A full house is a row, column, or 3x3 box with exactly one empty cell. Eight of the nine digits are already there, so the missing digit goes in the gap. Some books call it the last remaining cell or the last digit. It is the simplest placement in sudoku, and on an easy puzzle the final third of the solve is often a string of full houses.
How to spot a full house
You are looking for groups that are almost done. A few habits make them jump out:
- Watch the group you just touched. Every placement adds a digit to one row, one column, and one box. If any of the three now has eight digits, you have a full house. Checking those three groups after each move catches nearly all of them.
- Look for gaps, not digits. Your eye finds a lone white square in a filled row faster than it counts eight numbers. Scan for rows, columns, and boxes with a single hole.
- Name the missing digit by elimination. Run 1 through 9 in your head and stop at the one you do not see. With practice you stop running the list and just see which digit is absent.
Full house vs naked single vs hidden single
A full house is a special case of both singles. The empty cell has one candidate (a naked single), and the missing digit has one possible spot in the group (a hidden single). Solving guides list it separately because you can find it without any candidate checking at all. You only need to look at one group.
- Full house: one group, one empty cell. Look at the group only.
- Naked single: one cell, one candidate. Look at the cell's row, column, and box together.
- Hidden single: one digit, one possible cell in a group. Look at where that digit already sits across the grid.
Why full houses matter for speed
Full houses cost almost no thinking, so the time you spend on them is mostly eye movement and input. That makes them a good measure of scanning speed. The endgame of most easy and medium puzzles is a run of full houses, so a two-second delay on each one adds up to a slow finish. Our guide to solving sudoku faster covers the rest of the scanning routine.
Drill full houses in the Dojo
Sudoku Royale's Dojo has a short lesson and a drill for this pattern: board after board where it is the next move. Your record is your fastest run of correct answers in a row, and you can see how it compares with other players. Open Full House on your iPhone, or read how the Dojo works.
Get Sudoku Royale: Free on iOSFrequently Asked Questions
What is a full house in sudoku?
A full house is a row, column, or box with exactly one empty cell. The digit that is missing from the group goes in that cell.
Is a full house the same as a naked single?
A full house is a special case of a naked single and of a hidden single. The difference is how you find it: you only look at one group, so there is no candidate checking involved.
What is the last remaining cell technique?
Last remaining cell is another name for a full house: the only empty cell in a row, column, or box gets the only missing digit.