Beginner
Last Remaining Cell
A core Sudoku solving technique for beginner players
What is the Last Remaining Cell technique?
The Last Remaining Cell technique flips the perspective of Last Free Cell. Instead of looking at a unit that is nearly full, you look at a specific digit and find that it can only go in one cell within a particular row, column, or box.
All other empty cells in that unit are already blocked by the digit appearing in the same row, column, or box as those cells. Only one cell remains unblocked - So that digit must go there.
Step-by-step guide
- Pick a digit - For example, 7.
- Look at a row. Find all empty cells in that row.
- For each empty cell, check: does a 7 already appear in that cell's column or box?
- Cross off every empty cell where a 7 is already present in the column or box.
- If only one empty cell remains that is not crossed off, place 7 there.
- Repeat for all nine rows, then all nine columns, then all nine boxes.
Last Remaining Cell vs Last Free Cell
| Last Free Cell | Last Remaining Cell | |
|---|---|---|
| Starting point | A nearly-full unit | A specific digit |
| What you look at | How many empty cells are left | How many cells could hold the digit |
| Result | Fill the last empty cell with the missing digit | Fill the only valid cell with the chosen digit |
| Candidate marks needed | No | No (but helpful for complex boards) |
Common mistakes
| Mistake | Fix |
|---|---|
| Checking the row but forgetting to check columns and boxes of each empty cell | Always cross-check all three constraints before placing |
| Only scanning horizontally - Missing column-level eliminations | Apply the technique to columns and boxes as well as rows |
| Stopping after one pass - Digit placements open new opportunities | Restart the scan after every digit you place |
Pro tip: Combine Last Remaining Cell with Last Free Cell in a single pass. After filling a cell by Last Free Cell, immediately check if any digit now has only one remaining candidate in its row, column, or box.