How to Use the Packing Method to Scan Sudoku Faster

What is the Packing Method?

The packing method is a fixed scanning order you apply to the grid, moving from cell to cell, row to row, and block to block in a consistent pattern. Instead of letting your eyes jump randomly, this disciplined approach ensures you check every unit (row, column, and 3x3 box) for the most basic logical opportunities first. The primary goal is to find all available Naked Single and Hidden Single placements before you even think about pairs or other advanced strategies. This builds a strong foundation for the puzzle and often triggers a cascade of new placements.

Step 1: Prepare Your Pencil Marks

Before you begin your systematic scan, you need a clear view of all possibilities. Fill in 'pencil marks'—the small candidate numbers—in every empty cell. For a beginner's guide on this foundational step, see How to Solve Sudoku for Beginners. This process involves looking at each empty cell's row, column, and 3x3 box and writing down every digit from 1-9 that isn't already present in those three units. A fully marked grid is your map; the packing method is your navigation system for reading it efficiently.

• Don't skip pencil marking. Trying to scan mentally is far slower and more error-prone than working from a fully noted grid.
• Use a consistent notation style, like placing small numbers in the corners of the cell, to keep your grid readable.

Step 2: Define Your Scanning Path

The core of the method is following a set path. The most common and effective order is a row-by-row, block-by-block sweep. Start at the top-left 3x3 box (Box 1). Scan every cell in that box in a set order, typically left-to-right, top-to-bottom. Once finished with Box 1, move to the box immediately to its right (Box 2), and repeat. Complete the top row of boxes (1, 2, 3), then drop down to the middle row of boxes (4, 5, 6), and finally the bottom row (7, 8, 9). This ensures you methodically cover the entire grid.

Step 3: Scan Each Cell for Singles

As you land on each penciled cell during your path, perform two quick checks. First, look for a Naked Single: does this cell have only one candidate number left? If yes, place the final digit. Second, check for a Hidden Single: for each candidate in the cell, is it the only one in its row, column, or box? If a digit is unique in any one of those three units, it's a Hidden Single and must go in that cell. Place it immediately.

Step 4: The Iterative Loop - Rescan After Every Placement

The most critical part of the packing method is the loop. Every time you place a new digit, it changes the puzzle. You must update all pencil marks in the affected row, column, and box by erasing that digit as a candidate. Then, you restart your scanning loop from the beginning of your set path. Do not just continue from where you left off. A new placement might have created a Naked or Hidden Single in a box you already passed. Restarting the scan catches these new opportunities immediately.

• Treat each new digit placement as a 'reset' button for your scan. Go back to Box 1, Cell 1, and begin again.
• This iterative process is what 'packs' digits into the grid efficiently, unraveling the puzzle from the simplest logic outward.

Step 5: When to Move to More Advanced Techniques

You will eventually complete a full scan without finding any new Naked or Hidden Singles. This is the natural stopping point for the basic packing method. The grid is now 'packed' with all digits that can be found using singles logic. This is the perfect moment to look for the next level of patterns, like Naked Pairs or triples. Use the same disciplined, unit-by-unit scanning approach to search for these patterns. After you use a pair to eliminate candidates, return immediately to your packing scan, as new singles will often appear.