Indirect Hidden Single
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An Indirect Hidden Single is a single technique that determines a placement by first writing candidates on the board, then inspecting their distribution within a house (row, column, or box).
How to spot it
- First, mark all candidates in every unfilled cell. Remove candidates that have been ruled out by placed digits or by deductions from other techniques.
- For each digit
xfrom1to9, examine each house (row, column, or box) wherexhas not yet been placed. - If candidate
xappears in only one unfilled cell in that house,xmust be placed in that cell.
How it works
The rules of Sudoku require each digit from 1 to 9 to appear exactly once in every house. In a house where x has not yet been placed, if only one unfilled cell retains candidate x, x must be placed in that cell; otherwise, the house would be missing digit x, violating the Sudoku rules.
Examples
On the board below, candidates have been marked and some have already been eliminated using other techniques. Look at candidate 4 in row 5: it appears only in R5C1, so 4 must be placed in R5C1.
This cannot be found directly using cross-hatching (Direct Hidden Single), because candidate 4 in R5C9 was eliminated using the {1,4} naked pair in cells R1C9 and R2C9 in column 9. Only after retaining these eliminations can we see that digit 4 has just one possible location in row 5. This is an Indirect Hidden Single.
An Indirect Hidden Single can also appear in a column or a box. For example, in column 3 of the board below, candidate 8 appears only in R3C3, so 8 must be placed in R3C3. This also depends on earlier eliminations, because candidate 8 in R2C3 was eliminated using another technique.
As another example, in box 7 of the board below, candidate 2 appears only in R8C2, so 2 must be placed in R8C2.