A Complete Sudoku Walkthrough From First Pencil Mark to Solved

Step 1: Initial Scan for Naked Singles

We begin with a puzzle that has some numbers pre-filled. The first and easiest step is to scan each row, column, and 3x3 block (called a 'box') for any cell that has only one possible number left. This is known as a Naked Single. A quick scan of our puzzle reveals one in the top-left box: a cell that can only be a '9' because all other digits 1-8 are already present in its row, column, and box. We place that '9' in the grid. This immediate placement is the foundation of the solving cascade.

• Always do a quick visual scan for Naked Singles after every few placements, as they can appear at any time.

Step 2: Filling in Pencil Marks

With no more obvious singles, we need to see all possibilities. We systematically add 'pencil marks' (small candidate numbers) to every empty cell. For each empty cell, we check its row, column, and 3x3 box and write down every digit from 1-9 that is not already present in those three units. This process, often called 'noting candidates,' gives us the complete picture of logical options. A well-maintained candidate grid is essential for spotting the next level of patterns.

Step 3: Finding Hidden Singles

With all candidates noted, we look for Hidden Singles. A Hidden Single is a candidate number that appears only once in a specific row, column, or box, even though the cell itself may have other candidates. In our puzzle, in the central box, the digit '3' appears as a candidate in only one cell. Because a '3' must go somewhere in that box, this cell must be '3'. We place it and remove '3' as a candidate from the corresponding row and column. This is a classic example of how careful candidate notation reveals forced placements.

Step 4: Spotting a Naked Pair and Cleaning Up

Now we see a more advanced pattern. In the bottom row, two empty cells share the exact same two candidate numbers: '2' and '7'. This is a Naked Pair. The logic is powerful: these two digits must occupy these two cells in some order. Therefore, '2' and '7' can be eliminated as candidates from all other cells in that row. Performing this cleanup immediately creates a new Hidden Single ('5') in another cell of the same row. This chain reaction is typical of efficient solving.

Step 5: Using a Pointing Pair

Next, we examine box interactions. In the top-middle 3x3 box, all possible locations for the digit '8' are confined to a single column. This formation is called a Pointing Pair (or Line-Box interaction). Because the '8' for this box must be in that column, we can safely eliminate '8' as a candidate from all other cells in that column outside the box. This elimination, in turn, often creates new singles or simpler patterns in the affected column.

• Pointing Pairs and their counterpart, Claiming Pairs, are the most common 'intermediate' techniques for breaking open a puzzle.

Step 6: The Singles Cascade to Finish

After the Pointing Pair elimination, the puzzle's logic collapses into a series of singles. The removal of that one candidate '8' creates a new Naked Single elsewhere. Placing that number then creates another Hidden Single in a different unit. This domino effect, known as a 'singles cascade,' continues until the grid is completely filled. No further complex patterns are needed. The puzzle is solved purely through the repeated application of the simplest rule: if only one number can go in a cell, it goes there. For a broader view of this process, see our guide on How to Solve Sudoku Step by Step.