Volodymyr Sakhan  ·  March 20, 2026  ·  Updated March 29, 2026

The Last Remaining Cell technique helps you figure out where a specific digit must go inside a 3×3 box. Instead of looking at empty cells and asking what digit belongs there, you pick a digit and ask: in this box, which cell can it go to?

The logic is simple: each digit must appear exactly once in every row, column, and 3×3 box. If a digit already exists in a row that passes through a box, no cell in that row within the box can hold it. By scanning all intersecting rows and columns this way, you can eliminate every cell except one — and that is where the digit goes. Use our online sudoku puzzle to practice this technique right away.

Row and column elimination

Let's find where the digit 8 belongs in the top-left box. Start by scanning every row and column that passes through the box to see if 8 already appears there.

• Notice that 8 is missing from the top-left box (columns A–C, rows 1–3).
• Scan row 3: there is already an 8 at E3. This means A3, B3, and C3 cannot hold 8 — they are in the same row.
• Scan column C: there is already an 8 at C6. This means C1, C2, and C3 cannot hold 8 — they are in the same column.
• After those eliminations, only four cells remain in the box: A1, A2, B1, and B2. But A1, A2, and B1 are already filled with other digits.
• Only B2 survives. Place 8 there.

By crossing off every cell that shares a row or column with an existing 8, the top-left box is left with exactly one valid position.

When two rows are already blocked

Now let's find where 5 goes in the middle-right box (columns G–I, rows 4–6). This time, two of the three rows through the box are already blocked.

• Notice that 5 is missing from the middle-right box.
• Scan row 4: there is a 5 at B4. This eliminates G4, H4, and I4.
• Scan row 6: there is a 5 at D6. This eliminates G6, H6, and I6.
• Two of the three rows are completely blocked. Only row 5 remains viable inside the box: cells G5, H5, and I5.
• G5 is already filled with 3 and H5 is already filled with 6.
• Only I5 is empty. Place 5 there.

When two rows (or columns) through a box are already blocked by the same digit, you only need to look at the third row — and if just one cell there is empty, the answer is immediate.

Combining row and column elimination

Let's find where 7 belongs in the center box (columns D–F, rows 4–6). Here we need to use both a row constraint and a column constraint together.

• Notice that 7 is missing from the center box.
• Scan row 4: there is a 7 at A4. This eliminates D4, E4, and F4 — the entire top row of the box.
• Scan column F: there is a 7 at F7. This eliminates F4, F5, and F6 — the entire right column of the box.
• After these two eliminations, four cells remain: D5, D6, E5, and E6.
• D5, D6, and E5 are already filled with 9, 3, and 2 respectively.
• Only E6 is empty. Place 7 there.

Applying row and column eliminations together in one scan is the natural rhythm of this technique — sweep the intersecting lines, then check what is left.

When the technique reaches its limit

The Last Remaining Cell technique works only when cross-unit eliminations reduce a unit to a single valid cell for a digit. If, after scanning all intersecting rows and columns, two or more empty cells remain, this technique alone cannot decide between them — you will need to apply a more advanced strategy such as Hidden Singles or Naked Pairs.

As you grow more comfortable with scanning, you will find yourself applying this technique across rows and columns as well — not just boxes. Doing so is the same logical process and naturally leads into the Hidden Singles technique, which is the next step in your sudoku-solving journey.