Row 3 col 7, Row 3 col 9
- After further checking column constraints, Row 3, column 7 is the only valid position
This is the essence of crosshatching: by mentally projecting lines through the rows and columns that already have your target number, you "cross out" impossible positions until only one remains. The more instances of a number that exist on the board, the more positions you can eliminate, and the easier crosshatching becomes.
Example: Crosshatching for 9
Here's another example. We want to find where 9 goes in the center box (rows 4-6, columns 4-6).
Analysis: Row 4 already has a 9, eliminating the top row of the center box. Row 5 already has a 9, eliminating the middle row. That leaves only the bottom row (row 6) within the center box. Column 4 has 9 in rows above, and column 5 has 9 (row 2). Only row 6, column 6 is left — place the 9 there.
When Crosshatching Doesn't Fully Resolve
Crosshatching won't always narrow a number down to a single cell. Often, you'll be left with two or three possible positions within a box. This is completely normal and doesn't mean the technique failed — it just means you need more information before you can place the number.
When this happens, you have several productive options:
- Move to the next box — Try the same number in a different box where more constraints exist
- Switch to a different number — A different number might crosshatch cleanly in this box
- Note the partial result — Even narrowing from 3 possibilities to 2 is useful. If the remaining cells are in the same row, you've found a Pointing Pair — a more advanced pattern that lets you eliminate candidates elsewhere
- Come back later — After solving other cells, revisit this box. New placements elsewhere will add row/column constraints that may resolve the crosshatch
Tips for Effective Crosshatching
Start with Common Numbers
Count how many times each number appears in the starting grid. Numbers that appear 5, 6, or 7 times have very few remaining positions. Crosshatching these first gives you quick wins and builds momentum.
Be Systematic
Don't jump randomly between numbers and boxes. Pick a number and scan all 9 boxes for it. Then move to the next number. This ensures you never miss a placement and avoids redundant scanning.
Combine with Row/Column Scanning
After crosshatching boxes, try the same number along complete rows and columns. If a number is missing from a row and only one cell in that row is valid, you've found a Hidden Single.
Re-scan After Placements
Every number you place adds a new row and column constraint. After placing a number via crosshatching, immediately check neighboring boxes — your new placement may resolve a previously ambiguous crosshatch.
Crosshatching vs Other Beginner Techniques
Understanding how crosshatching relates to other techniques helps you know when to use each one:
| Technique | Approach | Question Asked | Best For |
|---|---|---|---|
| Crosshatching | Number-focused | "Where can this number go in this box?" | Early game, dense grids |
| Naked Single | Cell-focused | "What number can go in this cell?" | Cells with many filled neighbors |
| Hidden Single | Number-focused | "Where can this number go in this row/column?" | After crosshatching boxes |
| Last Free Cell | Unit-focused | "Which number is missing from this unit?" | Near-complete rows/columns/boxes |
In practice, experienced solvers use all of these simultaneously. Crosshatching and Hidden Singles are number-focused approaches, while Naked Singles and Last Free Cell are cell/unit-focused. Switching between perspectives gives you the best chance of finding placements quickly.
Practice Crosshatching
The best way to master crosshatching is repetition. Try these exercises to build speed and accuracy:
Exercise 1: Single-Number Sweep
Open an easy puzzle and pick one number. Crosshatch that number across all 9 boxes before looking at any other number. Count how many you can place in one sweep. Repeat with each remaining number.
Exercise 2: Speed Crosshatch
Try to complete an easy puzzle using only crosshatching and Last Free Cell. Time yourself and aim to improve. Most easy puzzles can be fully solved with just these two techniques.
Exercise 3: Partial Crosshatch Tracking
On a medium puzzle, when crosshatching narrows a number to 2-3 cells in a box, write those as pencil marks. Notice how often later placements resolve these partial crosshatches into placements.
Frequently Asked Questions
Q: Is crosshatching the same as Hidden Single?
A: Not exactly. Crosshatching is a scanning method — a process you perform. When crosshatching narrows a number to a single cell within a box, the result is a Hidden Single. Think of crosshatching as the technique and Hidden Single as the pattern it discovers.
Q: Can crosshatching solve an entire puzzle?
A: For easy puzzles, crosshatching combined with Last Free Cell can often solve the entire puzzle. Medium and harder puzzles typically require additional techniques like Naked Pairs and X-Wing that handle situations where crosshatching leaves multiple possibilities.
Q: Should I crosshatch rows and columns too, or just boxes?
A: Traditionally, crosshatching refers to scanning boxes. However, the same logic applies to rows and columns: check where a number can go within a row or column by eliminating positions based on box and column/row constraints. This extended form is sometimes called "line scanning."
Q: Which number should I crosshatch first?
A: Start with the number that appears most often in the starting grid. If 8 appears six times, there are only three remaining positions for 8 in the entire puzzle — crosshatching will likely resolve most or all of them immediately.
Q: How do I use crosshatching in Sudoku247?
A: Use the number highlighting feature — tap any number on the grid and all instances of that number will be highlighted. This makes it easy to see which rows, columns, and boxes already contain the number, letting you visually crosshatch without imaginary lines.
Next Steps
Once you're comfortable with crosshatching, advance to these related techniques:
Try Crosshatching Now
Practice crosshatching on a fresh puzzle. Easy puzzles are perfect for honing this technique.