Lesson 2 of 7 · Core technique
Scanning: find where a digit must go
The guide and all sudoku lessons
The last empty square needs a nearly full line. Scanning works much earlier, on boards that are still mostly empty, by asking a different question: not what goes in this square, but where can this digit go?
Pick a digit and a box. Every copy of that digit already on the board rules out its whole row and its whole column. Rule those out across the box, and if exactly one empty square survives, the digit goes there. The same works along a row or a column, where a copy anywhere in a box rules out that box's part of the line.
Scanning finds what notes would call a hidden single, without writing any notes. Some guides call it cross-hatching, after the lines you would draw on paper.
Example 1: In a box
Step 1 of 5
Pick a digit and a box: where can the 8 go in the bottom-right box? It has seven empty squares.
Where does the 8 go in the bottom-right box? It has seven empty squares. The 8 in row 7 rules out the box's top row, and the 8 in row 9 rules out its bottom row. That leaves the middle row, where the 8 in column 8 rules out one of the two empty squares. One survives, at row 8, column 7.
Example 2: In a row
Step 1 of 5
Where can the 8 go in row 7? It has five empty squares.
Rows and columns scan the same way. Row 7 has five empty squares, and the question is where its 8 goes. The 8 in the bottom-left box rules out the two squares of row 7 inside that box. The 8 in the bottom-middle box rules out the square in column 6. The 8 in column 8 rules out the square in column 8.
Only the square in column 7 is left. It could also hold a 3 or a 6, which is why looking at that square alone would not have found the answer: the digit had nowhere else to go.
Try it yourself
A new board, and the same idea. Get it wrong and the board tells you why.
Where must the 8 go in the highlighted box? Tap the square.
Tap a square on the board.
How to spot it faster
- Work one digit at a time across the whole board before moving to the next. Your eye learns where that digit already is, and each box takes seconds.
- Start with the digit that appears most often: the more copies on the board, the more squares they rule out.
- Boxes are usually the quickest place to look, but rows and columns work the same way.
- When a placement lands, scan again for the same digit. The new copy rules out a row, a column and a box of its own.
Common mistakes
Forgetting the box when scanning a line
Along a row or a column, a copy of the digit anywhere in the same box rules out every square of the line inside that box. Checking only the crossing columns misses it.
Placing with two survivors
A digit is placed only when every other empty square in the box or line is ruled out. Two survivors means you need more information, not a guess.
Scanning for two digits at once
Look for one digit at a time. Hunting for several at once is how a square ruled out for the 6 gets read as ruled out for the 9.
Questions
Try it
Pick one digit and scan every box for it, then move to the next. On an easy board, many of your early placements come this way.
Play solo on an easy 9×9