How to Use Scanning in Sudoku

Scanning is the technique most beginners discover on their own — and for good reason. It's fast, visual, and surprisingly powerful. Instead of analyzing one cell at a time, scanning lets you zero in on where a specific digit must go across the entire grid. This article explains exactly how it works and how to use it efficiently.

What Is Scanning?

Scanning means focusing on one digit at a time and asking: "In each 3×3 box that doesn't have this digit yet, which empty cell must it go in?"

You do this by using the existing placements of that digit to eliminate cells. Any empty cell that shares a row or column with an existing instance of the digit cannot hold another one. When elimination leaves only one valid cell in a box, you've found your answer.

A Step-by-Step Example

Let's scan for the digit 7.

Suppose 7 is already placed in the following locations on the grid:

• Row 1, column 3
• Row 4, column 8
• Row 6, column 1
• Row 9, column 5

Now look at the top-right 3×3 box (rows 1–3, columns 7–9). It doesn't have a 7 yet. Which of its empty cells can hold a 7?

• Row 1 already contains a 7 (at column 3) → every cell in row 1 is eliminated.
• No other existing 7 shares a column with columns 7, 8, or 9 in rows 2–3.

After eliminating row 1, the remaining candidates are the empty cells in rows 2 and 3, columns 7–9. If two of those cells are already filled with other digits, and only one remains empty, that cell must be 7.

For a concrete resolution: suppose in this box, row 2 columns 7 and 8 are filled with 3 and 5, and row 3 columns 7 and 9 are filled with 1 and 6. The remaining empty cells are row 2 column 9 and row 3 column 8. Row 4 has a 7 at column 8 — eliminating row 3 column 8. That leaves row 2, column 9 as the only valid cell. The 7 goes there. ✓

Cross-Hatching: The Visual Form of Scanning

Many solvers visualize scanning as drawing imaginary lines across the grid. When you find an existing 7, mentally draw a horizontal line through its entire row and a vertical line through its entire column. Any cell that a line passes through cannot hold a 7.

Do this for every existing 7 on the grid. The cells that no line touches — within a box that still needs a 7 — are your candidates. If only one such cell exists in a box, you've found the answer.

This visual approach, called cross-hatching, is fast enough to do in your head once you've practiced it a few times.

Which Digit Should You Scan First?

Scan the digits that appear most frequently on the current grid. If there are already seven 4s placed, only two boxes are missing a 4. With so many existing 4s casting row and column eliminations, pinning down those last two is usually quick.

A digit that appears only twice on the grid has fewer eliminations to offer and is harder to scan productively. Save those for later, after more of the puzzle is filled in.

Practical order:

1. Count how many times each digit 1–9 appears on the grid.
2. Sort them from most frequent to least frequent.
3. Scan in that order, starting with the digit that appears most often.

When Scanning Produces Two Candidates

Sometimes scanning a digit in a box leaves two empty cells as candidates, not one. That's fine — don't guess. Make a note (mentally or with a pencil mark) that the digit must be in one of those two cells, then move on.

After you've scanned all digits and filled in everything you can, come back to the boxes with two candidates. The rest of the puzzle will have advanced, and new eliminations may now resolve them.

Combining Scanning with Elimination

Scanning and cell-by-cell elimination are complementary, not competing. A good solving rhythm alternates between the two:

1. Elimination pass: Go through empty cells one by one. Check each cell's row, column, and box. Fill in any naked singles.
2. Scanning pass: Go through digits one by one, most frequent first. For each digit, scan incomplete boxes. Fill in any cells where only one position is possible.
3. Repeat. Each pass fills in new digits, which unlock more deductions in the next pass.

On easy puzzles, one or two cycles of this loop solves the entire grid. On medium puzzles, you may need four or five cycles before the grid is complete.

Scanning on Harder Puzzles

Scanning still works on medium, hard, and expert puzzles — it just produces fewer immediate answers. On a hard puzzle, a full scanning pass might only yield two or three placements. That's still progress.

On harder puzzles, scanning is most useful for establishing where a digit cannot go, even when it doesn't immediately tell you where it must go. These negative deductions feed into more advanced techniques like naked pairs and pointing pairs, which build on the candidate information that scanning helps establish.

Common Scanning Mistakes

• Forgetting to check columns, only rows. Cross-hatching requires both row and column lines from every existing instance of the digit. Missing a column elimination can leave you thinking a cell is valid when it isn't.
• Scanning a digit with too few existing placements. A digit that appears only once or twice offers very few eliminations. It's usually faster to scan other digits first and return to this one later.
• Placing a digit based on scanning without checking the box. Scanning tells you which cells in a box are valid based on rows and columns. But the box itself might already contain the digit in a cell you overlooked. Always confirm the box doesn't already have the digit before placing.

Try It Now

Open any sudoku puzzle and pick the digit that appears most often. Count its existing placements, draw imaginary cross-hatch lines, and see how many boxes you can resolve in under a minute. You'll be surprised how much progress one scanning pass can make.

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