When a cells candidates
contain the value or values being considered, and there are additional candidates in the cell making these values difficult to see, or "hiding" them, the candidates are referred to as Hidden Candidates
A Hidden Single
is a candidate that only exists in a single cell in a unit
(row, column or box). A Hidden Single is usually harder to notice than a Naked Single
because there are extra candidates in the cell hiding the fact that the Hidden Single candidate can only exist in a single cell in the unit. One way to identify Hidden Singles is by use Cross Hatching
A Hidden Single becomes the solution for a cell.
A Hidden Pair
is two candidates that can only be in the same two cells in a unit (row, column or box). There will be additional candidates in one or both of the two cells being considered.
When there are two candidates that can only be in the same two cells in a unit then these two candidate will eventually fill the two cells.
This doesn't determine which candidate goes into each cell but it does mean any other candidates in the two cells can be removed.
In the Hidden Pair example in Figure 1 the blue cells are a Hidden Pair with the candidates 2 and 4 in row 1.
The values 2 and 4 have to be placed in the blue cells in row 1 because neither of these values can be placed in any other cells in row 1. All other candidates can be removed from these two cells.
Also, it may be noticed that the non highlighted cells in row 1 form a Naked Set on the values 1, 3, 5, 6 and 9. It is often the case that the cells left over in a unit when a Hidden Set is found will contain a Naked Set.
A Hidden Triplet
is three candidates that can only be placed in three cells of a unit. Each candidate may not be able to be placed in all three cells but in total, some combination of the three candidates will be able to be placed in a total of three cells.
Just like the Hidden Pair, this pattern does not determine which of the three candidates goes into each of the three cells but it does mean that any other candidates in the three cells of the Hidden Triplet can be removed.
In the Hidden Triplet example in Figure 2 the three blue cells in row 3 are the only cells that can contain the values 3, 6 and 9.
The values 3, 6 and 9 have to end up in the three blue cells because they cannot be placed in any other cells in row 3. All other candidates in these cells can be removed.
The example puzzle has multiple Hidden Set instance that can be seen by starting it in the Helper. The Naked Sets Strategy will have to be disabled to see the hidden sets in this example.