Full House Sudoku: How to Use the Last Digit Technique in Rows, Columns, and Boxes

Full house Sudoku is one of the first techniques every solver should learn because it gives you a guaranteed placement without guesswork. If a row, column, or 3×3 box has only one empty cell left, the missing number must go there. Many apps and guides also call this the last digit Sudoku technique.

It sounds almost too simple, but it matters. Full houses help you start easy puzzles cleanly, recover after more advanced eliminations, and keep momentum when a board looks messy. If you miss them, you can end up adding notes or chasing harder patterns when a free placement is already sitting in front of you.

Quick Answer: What Is Full House Sudoku?

A full house in Sudoku happens when a single row, column, or box has exactly one empty cell. Because every house must contain the digits 1 through 9 once each, the missing digit is forced.

• If the house is a row, fill the only missing number in that row.
• If the house is a column, fill the only missing number in that column.
• If the house is a box, fill the only missing number in that 3×3 box.

That is why some guides call it the last digit technique: you are simply identifying the last missing digit in a house.

How the Last Digit Technique Works

Sudoku has one basic rule that drives this technique: each row, column, and 3×3 box must contain the digits 1 to 9 exactly once. So if eight digits are already present in a house, there is only one digit left to place.

Example in a Row

Imagine row 4 already contains 1, 2, 3, 4, 5, 7, 8, 9. The only missing digit is 6, so the last empty cell in that row must be 6.

Example in a Column

If column 8 contains every digit except 2, the remaining empty cell in that column must be 2.

Example in a Box

If a 3×3 box has eight filled cells and the only missing digit is 9, the open cell in that box must be 9.

How to Spot Full House Sudoku Faster

The best way to find this move is not to stare at individual cells. Scan houses instead.

1. Look across the grid for rows that are almost complete.
2. Then scan columns with only one gap left.
3. Finally, check each 3×3 box for a single empty cell.

This quick loop works well at the start of easy puzzles and after every successful placement. A new number often creates another full house somewhere else.

A Simple Scanning Routine

• First pass: rows with 7 or 8 filled cells
• Second pass: columns with 7 or 8 filled cells
• Third pass: boxes that look nearly complete

You do not need pencil marks for this. In fact, full house Sudoku is one of the few techniques that is usually faster without them.

Full House vs Hidden Single vs Naked Single

These three ideas are related, but they are not the same.

Full House

A house has one empty cell left. You place the only missing digit in that house.

Hidden Single

A digit can go in only one place inside a row, column, or box, even though several cells are still empty. The correct placement is hidden among other possibilities.

Naked Single

A cell has only one possible candidate left after considering its row, column, and box.

The difference matters because a full house is usually the most obvious of the three. If you are a beginner, this is the first single to train your eye on before moving to Hidden Single Sudoku or note-based techniques.

Why Full Houses Matter More Than People Think

Beginners often ignore full houses because they seem trivial. That is a mistake. Easy placements are the foundation of efficient Sudoku solving.

• They reduce clutter fast.
• They can trigger chains of new easy placements.
• They help you avoid unnecessary notes.
• They stop you from reaching for advanced strategies too early.

Even in tougher puzzles, advanced eliminations often create fresh full houses afterward. Good solvers keep rechecking for them instead of jumping immediately to the next complex pattern.

Common Mistakes With the Last Digit Sudoku Technique

1. Looking at the wrong house

Players sometimes see one gap in a row and fill it too quickly without confirming the missing digit carefully. Count the digits before placing anything.

2. Forgetting that boxes count as houses too

Many beginners scan only rows and columns. That misses easy full houses sitting in nearly complete 3×3 boxes.

3. Moving on too soon

After one placement, the board changes. Another row, column, or box may now have only one missing digit. Always rescan.

4. Confusing a full house with a hidden single

If a house has multiple empty cells, it is not a full house. It may still contain a hidden single, but that requires a different check.

When to Use Full House Sudoku in a Real Puzzle

This technique is most useful in three moments:

1. At the start of easy puzzles, when several houses are almost complete.
2. After basic singles, when one placement opens another.
3. After advanced eliminations, when the grid loosens and simple placements reappear.

If you ever feel stuck, run a quick full-house scan before doing anything else. It is one of the fastest ways to catch an overlooked move.

Beginner Practice Tip

If you want to get faster, train your eyes to ask one question repeatedly: Which row, column, or box is missing only one digit? That habit builds the right foundation for every later technique.

It also pairs well with a clean opening routine. If you have trouble getting started, read How to Start a Sudoku Puzzle and keep a simple Sudoku Cheat Sheet for Beginners nearby while you practice.

FAQ: Full House Sudoku

What is a full house in Sudoku?

A full house in Sudoku means a row, column, or 3×3 box has only one empty cell left. The missing digit for that house must go in the empty cell.

Is full house the same as last digit in Sudoku?

Usually, yes. Many Sudoku guides use full house and last digit for the same basic idea. Some use last digit more loosely, but for beginners they are effectively the same technique.

Is full house easier than hidden single?

Yes. A full house is usually easier to spot because the house has only one gap. A hidden single requires checking where one specific digit can still go inside a house.

Can a full house appear in hard Sudoku?

Yes. Hard puzzles may not start with many full houses, but advanced steps often create them later. That is why experienced solvers keep rescanning for easy placements.

Should I use notes for full house Sudoku?

No, not usually. Full houses are best found by scanning nearly complete rows, columns, and boxes. Notes become more useful when you move into hidden singles, pairs, and harder techniques.

Conclusion

Full house Sudoku is simple, but it is not optional. It teaches you to read the grid correctly, recognize forced placements, and keep solving with logic instead of guesses. If you make a habit of scanning for the last digit Sudoku move after every placement, easy puzzles become smoother and harder puzzles become less cluttered.

Want to build from here? Play a fresh puzzle at Pure Sudoku, then practice spotting full houses before moving on to hidden singles and note-taking.