The Last Remaining Cell in a Row or Column: An Easy Win
When every cell in a row, column, or box is filled except one, that last remaining cell must contain the missing digit. This is the simplest form of a [Hidden Single](/techniques/hidden-singles), a foundational Sudoku rule that resolves a cell by process of elimination. Spotting this pattern is often the first logical step a player takes after placing obvious [Naked Singles](/techniques/naked-singles). It’s a direct application of Sudoku's core rule: each digit 1-9 must appear exactly once in every row, column, and 3x3 box. Mastering this basic scan is crucial, as it clears the board and sets the stage for more complex patterns like [Naked Pairs](/techniques/naked-pairs).
How the Last Remaining Cell Rule Works
The logic is simple: if eight of the nine possible digits are already placed in a row, column, or box, the one digit that isn't there yet is the only candidate for the single empty cell. You don't need to look at the cell's other candidate possibilities; you just identify the missing number from the set. This is different from a Naked Single, where you look at a single cell and see only one digit can go there. For the last remaining cell, you look at the entire row, column, or box and see only one digit is missing.
Step 1: Scanning for the Last Cell in a Row
Start by looking across any row. Count the digits 1 through 9. If you find eight digits are already placed, locate the single empty cell in that row. The digit not yet present is the solution for that cell.
**Example (Row 5):** Imagine Row 5 has digits 1, 2, 3, 4, 5, 6, 7, and 8 filled in various columns, with only column 2 (cell R5C2) empty. The digit 9 is missing from the set {1,2,3,4,5,6,7,8}. Therefore, R5C2 must be 9.
- Systematically scan rows from top to bottom. Mentally check off digits 1-9 as you see them.
Step 2: Scanning for the Last Cell in a Column
Apply the same logic vertically. Look down any column. If eight cells are filled, find the empty one. The digit absent from the column is the answer.
**Example (Column 7):** Suppose Column 7 has digits 1, 3, 4, 5, 6, 7, 8, and 9 placed in various rows, with only row 1 (cell R1C7) empty. The missing digit from the set is 2. So, R1C7 must be 2.
- Scan columns from left to right. It helps to use your finger or pencil to trace down the column.
Step 3: Scanning for the Last Cell in a 3x3 Box
Finally, examine each 3x3 box. If a box has eight cells filled, the empty cell's value is the one digit not yet inside that box.
**Example (Center Box):** In the central 3x3 box (rows 4-6, columns 4-6), imagine digits 1, 2, 3, 4, 5, 6, 8, and 9 are present. If the cell at row 5, column 5 (R5C5) is empty, the missing digit is 7. Thus, R5C5 = 7.
- Work box by box. It's often easier to spot a nearly complete box than a nearly complete row or column.
Why This Basic Technique Matters for Advanced Play
Solving these last cells is not just an easy win; it's a critical board-clearing operation. Each number you place creates new interactions. A digit placed in a row also eliminates that candidate from the corresponding column and box, potentially creating new Naked Singles or revealing other Hidden Singles.
This foundational elimination is the engine that drives the puzzle forward. Without consistently applying this simple scan, the grid stays cluttered with candidates, making it impossible to see more advanced patterns like Naked Pairs or X-Wings. Our hint engine data shows that failing to spot these last cells is a primary reason beginners get stuck on easy puzzles.
Key Facts
- ▪The last remaining cell in a row, column, or box is solved by identifying the single digit from 1-9 that is not yet present in that unit.
- ▪This pattern is the simplest type of Hidden Single, where a digit's only possible position is found by looking at an entire row, column, or box.
- ▪To find it, scan a unit (row/column/box), note the eight digits already placed, and the missing digit goes in the single empty cell.
- ▪Placing a number using this rule often creates new Naked Singles or Hidden Singles in intersecting rows and columns.
- ▪This technique relies solely on Sudoku's basic rule: each digit must appear exactly once in every row, column, and 3x3 box.
- ▪Consistently scanning for last cells is the most efficient way to start solving any Sudoku puzzle and clear the board.
- ▪Overlooking a last remaining cell is a common mistake that prevents progress and obscures more complex patterns.
- ▪Mastering this basic scan is a prerequisite for learning intermediate techniques like Naked Pairs and Locked Candidates.
Frequently Asked Questions
What's the difference between a Naked Single and this last cell?
A Naked Single looks at one empty cell and finds only one candidate digit possible there. The last cell pattern looks at an entire row, column, or box to find the one missing digit for its single empty cell.
Do I need to check all rows, columns, and boxes every turn?
Yes. After placing new numbers, always re-scan. A newly placed digit can complete a set in a different row, column, or box, creating a new last cell opportunity. Systematic scanning is key.
What if two cells are empty in a row? Can I use this?
No. This technique only works when exactly one cell is empty in the unit. With two empty cells, you don't know which gets the missing digit. You must use other methods like candidate notation.
Is this the same as a Hidden Single?
Yes, it's the most straightforward case. A general Hidden Single finds a digit that can only go in one cell of a unit, even if other cells in the unit are empty. The last cell is a special, simpler case.