Full House / Last Digit

A Full House is the simplest forced placement in Sudoku.

If a row, column, or 3×3 box has exactly one unsolved cell, only one digit is missing from that house. The empty cell must contain that digit.

The proof does not require candidate notation, a pattern search, or advanced elimination.

You only need to ask:

Which digit from 1–9 is missing from this nearly complete house?

That makes Full House one of the best first techniques to learn and one of the most useful checks to repeat after every successful move.

Quick rule

A Full House requires:

1. one row, column, or box with exactly one empty cell;
2. eight solved digits already present in that house;
3. one digit from 1–9 therefore missing;
4. the empty cell takes that missing digit.

For example, if a row contains:

1 2 3 4 5 6 7 _ 9

the only missing digit is 8.

So the empty cell must be 8.

Why Full House works

Every Sudoku row, column, and 3×3 box must contain the digits 1 through 9 exactly once.

Suppose a box already contains:

1, 2, 3, 4, 5, 6, 7, 9

Only 8 is absent.

There is only one empty cell in the box, so that cell cannot receive any other value. Placing 8 completes the house and satisfies the Sudoku rule.

This is a direct house-completion proof.

Unlike many techniques, you do not need to combine information from three houses to determine the cell's candidate list. The nearly completed house already gives the answer.

Step-by-step Full House example

Full House can appear in a row, column, or box

The technique is identical in all three house types.

Row Full House

One row has eight solved cells and one empty cell.

List the digits already present and place the one missing digit.

Column Full House

One column has eight solved cells and one empty cell.

Again, the missing digit is forced into that cell.

Box Full House

One 3×3 box has eight solved cells and one empty cell.

The final missing digit completes the box.

The orientation changes, but the proof does not.

Full House vs Last Digit

Sudoku terminology is not perfectly universal.

Full House is a common name for completing the final unsolved cell of a house.

Last Digit is also widely used for the same idea. Some sources use the phrase more narrowly for the final placement in an entire puzzle, while others use it as a synonym for Full House in any row, column, or box.

For solving purposes, the important concept is the same:

one house has one empty cell, so one digit is missing.

VeyraPlay uses Full House / Last Digit together so players can recognize both names.

Full House vs Naked Single

These two techniques can lead to the same placement, but they use different proofs.

Full House

Start with a house.

Ask:

Which digit is missing from this row, column, or box?

The house has one empty cell, so the answer is forced.

Naked Single

Start with a cell.

Ask:

Which digits are legal in this cell after checking its row, column, and box?

If only one candidate survives, the cell is a Naked Single.

A cell can therefore be both:

• the last empty cell in a house;
• and a Naked Single after candidate calculation.

The final digit is the same, but the reasoning used to notice and prove it is different.

Full House vs Hidden Single

A Hidden Single does not require the house to be almost complete.

Instead, choose one digit and one house. If that digit has only one legal position left in the house, it must go there — even if several other cells in that house are still unsolved.

So the viewpoints are:

• Full House: one empty cell remains in the house;
• Hidden Single: one position remains for a particular digit;
• Naked Single: one candidate remains in a particular cell.

Learning those three distinctions gives you the complete basic Singles toolkit.

How to spot Full Houses quickly

Full Houses are easiest to find by scanning for nearly complete houses.

1. Look for houses with many solved cells

Rows, columns, and boxes containing seven or eight solved digits deserve immediate attention.

If there is only one empty cell, you have a Full House.

2. Count what is missing, not what is present

Instead of repeatedly reading all eight solved digits, ask which digit from 1–9 is absent.

With practice, the missing value becomes visually obvious.

3. Re-scan after every placement

One move often completes another house to eight solved cells.

That means a single placement can create a chain of Full Houses.

4. Check boxes as well as lines

Beginners often scan rows first and forget that a 3×3 box follows the same 1–9 completion rule.

A box Full House is just as direct as a row or column Full House.

Why Full House should stay near the front of your solving order

Full House is not merely a beginner exercise.

Even in difficult puzzles, an advanced elimination can leave one house with a single empty cell. When that happens, the correct next move is the Full House — not another advanced pattern search.

A strong solving loop therefore looks like:

make progress
→ re-scan for Full Houses and Singles
→ use another elimination only if simple placements are exhausted

This keeps the solve efficient and reduces candidate clutter.

Full House chains

Sometimes one Full House creates another immediately.

For example:

1. a row has one empty cell, so you place 6;
2. that 6 completes a box except for one cell;
3. the box now has a Full House, so you place 2;
4. that placement completes a column except for one cell;
5. the column gives another Full House.

This is not a separate advanced technique.

It is simply the consequence of re-checking the grid after every forced placement.

Do you need pencil marks for Full House?

No.

Full House can be solved directly from completed digits in the house.

Candidate notes may already be visible in a digital puzzle, but they are unnecessary to prove the move.

That is one reason Full House is useful when learning Sudoku on paper: it teaches you to read the solved structure before adding notation.

Common Full House mistakes

Mistake 1: the house has two empty cells

Then the Full House condition is not met.

You may still be able to solve one of those cells by Naked Single or Hidden Single logic, but it is not a Full House.

Mistake 2: forgetting one solved digit while identifying the missing value

Slow down and compare the house against the complete set 1–9.

A misread clue can turn the simplest deduction into a wrong placement.

Mistake 3: checking only the row

A cell belongs to a row, column, and box, but Full House is triggered by any one of those houses becoming complete except for one cell.

Scan all three house types.

Mistake 4: treating Full House as guessing because you did not write candidates

Candidate notation is not required for a logical proof.

If the house contains eight different solved digits, the missing ninth digit is forced by the rules.

Mistake 5: continuing an advanced search after a breakthrough

After every elimination or placement, go back to Full Houses and Singles.

The easiest new move is usually the best move.

A practical Full House routine

When opening a Sudoku or after making progress:

1. scan every box for one empty cell;
2. scan every row for one empty cell;
3. scan every column for one empty cell;
4. place each missing digit you can prove;
5. restart the scan because one placement may have created another Full House;
6. only then move on to Naked/Hidden Singles and candidate techniques.

The exact order of boxes, rows, and columns is personal preference. The important habit is to check all houses systematically.

FAQ

Is Full House the easiest Sudoku technique?

It is usually considered the simplest named placement technique because the house itself contains all the information required: one cell is empty and one digit is missing.

Is Full House the same as Last Digit?

They are often used as synonyms. Some Sudoku sources reserve “Last Digit” for the final digit of the whole puzzle, so terminology can vary.

Can a Full House also be a Naked Single?

Yes. The same cell can satisfy both descriptions. Full House proves the value from a nearly complete house; Naked Single proves it from the cell's candidate set.

Can a Full House appear in a box?

Yes. Rows, columns, and 3×3 boxes all contain digits 1–9 exactly once, so any of them can produce a Full House.

Do hard Sudokus still contain Full Houses?

Yes. Advanced eliminations frequently create simple placements afterward. Difficulty describes the complete solve path, not the complexity of every individual move.

What to learn next

After Full House, learn the two other core Single viewpoints: Naked Single and Hidden Single. Then use Scanning to search for all three efficiently across a live grid.