Hidden Singles
The method Hidden Single is similar to a Naked Singles in the sense that a given cell will have only one
possible value. The elimination is done differently. A collection of cells with the same number will force
(pin down) the number in a given cell.
Hidden Singles - Example 1
The following example illustrates a Hidden Single in B2 with respect to row B. Consider row B and the cells with value 9 in blue. There cannot be a 9 in cells B1, B4, B6 and B8, because the blue cells contain a 9 and are aligned in columns 1, 4, 6 and 9. Hence, the only possible place for a 9 in row B is in B2. Note that if we just focus on the possible values of a given cell (as in Naked Singles), then B2 can be either 6 or 9 and both will be possible. The Hidden Single elimination considers the positions of all (or some) cells with value 9 and not just the possibilities for a given cell.
Hidden Singles - Example 2
In the previous example we looked at a Hidden Single in a row. In fact we can do this for columns and squares in the same way. Here is an example where we consider the top-left square. The number 9 cannot be placed in A2, B2 or C2 because of the blue G2 cell with value 9. Hence the only possibility for C1 is 9.
Hidden Singles - Example 3
If you have the candidates option turned on, a Hidden Single can easily be found as a cell where a given candidate appears only once in its row, column or square. In this example, candidate 8 in cell C5 appears only once in column 5. Therefore, it is a Hidden Single and C5 has value 8.
