Full House Sudoku Technique

Updated 11 August 2026

A full house is a row, column or box in which exactly one cell is still empty, and the digit that belongs in it is simply the one value that unit has not used yet.

When a full house applies

Sudoku has one rule: every row, every column and every 3×3 box holds each digit from 1 to 9 exactly once. That rule makes a unit with a single empty cell answer itself. Eight of the nine digits are already on the board, so the ninth has nowhere else to go and the cell can be filled without looking at anything outside the unit.

Full houses turn up in three situations. They are common at the end of a puzzle when the grid is nearly complete, they appear the moment you place a digit that happened to be a unit’s second-to-last value, and easy puzzles often ship with one or two already on the board. Because a full house costs a single count to verify, Suuudokuuu’s technique engine ranks it as the very first strategy to try, ahead of the naked single.

The technique is worth naming even though it looks trivial. When a solver reports that a puzzle was finished with nothing but full houses and singles, that is a precise statement about difficulty: no candidate bookkeeping was ever required.

Worked example

Row 4 of this position reads 7, 9, 5, 6, blank, 2, 1, 3 and 8. Comparing that list against 1 to 9 leaves exactly one absent digit, 4, so r4c5 takes 4. No other cell in the grid needs to be examined and no pencil marks are involved.

The board above is not a drawing. The grid string is handed to the technique engine that ships inside the Suuudokuuu app, and the highlighted reason cells, the placed digit and the coordinates listed under the board are exactly what the engine returned for this position at build time. If the engine ever stopped reporting a full house here, this page would fail to build.

How to spot a full house

1. Scan for units with one blankRun your eye along each row, then each column, then each box, and stop at the first unit that has a single empty cell.
2. Read the digits already presentList the eight digits written in that unit. Reading them in board order is faster than trying to hold them in memory.
3. Name the missing digitCompare your list against 1 to 9. Exactly one digit is absent, and that digit is the answer for the empty cell.
4. Place it and rescan the crossing unitsWriting the digit often reduces the crossing row, column or box to one blank as well, so immediately re-check all three units that pass through the cell you just filled.

Common mistakes

• Counting empty cells instead of missing digits, which turns a one-second check into a guess.
• Stopping after one placement. Full houses cascade, and the next one is usually adjacent to the cell you just filled.
• Applying the technique on a grid that already contains a mistake. A full house is only as trustworthy as the eight digits you are reading, so a wrong digit earlier in the solve produces a confident wrong answer here.
• Treating a box with one blank as less reliable than a row with one blank. All three unit types work identically.