This can be for 1, 2 or 3 candidates. Of course, for 1 candidate we have a single candidate and this is detailed in the Single Candidate search. For 2 and 3 candidates we must always have a combination of a row and a box or a column and a box, because only the intersection of these units has 3 cells. (The intersection of a row and a column is always one cell). Pairs (twins),triples and quads are a practical extension of this rule.
Again we have two possibilities:
If you look carefully what we did in the first step was to remove all possible candidates for a value in a unit, until only one cell (a single candidate) was left for that value in the unit. (As shown with the red lines in the previous example). In step two, we do just the same, but we now remove all possible candidates for a value in a unit, until only 2 or 3 cells are left for that value in the unit. When these cells are also in only one other unit, then they are the only candidates for that value in that other unit. These candidates are normally called single unit candidates.
When we look back to the sudoku and try to solve value 5 for the bottom-left box we find 2 possibilities, both in the second column. With the set theory, we can now prove that the value 5 can not be somewhere else in the second column:
Both sets, the box and the column, must have the values 1 to 9 just only once. When we look to the box we find that the value 5 only can be in one of the cells from the intersection. As the value 5 can only be once in the second column, the value 5 can not be in the cells out side the intersection. So these candidates for the value 5 in the second column can be removed. This gives us new information. (Marked with a red 5).
When we now look to the third row, the only candidates left for value 5 lie in the upper-right box. We find again the same pattern, but now we start from a row and can remove candidates in a box. (See again the red marks). This gives us new information over the value 5 in column 8. If we now look carefully, the value 5 can only be in the last row of column 8. Looking back again to the lower-left box, we can now fill in the value 5 in row 8, and we are back at ower starting point. We also met some of the magic of sudoku, indeed, the value 5 was on option for the lower-right box, but we went around the grid and found it.
In fact, finding the 5 in the last row was the clue to solve this puzzle. At this point we have reduced a medium puzzle to a gentle puzzle. The rest of the puzzle can now be solved with the simple single candidate strategy.