Volodymyr Sakhan  ·  March 16, 2026  ·  Updated March 29, 2026

The Last Free Cell technique is the simplest way to fill in a sudoku digit. The idea is straightforward: when a row, column, or 3×3 box has only one empty cell left, that cell's value is completely determined. Since every unit must contain each digit from 1 to 9 exactly once, eight filled cells leave only one digit unaccounted for — and that digit must go in the empty cell. No pencil marks or candidate lists are needed.

This technique is closely related to two others: Last Remaining Cell (which asks "where is the only place a specific digit can go in a unit?") and Last Possible Number (which asks "what is the only digit that fits in this specific cell?"). Last Free Cell is the simplest of the three — it requires only a count, not an elimination.

Last free cell in a row

Take a look at row 5 in the diagram below. Eight of its nine cells are already filled:

• A5 = 1, B5 = 2, C5 = 4, D5 = 5
• F5 = 6, G5 = 7, H5 = 8, I5 = 9
• E5 is the only empty cell — and the only missing digit is 3.

No cross-referencing with other rows or columns is needed. The digits 1, 2, 4, 5, 6, 7, 8, and 9 are present — 3 is absent — so 3 goes in E5.

Last free cell in a box

The same reasoning applies to 3×3 boxes. In the diagram below, the top-right box contains eight digits — 7, 8, 9, 3, 6, 1, 2, and 5 — spread across its nine cells:

• G1 = 7, H1 = 8, I1 = 9
• H2 = 3, I2 = 6
• G3 = 1, H3 = 2, I3 = 5
• G2 is the only empty cell — the only missing digit is 4.

One empty cell, one missing digit: place 4 in G2 with complete confidence.

The cascade effect

One of the most useful properties of Last Free Cell is that placements chain together. Filling one cell reduces the count of empty cells in every intersecting row, column, and box — which can immediately create new Last Free Cell opportunities.

In the example below, 3 has just been placed in E5 (highlighted in blue). Now look at row 3: it has eight filled cells and a single empty cell at C3. The digits present are 4, 9, 3, 6, 8, 1, 2, and 5 — the missing digit is 7.

• A3 = 4, B3 = 9, D3 = 3, E3 = 6
• F3 = 8, G3 = 1, H3 = 2, I3 = 5
• C3 is the only empty cell — place 7 there.

This cascade — one placement triggering the next — can resolve large parts of the puzzle in a single sweep when you scan systematically row by row, then column by column, then box by box.

When to use a different technique

Last Free Cell only works when a unit has exactly one empty cell. If a row, column, or box still has two or more empty cells, this technique cannot be applied to it directly.

In those cases, move on to the next beginner techniques: Last Remaining Cell can find where a specific digit must go even when several cells are empty, and Last Possible Number can determine which digit belongs in a specific cell by eliminating all other candidates. Together, these three techniques form the complete beginner toolkit for solving easy and medium sudoku puzzles without guessing.