Three Rows at a Time: An Intermediate Sudoku Scanning Technique
Scanning three Sudoku rows and their corresponding three boxes simultaneously reveals placements that one-row scanning misses. This is because a digit already placed in two of the three boxes within a band often forces its possible position in the third, creating locked candidates and leading to [Hidden Singles](/techniques/hidden-singles). This systematic, multi-row approach is more efficient than checking rows and boxes in isolation and is a core intermediate scanning skill.
Why Scan Three Rows at Once?
Standard scanning checks one row, column, or box at a time. While effective for finding obvious Naked Singles, it can miss more subtle interactions. The 'three rows at a time' method, also called scanning a 'band', examines the puzzle in larger, logically connected chunks. Each band consists of three horizontal rows and the three 3x3 boxes they pass through. By looking at all three together, you can see how a digit's placements in two boxes directly restrict where it can go in the third box of that band. This often confines the digit to a single row within that third box, creating what is known as a Pointing Pair.
Our hint engine finds that players who master this technique solve intermediate puzzles faster because they spot these forcing patterns earlier. It transforms a scattered search into a targeted one. This method works identically for vertical stacks of three columns, which are scanned in the same way. For a broader look at combining scanning directions, see our guide on Scanning Multiple Directions.
Step-by-Step: How to Scan a Three-Row Band
1. **Pick a Band**: Select any block of three adjacent horizontal rows. This forms one complete horizontal third of the puzzle, containing three full 3x3 boxes.
2. **Choose a Digit**: Pick a digit from 1 to 9 that is not yet fully placed in those three rows. Focus on digits that appear two or three times already within the band.
3. **Map Its Placements**: Note which of the three boxes in the band already contain this digit. For the technique to work, the digit should be placed in exactly two of the three boxes.
4. **Analyze the Third Box**: Look at the one box in the band that does NOT yet contain your chosen digit. Because the digit is already in the other two boxes of the same three rows, it cannot appear again in those rows. This often means all possible positions for the digit in the empty box are confined to just one of the three rows that pass through it.
5. **Identify the Pattern and Consequence**: This confinement creates a 'pointing' candidate line. If all candidates for the digit in that box are in one row, you can eliminate that digit as a candidate from the rest of that row outside the box. Conversely, this confinement within the box might immediately reveal a Hidden Single if only one cell in that row is available.
- Start with digits that have the most givens in the band.
- Always verify the 'confinement' by checking the other two boxes in the band to ensure the digit truly cannot go in the other rows of the third box.
Applying the Technique Vertically and Combining Scans
The process is identical for vertical 'stacks' of three columns. Pick a stack, choose a digit, and see if its placement in two of the three boxes forces its position in the third, confining it to a single column.
True power comes from combining horizontal band scans with vertical stack scans. A digit confined to a single row within a box by a horizontal scan creates a strong candidate line. A subsequent vertical scan of the columns intersecting that row can then pinpoint the exact cell. This cross-referencing is how the technique frequently uncovers a Hidden Single—a cell that is the only valid place for a digit in its row, column, and box. The three-row scan sets up the conditions; the full row and column scan delivers the final placement.
Key Facts
- ▪Scanning three rows at a time, called a 'band', is a systematic intermediate Sudoku technique that reveals interactions between rows and boxes.
- ▪The method works by observing how a digit placed in two boxes of a three-row band restricts its possible locations in the third box of that band.
- ▪This restriction often confines the digit's candidates to a single row within the third box, creating a locked candidate or Pointing Pair pattern.
- ▪You can use the identical technique on vertical 'stacks' of three columns to achieve the same confining effect.
- ▪The primary goal of three-row scanning is to create candidate limitations that lead to Hidden Singles, not directly to Naked Singles.
- ▪Combining the results of horizontal band scans and vertical stack scans is the most effective way to pinpoint a digit's exact cell.
- ▪This technique is more efficient than single-row scanning because it processes three logical units (rows and their boxes) in one logical step.
- ▪Mastering this scan is a prerequisite for understanding more advanced Sudoku strategies that depend on row and column interactions.
Frequently Asked Questions
What is the main benefit of scanning three rows instead of one?
It reveals how a digit's placement in two boxes forces its position in the third box of the same band. This creates locked candidates that single-row scanning often misses, setting up Hidden Singles.
Does this technique directly place numbers?
Not always directly. It primarily creates eliminations by confining a digit to one row/column within a box (a Pointing Pair). Combining this with a full row/column scan is what usually reveals the final Hidden Single placement.
Should I always start with a three-row scan?
On intermediate puzzles, yes, after filling in obvious Naked Singles. Systematically scanning each horizontal band and vertical stack is an efficient way to progress when simple scans stop working.
What if the digit is in all three boxes of the band?
If the digit is already placed in all three boxes of the band, the scan for that digit is complete in that area. Move to a different digit or a different band where the digit appears in only two boxes.
How is this different from a Hidden Single?
This scanning technique is the *process* of finding the conditions that create a Hidden Single. A Hidden Single is the *result*: the one cell left for a digit after using techniques like this to eliminate all other options in a row, column, and box.