Sudoku Scanning and Cross-Hatching: The First Technique to Learn

Before pencil marks, before pairs, before any of the techniques with intimidating names, there's scanning. Sudoku scanning is how you place your first numbers and how you'll solve most of an easy or medium grid. It needs no notes and no setup, just your eyes and the rule that each digit appears once per row, column, and box. If you only ever learn one technique, this is the one that does the most work.

Scanning and cross-hatching are really the same idea at two scales, so let's build it up from the simple version.

What scanning is

Scanning means picking a single digit and asking, box by box, "where can this number go?" You let the existing copies of that digit rule out rows and columns until, in some box, only one legal cell remains.

Pick a number that already appears several times on the board. The more copies are placed, the more lines they block, and the more likely scanning resolves a cell. Starting with a digit that appears once or twice is usually a waste, since there isn't enough information yet.

Cross-hatching, step by step

Cross-hatching is scanning aimed at one box. Here's the routine:

1. Choose a digit, say 3.
2. Pick a 3x3 box that doesn't have a 3 yet.
3. Look at the rows passing through that box. Any row already containing a 3 is blocked, so the 3 can't go in those rows inside this box.
4. Do the same for the columns through the box.
5. Cross out every blocked cell. If exactly one empty cell survives, the 3 goes there.

The "cross" in cross-hatching is literally the crossing lines from the surrounding rows and columns slicing into the box. Once you've seen it a few times, you stop drawing imaginary lines and just see the surviving cell.

A worked example

Imagine the top-left box is missing a 3. The top row of the whole grid already has a 3 somewhere to the right. The middle row of that box also has a 3 out in another box. That blocks two of the box's three rows. Now a column on the left already contains a 3, knocking out a cell in the remaining row. If that leaves a single empty cell in the box, the 3 is forced there. No guessing, no notes, just lines ruling out space until one cell is left.

Slicing and dicing

"Slicing and dicing" is just cross-hatching taken across a band of three boxes at once. Three boxes sit side by side in a horizontal band, sharing the same three rows. If two of those boxes already have your digit, the two rows they sit in are blocked across the whole band, so in the third box, the digit is squeezed into the one remaining row. Often that's enough to place it immediately.

Working a full band like this is faster than checking boxes one at a time, because you reuse the same row information across all three boxes. Strong solvers slice and dice almost on autopilot.

When scanning runs out

Scanning has a ceiling. At some point you'll sweep all nine digits and place nothing new, because the remaining cells each have two or more legal spots and no single digit is forced. That's not a dead end. It's a signal to change tools.

The next step is checking for hidden singles (a digit with only one home in a unit, even when scanning didn't flag it), and then writing pencil marks so you can spot pairs and triples. The full strategy guide shows exactly where scanning hands off to the next technique.

Drills to build speed

Scanning gets faster purely through reps, and there's a clean way to practice it. Open an easy puzzle and solve it using only scanning and forced cells, with no pencil marks allowed. Easy grids are designed to fall to scanning alone, so you can finish them this way every time. Do that until the surviving cell jumps out at you without conscious effort, then carry that instinct up to medium.

That automatic, no-thinking-required scan is the foundation every other technique sits on. Build it first, and everything above it gets easier.

Give it a go: open a grid, pick your most common digit, and start cross-hatching.