Basic technique · 01
Learn to sweep the grid with purpose: rows, columns, and boxes all tell you what can and cannot happen next.
The idea
Scanning is the habit of sweeping rows, columns, and boxes to see what the existing numbers already rule out. It is the foundation underneath almost every beginner placement. Scanning is the habit of looking across the three houses that make up a Sudoku cell: its row, column, and 3×3 box. Instead of guessing a number, you first ask what the existing numbers already tell you, what are missing.
The question: What information is already visible here?
Walkthroughs
A quick scan can solve certain cells quickly.
Walkthrough
The first thing to notice via a quick scan is row 9, where only one unsolved cell left (a Full House). looking through all numbers presented in row 9, the missing number 1 is the solution
What to notice: Scan rows, columns, and boxex to find out which one has the most cells filled; a solution is revealed if there is only one empty cell in a house.
Walkthrough
Digit 4 occupies row 7 and column 1, resulting only one empty cell r9c2 in box 7 where number 4 can be placed; so number 4 is the solution for that cell (Naked Single).
What to notice: Look at a specific number, trace the rows and columns where the number already appears to block out rows and columns in a target box, finding the only open space left for the number
How it works
Every placed number restricts the cells that share its row, column, or box. Scanning simply makes those restrictions visible.
Starting with the number that already appears several times, preferably with the one that appears the most; then follow where those placements restrict the empty cells. For any empty cell, remember that its row, column, and 3×3 box all participate in the decision.
Look across the row for the number that are already present and note the gaps.
Look down the column for the same number from a second direction.
Rows and columns where the number already appears block out the rows and columns in a box, resulting the only open space left for that number
A little history
Scanning is best understood as a natural solving habit that follows directly from Sudoku's rules. It is not generally credited to one inventor or a particular publication.
Watch & learn
Coming soon...
Practice
In the example 2 above, after placing 4 in cell r9c1, scan one more time and find the next cell where 4 can be placed, then scan again...
