Hidden Pair, Triplet, Quad
This technique is known as “hidden pair” if two candidates are involved,”hidden triplet” if three, or ”hidden quad” if four. While the pattern occurs in easier puzzles, it is not required to use it for solving until the Tough level.
This technique is very similar to naked subsets, but instead of affecting other cells with the same row, column or block, candidates are eliminated from the cells that hold the subset. If there are N cells, with N candidates between them that don't appear elsewhere in the same row, column or block, then any other candidates for those cells can be eliminated.
For example, consider a block that has the following candidates:
{4, 5, 6, 9}, {4, 9}, {5, 6, 9}, {2, 4}, {1, 2, 3, 4, 7}, {1, 2, 3, 7}, {2, 5, 6}, {1, 2, 7}, {8}
(The single 8 indicates that this cell already holds the value 8.) You can see that there are only three cells that have any of the candidates 1, 3 or 7. (These cells have other candidates too, but they're the ones that we can eliminate.) Three candidates with only three possible cells between them, leads to the conclusion that one of the candidates must be in each of the cells, although we can't say which is which. So, obviously, these three cells cannot hold any other value, meaning we can eliminate any other candidates for these cells.
After making the elimination in this example, we're left with:
{4, 5, 6, 9}, {4, 9}, {5, 6, 9}, {2, 4}, {1, 3, 7}, {1, 3, 7}, {2, 5, 6}, {1, 7}, {8}
You may notice that one of the cells doesn't have 3 as a candidate, but this makes no difference at all. The important point is that there are only three cells in which three candidates appear, even if they're not all in each.
You may ask why not make the subset 1, 2 and 7? The answer is because there are five cells containing any of these numbers, and three candidates over five cells doesn't allow any eliminations at all.
In the Sudoku puzzle below, the green cells have the hidden pair 3 and 5.
So why is this technique called hidden subset? Simply because if you exhaustively mark all the possibilities for every cell, these cells are the only ones (in their container) to have a set of certain digits, but they're hidden amongst the other candidates for the cells. Contrast this to naked subsets, where their placement is more obvious.