"Last Free Cell" Technique

What is the "Last Free Cell" Technique?

This is the most basic and important strategy in Sudoku, based on the game's core rule: every 3x3 block, every row, and every column must contain the numbers 1 through 9 exactly once.

This technique is used when a specific area (a block, row, or column) is almost full, with only one empty space remaining.

How to Use the "Last Free Cell" Technique

The method is simple: when a player scans the board and finds any 3x3 block, row, or column that has only one empty cell (the "last free cell"), they can instantly solve it.

Example 1: Checking a Block

Let's look at the first example.

Sudoku puzzle showing last free cell in 3x3 block with 8 numbers filled Completed 3x3 block using last free cell technique - missing number is 1

Target Area: The top-left 3x3 block.
Highlighted Cell: C3,R3 (Column 3, Row 3).
Analysis: We check this block and find the other 8 cells are already filled with the numbers 2, 3, 4, 5, 6, 7, 8, and 9.
Conclusion: The only number from 1 to 9 that is missing is 1. Therefore, this "last free cell" at C3,R3 must be 1.

Example 2: Checking a Row

This same technique applies to rows and columns.

Sudoku puzzle showing last free cell in row with 8 numbers already filled Completed row using last free cell technique - final number is 1

Target Area: The first row (Row 1).
Highlighted Cell: R1,C9 (Row 1, Column 9).
Analysis: We check this row and find (from left to right) it is already filled with the numbers 9, 8, 7, 6, 5, 4, 3, and 2 (in columns C1 through C8).
Conclusion: The only number from 1 to 9 that is missing is also 1. Therefore, this "last free cell" at R1,C9 must be 1.

Master the Basics, Move On to Strategy

This is the main basic rule. After you have learned it and feel comfortable finding these easy solutions, you can move on to the next Sudoku strategies.