Techniques › Full House
Full House
A house with one empty cell left. The first thing anyone learns.
A Full House is a row, column or box with exactly one empty cell. Eight of the nine digits are already placed, so the ninth has nowhere else to go.
It needs no reasoning at all beyond noticing, which is why it is worth naming separately from the Hidden Single it technically is: at the end of a solve, most of the remaining placements are Full Houses, and they cascade. Fill one and you often complete a column, which completes a box, which completes another row.
A worked example
Taken from a real puzzle in our bank, at the point where this was the cheapest move available. Pattern candidates are marked in amber; anything the step eliminates is struck through in red.
| 14 | 17 | 8 | 469 | 4569 | 579 | 3 | 2 | 369 |
| 5 | 6 | 2 | 8 | 3 | 9 | 4 | 1 | 7 |
| 47 | 9 | 3 | 247 | 24 | 1 | 8 | 6 | 5 |
| 789 | 5 | 6 | 4679 | 4689 | 2 | 13 | 9 | 3489 |
| 289 | 2378 | 1 | 49 | 489 | 379 | 6 | 5 | 3489 |
| 89 | 38 | 4 | 5 | 1 | 369 | 2 | 7 | 389 |
| 128 | 128 | 5 | 3 | 7 | 4 | 9 | 68 | 26 |
| 3 | 48 | 79 | 26 | 26 | 59 | 57 | 48 | 1 |
| 6 | 24 | 79 | 1 | 59 | 8 | 57 | 34 | 23 |
- NudgeOne house has a single empty cell left in row 2.
- WhereFull House in row 2: r2c6
- Do itr2c6 = 9
How to spot it
Scan for a house with a single gap. Late in a solve they appear constantly, so after every placement glance at the three houses that cell belonged to.
Where you will meet it
Full House sits at tier 0 of our ladder, which means it first becomes necessary at Very Easy. Puzzles below that band never require it, though it may still appear as a shortcut.
Read next
- Hidden Single A digit with only one home left in a house, even though that cell has other candidates.
- Naked Single A cell with only one candidate left.