Cross-Hatching: Slicing and Dicing
Cross-hatching — also called slicing and dicing — is the scanning method that places a digit inside a 3×3 box by reading the rows and columns that pass through it. It's how experienced solvers fill in numbers quickly without writing a single pencil mark, and it's the most efficient way to find hidden singles in a box.
The idea is simple. A box needs each digit exactly once. If the rows and columns crossing that box already contain a particular digit, they block most of the box's cells. Often they block all but one — and that surviving cell is where the digit must go.
Slicing and dicing in action
- the unit in focus
- the pattern
- a placement
- an elimination
We want to place a 1 in the bottom-left box. Look at the rows passing through it: the top two rows of the box already contain a 1 elsewhere on the board (the amber lines), so a 1 can't go in either of those rows inside the box. That leaves only the bottom row. Now look at the columns: the left and right columns of the box already have a 1, leaving only the middle column. The one cell that sits on both the open row and the open column is forced — the 1 goes there.
"Slicing" refers to the horizontal scan across rows; "dicing" is the vertical scan down columns. Doing both narrows a box from nine cells to one without any notes.
How to do it efficiently
Pick a digit that already appears several times on the board — a digit with five or six placements gives you the most blocking lines to work with. Then check each box that's still missing it. For every such box, mentally extend the rows and columns that already contain the digit; if they cut the box down to a single open cell, place it.
Cycle through the digits this way, 1 to 9, and you'll place a surprising number of cells. When a digit stops yielding placements, move to the next. This systematic sweep is the engine of fast solving on easy and medium boards.
Cross-hatching vs. hidden singles
These are two views of the same logic. Hidden singles describe the result — a digit with only one legal cell in a unit. Cross-hatching is the technique you use to find that result inside a box, by scanning the crossing lines. If you prefer working from pencil marks, you'll spot the hidden single in the notes; if you prefer scanning a clean board, you'll cross-hatch your way to the same cell.
When it runs out
Cross-hatching solves easy boards almost entirely and gets you deep into medium ones. When no box can be sliced down to a single cell, it's time to start pencil-marking and move to candidate-elimination techniques like naked pairs and pointing pairs. Those don't place digits directly — they remove candidates until cross-hatching works again.
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