Full House

Level 1 · White Belt

Strategy:

Overview

Full House is the most fundamental Sudoku solving technique. It applies when a house (row, column, or block) has exactly eight cells filled, leaving only one empty cell. The missing digit is the only possibility for that cell.

How It Works

Look for any row, column, or 3x3 block that has exactly 8 cells already filled.
Count which digits from 1-9 are already present in that house.
The one missing digit is the solution for the empty cell.

Example

Starting position

Look for Full House.

Sudoku grid showing the initial puzzle state for Look for Full House.

1

Box 5 has one empty cell

Check box 5 - it has 8 of 9 cells filled in.

Sudoku grid illustrating step 1: Box 5 has one empty cell — Check box 5 - it has 8 of 9 cells filled in.

2

1 is blocked from r5c5 by the row

Digit 1 cannot go in r5c5 because r5c4 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 2: 1 is blocked from r5c5 by the row — Digit 1 cannot go in r5c5 because r5c4 is already in this row. Remove the entry or choose a different digit.

3

3 is blocked from r5c5 by the column

Digit 3 cannot go in r5c5 because r6c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 3: 3 is blocked from r5c5 by the column — Digit 3 cannot go in r5c5 because r6c5 is already in this column. Remove the entry or choose a different digit.

4

4 is blocked from r5c5 by the column

Digit 4 cannot go in r5c5 because r4c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 4: 4 is blocked from r5c5 by the column — Digit 4 cannot go in r5c5 because r4c5 is already in this column. Remove the entry or choose a different digit.

5

5 is blocked from r5c5 by the box

Digit 5 cannot go in r5c5 because r6c6 is already in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 5: 5 is blocked from r5c5 by the box — Digit 5 cannot go in r5c5 because r6c6 is already in this box. Remove the entry or choose a different digit.

6

6 is blocked from r5c5 by row, column and box

Digit 6 cannot go in r5c5 because r5c7 is in this row, r3c5 is in this column, and r4c6 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 6: 6 is blocked from r5c5 by row, column and box — Digit 6 cannot go in r5c5 because r5c7 is in this row, r3c5 is in this column, and r4c6 is in this box. Remove the entry or choose a different digit.

7

7 is blocked from r5c5 by the box

Digit 7 cannot go in r5c5 because r4c4 is already in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 7: 7 is blocked from r5c5 by the box — Digit 7 cannot go in r5c5 because r4c4 is already in this box. Remove the entry or choose a different digit.

8

8 is blocked from r5c5 by the row

Digit 8 cannot go in r5c5 because r5c6 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 8: 8 is blocked from r5c5 by the row — Digit 8 cannot go in r5c5 because r5c6 is already in this row. Remove the entry or choose a different digit.

9

9 is blocked from r5c5 by row, column and box

Digit 9 cannot go in r5c5 because r5c3 is in this row, r7c5 is in this column, and r6c4 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 9: 9 is blocked from r5c5 by row, column and box — Digit 9 cannot go in r5c5 because r5c3 is in this row, r7c5 is in this column, and r6c4 is in this box. Remove the entry or choose a different digit.

10

2 is the missing digit

The only missing digit is 2.

Sudoku grid illustrating step 10: 2 is the missing digit — The only missing digit is 2.

11

Full House in the box

This is a Full House: one cell is empty in a row, column, or box, so the missing digit is forced.

Sudoku grid illustrating step 11: Full House in the box — This is a Full House: one cell is empty in a row, column, or box, so the missing digit is forced.

12

Place 2 at r5c5

Place 2 in the remaining empty cell at r5c5.

Sudoku grid illustrating step 12: Place 2 at r5c5 — Place 2 in the remaining empty cell at r5c5.

13

Result

Result after applying the technique.

Sudoku grid showing the result after applying the technique

Tips & Patterns

Always scan the puzzle for Full House opportunities first - they're the easiest wins.
Full Houses often appear after you've placed several digits using other techniques.
Check all three house types: rows, columns, and blocks.