Volodymyr Sakhan  ·  March 23, 2026  ·  Updated March 29, 2026

The Last Possible Number technique lets you solve a cell by elimination. You pick one empty cell, collect every digit already placed in its row, column, and 3×3 box, and see which digit from 1–9 has not appeared in any of those three units. If only one digit is missing, that digit is the answer — and you can place it immediately.

This technique works on easy puzzles and beyond. Unlike Last Free Cell, which requires a unit to have just one empty cell, Last Possible Number can find answers even when the row, column, and box each have several empty cells — as long as their combined placed digits account for eight of the nine possible values.

What is the Last Possible Number technique?

Every empty cell in a sudoku grid belongs to exactly three units: one row, one column, and one 3×3 box. The rules of sudoku require each of those units to contain every digit from 1 to 9 exactly once. That means:

• Any digit already in the cell's row cannot go in that cell.
• Any digit already in the cell's column cannot go in that cell.
• Any digit already in the cell's box cannot go in that cell.

When you combine the digits eliminated by all three units and only one digit from 1–9 is left, that is the Last Possible Number for the cell.

When to use this technique

Look for cells that sit at a "busy intersection" — where the row, column, and box together already contain many filled digits. Good candidates are cells where:

• The row has six or more filled cells.
• The column has several filled cells that cover different digits.
• The 3×3 box contributes at least one or two digits not yet covered by the row or column.

Example: row and column eliminate eight digits

Look at cell E5 (highlighted in green). The row and column together already contain eight of the nine digits — which means only one digit can possibly go here.

Here is the step-by-step reasoning:

1. Pick cell E5 — it sits at a busy intersection of a well-filled row and column.
2. Scan row 5: the digits 9, 3, 1, 8, 4, 7, 2, 6 are already placed (highlighted in blue).
3. Scan column E: digits 1 and 3 are placed — both already covered by row 5, so no new exclusions.
4. Scan box 5 (center box): digits 6, 8, 4 — all already covered by row 5.
5. Combined excluded digits: {1, 2, 3, 4, 6, 7, 8, 9} — eight digits eliminated.
6. Only 5 remains. Place 5 at E5.

Because the combined row, column, and box already hold every digit except 5, the cell has only one possible answer.

Example: the box makes the difference

Sometimes the row and column alone do not provide enough eliminations. Here, cell H2 (green) has only four digits in its row and two in its column — that is six, not enough. But the 3×3 box contributes two more unique digits, bringing the total to eight.

Step by step:

1. Pick cell H2 — its row, column, and box are collectively busy even if individually sparse.
2. Scan row 2: digits 8, 3, 7, 6 are placed (only 4 — not enough alone).
3. Scan column H: digits 2, 9 are placed — adds 2 new exclusions.
4. Scan box 3 (top-right): digits 4, 1 are placed — adds 2 more exclusions.
5. Combined excluded: {1, 2, 3, 4, 6, 7, 8, 9} — eight digits.
6. Only 5 remains. Place 5 at H2.

When no single unit provides enough eliminations, combining all three units often completes the picture.

Cascade: one placement unlocks the next

Every digit you place changes the board — and can immediately create a new Last Possible Number opportunity. In this example, digit 6 was just placed at D8 (shown in blue). That single placement is enough to solve E8.

Step by step:

1. Digit 6 was placed at D8 using another technique (shown in blue).
2. Now examine E8: scan row 8 → digits 7, 2, 6, 9, 3, 8 are placed (including the newly placed 6).
3. Scan column E → digits 4, 5 are placed — two more exclusions.
4. Combined: {2, 3, 4, 5, 6, 7, 8, 9} — eight digits eliminated.
5. Only 1 remains. Place 1 at E8.

Each number you place can immediately open new Last Possible Number opportunities — always re-scan after each placement.

Practice and next steps

The best way to master Last Possible Number is to play sudoku and actively scan cells at busy intersections. Start on easy puzzles where many cells already have most of their row, column, and box filled.

Together with Last Free Cell and Last Remaining Cell, the Last Possible Number technique forms the complete beginner toolkit. If you find a cell where the combined eliminations leave two or more candidates, move on to pencil marks and more advanced strategies — but on easy and medium puzzles, these three techniques will take you far.