Hidden Single is a basic trick for solving Sudoku. Most Sudoku beginners first use this technique to solve very easy Sudoku puzzles. In fact, this technique is essential for solving Sudoku puzzles at all levels.
Each 9-cell unit (each row, each column, and each 3x3 block) in a Sudoku grid must contain each digit from 1 to 9 once and only once. Therefore, if there is only one cell that is possible for a certain digit to be placed in a 9-cell unit (a row, a column, or a 3x3 block), then that cell must be the correct place for that certain digit. We can fill that cell with that certain digit.
Let's use the following Sudoku grid filled with just a few digits as a demonstration.
The Sudoku grid above is not a real Sudoku puzzle. There are only a few digits in the grid. We just use it to demonstrate how to use this technique to determine the cell position for a digit in a 3x3 block.
The digit 2 is not yet in block B4 of this grid. We try to determine which of those seven empty cells in this block should be filled with the digit 2. In Row R4, there is a digit 2 in cell (R4,C6). So the three blue cells in Block B4, which are in the same row R4 as the cell (R4,C6), cannot be 2. Also, there is another digit 2 in the cell (R6,C8). Therefore, the three pink cells in Block B4, which are in the same row R6 as the cell (R6,C8), cannot be 2. Now the yellow cell is the only possible position in Block 4 for the digit 2, and therefore, we can determine that the yellow cell must be filled with the digit 2 as shown in Figure 2.
2
The demonstration above is to look for a correct cell position for a digit in a 3x3 block with the Hidden Single technique. Actually, this technique can be applied in a row or in a column as well. We will use real Sudoku puzzles to demonstrate this technique in all these three cases.