Full House/Last Digit
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A Full House/Last Digit is a single technique that determines a placement by inspecting the unfilled cells remaining in a house (row, column, or box), without writing candidates.
How to spot it
- Examine the unfilled cells in each house (row, column, or box) in turn.
- If a house has only one unfilled cell left, it must also have only one missing digit
x.xmust be placed in that cell.
How it works
According to the rules of Sudoku, if a house (row, column, or box) has only one unfilled cell left, then there must also be only one digit missing from that house. Therefore, that digit must be placed in that cell.
Examples
Look at row 5 on the board below: only R5C2 is still unfilled, and 7 is the only digit missing from that row, so 7 must be placed in R5C2.
Full House can also appear in a column or a box. For example, in column 5 of the board below, only R8C5 is still unfilled, and 7 is the only digit missing from that column, so 7 must be placed in R8C5.
Now look at box 6 on the board below: only R6C8 is still unfilled, and 2 is the only digit missing from that box, so 2 must be placed in R6C8.
Full House is a special case of Direct Naked Single. You only need to inspect one house (a row, column, or box) to determine the only possible digit for a cell, whereas a Direct Naked Single usually requires considering all three related houses of the target cell: its row, column, and box.