"Last Remaining Cell" Technique

What is the "Last Remaining Cell" Strategy?

The "Last remaining cell" is another basic Sudoku strategy. It is based on the fact that a number (like "8") cannot be repeated in each 3x3 block, each row, or each column.

This technique is the reverse of our first strategy ("Last Free Cell"). Instead of finding the last empty cell in a block, you are finding the last possible cell for a specific number (like "8") within that block.

How to Use This Technique

Let's look at this specific example. Our goal is to find which number goes in the highlighted empty cell at R2,C1 (Row 2, Column 1).

The board shows us clues in the intersecting Row 3 and Column 3. We can use these to find our answer.

Sudoku puzzle showing row and column constraints for last remaining cell technique Final step - completing the last remaining cell in Sudoku block using elimination

The Goal: Find the '8' in the Top-Left Block

This technique shines when we are hunting for a specific number. Let's try to find where the number 8 must go in the top-left 3x3 block.

Check Intersecting Rows (Row 3): The highlighted Row 3 contains an 8 (at position R3,C5). Because of this, no '8' can be placed in any cell of Row 3. This rules out the bottom row of our target block (cells R3,C1, R3,C2, R3,C3).
Check Intersecting Columns (Column 3): The highlighted Column 3 contains an 8 (at position R6,C3). This rules out the entire right-most column of our target block (cells R1,C3, R2,C3, R3,C3).
Check Inside the Block: Inside the top-left block, we can see cells are already filled with 6 (at R1,C1), 1 (at R1,C2), and 9 (at R2,C2).

Find the Last Remaining Cell

We have now eliminated every cell in the top-left block except one.

The bottom row is ruled out by the 8 in Row 3.
The right column is ruled out by the 8 in Column 3.
The other cells are already filled with 6, 1, and 9.
This means there is only one cell remaining (our target cell, R2,C1) where the number 8 must go.

Master This Technique

The same solving method also applies to rows and columns. This is how you use the "Last remaining cell" technique when solving Sudoku. Once you have learned it, you can move on to the next Sudoku strategy.