Basic technique · 02
Find a row, column, or 3×3 box with one empty cell. The missing number has only one place to go.
The idea
A Full House is the absolute easiest situation in a puzzle, it occurs when a house has eight filled cells and one empty cell. Because every house must contain 1–9 exactly once, the missing number is forced.
The question: Which number is missing from this one-empty-cell house?
Walkthroughs
Let’s look at a few examples.
Walkthrough
In this example, row 9 already has numbers 2 to 9 filled into column 2 to column 9, 1 is the only number left; since row 9 only has one empty cell r9c1 left, so 1 is definitely the solution for cell r9c1.
What to notice: Identify a house that has most of its cells filled; if eight numbers already present, then the only remaining number is the solution.
Walkthrough
One placement could create a new Full House nearby. in the following example, number 9 is the only solution for cell r5c7 (see Naked Single); when 9 is placed, row 5 has only one empty cell r5c1 left; since row 5 used all number except 6, so 6 is the solution for that empty cell.
What to notice: Every placement could create a new Full House, which reveals an obvious solution for an empty cell; it is to remember that rescanning after every placement matters.
How it works
Full House is often the first thing worth checking because it requires no candidate notes.
Look across rows, down columns, and inside boxes for exactly one empty cell.
Identify which number from 1–9 is absent from that house.
The empty cell must contain that missing number. Then scan the affected houses again.
A little history
Full House is not generally attributed to a single inventor. It is a direct consequence of Sudoku's fundamental requirement that every row, column, and box contain each number exactly once.
It is also commonly called Last Digit, especially when the final missing number in a house is being placed.
Watch & learn
Coming soon...
Practice
Before reaching for notes or advanced patterns, look for a house with exactly one empty cell.
