This example is to demonstrate how to apply the Hidden Single technique in a column.
In column C6 of this puzzle, there are six empty cells, which are (R1,C6), (R2,C6), (R3,C6), (R7,C6), (R8,C6), and (R9,C6). The digit 4 is not in this column yet. We want to decide which of these six empty cells should be filled with the digit 4. The Hidden Single technique is to look for the cells that are possible to accommodate the digit 4 in the column. If there is only one such cell, then that cell must be the digit 4.
As shown in Figure 2, the cell (R1,C3) in row R1 is 4. Since each row can only contain the digit 4 once, the cell (R1,C6) in the same row cannot be 4. This cell is eliminated as a possible position for the digit 4. Now five empty cells (R2,C6), (R3,C6), (R7,C6), (R8,C6), and (R9,C6) remain for the digit 4 in column C6.
As shown in Figure 3, the cell (R3,C8) in row R3 is 4. Since each row can only contain the digit 4 once, the cell (R3,C6) in the same row cannot be 4. It is eliminated as a possible position for the digit 4. Now four empty cells (R2,C6), (R7,C6), (R8,C6), and (R9,C6) remain for the digit 4 in column C6.
As shown in Figure 4, the cell (R7,C5) in block B8 is 4. Since each block can only contain the digit 4 once, three cells (R7,C6), (R8,C6), and (R9,C6) in the same block cannot be 4. These three cells are eliminated as possible positions for the digit 4. Now only one empty cell (R2,C6) remains for the digit 4 in column C6.
The cell (R2,C6) is located in row R2, column C6, and block B2. No digit 4 appears in the same row, the same column, or the same 3x3 block. So the cell (R2,C6) can be a possible position for the digit 4 (Figure 5).
As we can see in Figure 5, the only possible position for the digit 4 in column C6 is the cell (R2,C6). Since each column must contain the digit 4 once, we can conclude that the cell (R2,C6), as the only possible position for the digit 4 in column C6, must be 4. The cell (R2,C6) should be filled with the digit 4, as shown in Figure 6 above.