Number-First vs Cell-First Scanning in Sudoku

How Number-First Scanning Works

Number-First scanning, also called digit scanning, involves picking one number from 1 to 9 and examining all three units (row, column, and 3x3 box) for every cell where that number could logically go. You systematically ask, 'Where can digit 7 go in this row?' and then 'In this column?' and finally 'In this box?' The goal is to find a unit where the digit can only fit into one specific cell, which is a Hidden Single.

This method is highly efficient for spotting constraints across large sections of the grid. It directly reveals placements that are forced by the positions of other digits, often before you even consider what other numbers might go in a cell. For instance, if you scan for the digit 3 and find it already placed in two rows and columns that intersect a particular box, the only remaining cell in that box becomes the obvious home for the 3.

• Start your scan with digits that appear most frequently in the givens, as they impose the most constraints.
• After placing a digit using this method, immediately re-scan that same digit; its new position creates fresh constraints.

How Cell-First Scanning Works

Cell-First scanning takes the opposite approach. You select a single empty cell and determine all candidate digits that could legally occupy it by checking its row, column, and box. You mentally or physically pencil in these possibilities. The goal is to find a cell with only one possible candidate, which is a Naked Single.

This method builds a detailed map of possibilities for individual cells. It is the foundational step for more advanced candidate-based techniques. By filling a cell's candidates, you often notice that one candidate digit is eliminated from all but one cell in a unit, which then reveals a Hidden Single from a different perspective. This process is thorough but can be slower for initial placements in an open grid.

• Focus on cells within the most crowded rows, columns, or boxes first, as they tend to have fewer candidates.
• Use short pencil marks (corner marks) to note candidates if you are not using full notation.

Direct Comparison: Strengths and Weaknesses

Each scanning order has distinct advantages. Number-First scanning is exceptionally fast for finding Hidden Singles, making it ideal for the opening phase of a puzzle and for speed solving. Cell-First scanning is slower to start but is superior for finding Naked Singles and is essential for progressing through mid-game and harder puzzles where candidates must be tracked.

To visualize the trade-offs, consider this comparison:

| Dimension | Number-First Scanning | Cell-First Scanning | | :--- | :--- | :--- | | **Primary Target** | Hidden Singles | Naked Singles | | **Speed on Open Grids** | Very Fast | Slower | | **Foundation for Advanced Logic** | Indirect | Direct (creates candidate lists) | | **Best For** | Easy/Medium puzzles, Speed solving | Hard/Expert puzzles, Learning technique | | **Mental Load** | Low (focus on one digit) | Higher (track multiple digits per cell) |

Number-First scanning can feel like making broad sweeps to pick 'low-hanging fruit.' Cell-First scanning is like careful detective work, building the evidence needed to make a confident placement.

Choosing the Right Method for Your Goal

Your solving goal should dictate your primary scanning method. If you are practicing for speed or tackling easier puzzles, lead with Number-First scanning. It will rapidly clear many placements. Our analysis shows most players can shave significant time off their solves by mastering efficient digit scanning.

If you are learning advanced techniques or solving a difficult puzzle, start with Cell-First scanning. Writing down candidates for a block of cells is a prerequisite for spotting patterns like Naked Pairs or X-Wings. This method builds the foundational knowledge for why a placement is correct, which is crucial for improvement. For advice on starting a puzzle effectively, see our guide on choosing your first move.

Switching Strategies Mid-Solve

Expert solvers do not stick rigidly to one method. They fluidly switch between Number-First and Cell-First scanning based on the puzzle's state. A common hybrid approach is to start with a few rounds of Number-First scanning to place obvious digits. Once that flow slows down, switch to Cell-First scanning for a key region to establish candidates.

For example, you might scan digits 1 through 9 until no more Hidden Singles appear. Then, select a promising row or box that has several empty cells and use Cell-First scanning to pencil in candidates for those cells. Often, this act of notation will immediately reveal a Naked Single or a new Hidden Single that was masked before. This cycle of switching methods is a core component of efficient scanning in multiple directions.

Common Pitfalls and How to Avoid Them

A common mistake with Number-First scanning is to scan each digit only once and then give up. You must re-scan digits after every placement, as each new number changes the constraints. Another error is forgetting to check all three units (row, column, box) for a digit's possible positions, which can cause you to miss a Hidden Single.

With Cell-First scanning, the major pitfall is spending too much time fully notating candidates for every empty cell early on. In easier puzzles, this is unnecessary. Instead, use a focused approach: only note candidates for cells in a single row, column, or box where you suspect progress can be made. This balances thoroughness with speed.