Full House

Level 1 · White Belt

Strategy:

Learn after:

Hidden Single Naked Single

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

Look for Full House.

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

1

Full House

Check column 7 - it has 8 of 9 cells filled in.

Sudoku grid illustrating step 1: Full House — Check column 7 - it has 8 of 9 cells filled in.

2

Full House

Digit 1 cannot go in r2c7 because r6c7 is in this column and r1c9 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 2: Full House — Digit 1 cannot go in r2c7 because r6c7 is in this column and r1c9 is in this box. Remove the entry or choose a different digit.

3

Full House

Digit 2 cannot go in r2c7 because r9c7 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 3: Full House — Digit 2 cannot go in r2c7 because r9c7 is already in this column. Remove the entry or choose a different digit.

4

Full House

Digit 3 cannot go in r2c7 because r3c7 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 4: Full House — Digit 3 cannot go in r2c7 because r3c7 is already in this column. Remove the entry or choose a different digit.

5

Full House

Digit 4 cannot go in r2c7 because r2c3 is in this row, r7c7 is in this column, and r1c8 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 5: Full House — Digit 4 cannot go in r2c7 because r2c3 is in this row, r7c7 is in this column, and r1c8 is in this box. Remove the entry or choose a different digit.

6

Full House

Digit 5 cannot go in r2c7 because r2c1 is in this row, r5c7 is in this column, and r3c8 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 6: Full House — Digit 5 cannot go in r2c7 because r2c1 is in this row, r5c7 is in this column, and r3c8 is in this box. Remove the entry or choose a different digit.

7

Full House

Digit 6 cannot go in r2c7 because r2c9 is in this row and r8c7 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 7: Full House — Digit 6 cannot go in r2c7 because r2c9 is in this row and r8c7 is in this column. Remove the entry or choose a different digit.

8

Full House

Digit 7 cannot go in r2c7 because r2c8 is in this row and r4c7 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 8: Full House — Digit 7 cannot go in r2c7 because r2c8 is in this row and r4c7 is in this column. Remove the entry or choose a different digit.

9

Full House

Digit 8 cannot go in r2c7 because r1c7 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 9: Full House — Digit 8 cannot go in r2c7 because r1c7 is already in this column. Remove the entry or choose a different digit.

10

Full House

The only missing digit is 9.

Sudoku grid illustrating step 10: Full House — The only missing digit is 9.

11

Full House

This is a Full House - a row/column/box with one empty cell, so the digit is forced.

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

12

Full House

Place 9 in the remaining empty cell at r2c7.

Sudoku grid illustrating step 12: Full House — Place 9 in the remaining empty cell at r2c7.

13

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.