Treating a unit with two or more empty cells as a Last Remaining Cell.
Sudoku technique · Foundation
Last Remaining Cell
When a row, column, or box has exactly one empty cell, the digit missing from that unit must go in the remaining cell.
Learning order
Topic relationships
These links express the same learning and proof relationships used throughout the library.
- Maps to proofNaked Single
- Maps to proofHidden Single
Verified example
Work through the example
R1C1: target candidates; Before 1 | R1C2: given 22 | R1C3: given 33 | R1C4: given 44 | R1C5: given 55 | R1C6: given 66 | R1C7: given 77 | R1C8: given 88 | R1C9: given 99 |
R2C1: given 44 | R2C2: given 55 | R2C3: given 66 | R2C4: given 77 | R2C5: given 88 | R2C6: given 99 | R2C7: given 11 | R2C8: given 22 | R2C9: given 33 |
R3C1: given 77 | R3C2: given 88 | R3C3: given 99 | R3C4: given 11 | R3C5: given 22 | R3C6: given 33 | R3C7: given 44 | R3C8: given 55 | R3C9: given 66 |
R4C1: given 22 | R4C2: given 33 | R4C3: given 44 | R4C4: given 55 | R4C5: given 66 | R4C6: given 77 | R4C7: given 88 | R4C8: given 99 | R4C9: given 11 |
R5C1: given 55 | R5C2: given 66 | R5C3: given 77 | R5C4: given 88 | R5C5: given 99 | R5C6: given 11 | R5C7: given 22 | R5C8: given 33 | R5C9: given 44 |
R6C1: given 88 | R6C2: given 99 | R6C3: given 11 | R6C4: given 22 | R6C5: given 33 | R6C6: given 44 | R6C7: given 55 | R6C8: given 66 | R6C9: given 77 |
R7C1: given 33 | R7C2: given 44 | R7C3: given 55 | R7C4: given 66 | R7C5: given 77 | R7C6: given 88 | R7C7: given 99 | R7C8: given 11 | R7C9: given 22 |
R8C1: given 66 | R8C2: given 77 | R8C3: given 88 | R8C4: given 99 | R8C5: given 11 | R8C6: given 22 | R8C7: given 33 | R8C8: given 44 | R8C9: given 55 |
R9C1: given 99 | R9C2: given 11 | R9C3: given 22 | R9C4: given 33 | R9C5: given 44 | R9C6: given 55 | R9C7: given 66 | R9C8: given 77 | R9C9: given 88 |
R1C1 has derived candidates 1. Place 1.
- Target cell
- R1C1
- Derived candidates
- 1
- Verified result
- Place 1
- Unit in this example
- Row 1
- Scan for a row, column, or box with one empty cell.
- Compare the filled digits with 1 through 9 and identify the missing digit.
- Check that the digit is absent from the target cell’s row, column, and box.
- Place the digit, then rescan the affected units and update any notes.
Fixed practice
Count the empty cells in each row, column, and box first; begin with the unit that has exactly one gap.
Fixed practice · R9C9
R1C1: given 11 | R1C2: given 22 | R1C3: given 33 | R1C4: given 44 | R1C5: given 55 | R1C6: given 66 | R1C7: given 77 | R1C8: given 88 | R1C9: given 99 |
R2C1: given 44 | R2C2: given 55 | R2C3: given 66 | R2C4: given 77 | R2C5: given 88 | R2C6: given 99 | R2C7: given 11 | R2C8: given 22 | R2C9: given 33 |
R3C1: given 77 | R3C2: given 88 | R3C3: given 99 | R3C4: given 11 | R3C5: given 22 | R3C6: given 33 | R3C7: given 44 | R3C8: given 55 | R3C9: given 66 |
R4C1: given 22 | R4C2: given 33 | R4C3: given 44 | R4C4: given 55 | R4C5: given 66 | R4C6: given 77 | R4C7: given 88 | R4C8: given 99 | R4C9: given 11 |
R5C1: given 55 | R5C2: given 66 | R5C3: given 77 | R5C4: given 88 | R5C5: given 99 | R5C6: given 11 | R5C7: given 22 | R5C8: given 33 | R5C9: given 44 |
R6C1: given 88 | R6C2: given 99 | R6C3: given 11 | R6C4: given 22 | R6C5: given 33 | R6C6: given 44 | R6C7: given 55 | R6C8: given 66 | R6C9: given 77 |
R7C1: given 33 | R7C2: given 44 | R7C3: given 55 | R7C4: given 66 | R7C5: given 77 | R7C6: given 88 | R7C7: given 99 | R7C8: given 11 | R7C9: given 22 |
R8C1: given 66 | R8C2: given 77 | R8C3: given 88 | R8C4: given 99 | R8C5: given 11 | R8C6: given 22 | R8C7: given 33 | R8C8: given 44 | R8C9: given 55 |
R9C1: given 99 | R9C2: given 11 | R9C3: given 22 | R9C4: given 33 | R9C5: given 44 | R9C6: given 55 | R9C7: given 66 | R9C8: given 77 | R9C9: target candidates; Before 8 |
R9C9 has derived candidates 8. Place 8.
- Target cell
- R9C9
- Derived candidates
- 8
- Verified result
- Place 8
- Unit in this example
- Row 9
Common mistakes
Common mistakes
Checking only the nearly complete unit and missing a conflict in the target cell’s other units.
Verification details
What is verified here
The verifier confirms that the unit has exactly one empty cell and that its missing digit is legal in the target row, column, and box.
- Example reference
- p2-naked-single-01 / p2-naked-single-03
- Engine version
- legen-sudoku-engine/1.3.0
- Example verification
- Verified placement step
- Last checked
- 2026-07-18
The coordinates, candidates, and results on these pages come from reproducible board states and are checked with the published engine.