## Hidden Pair, H2

If the same pair of unique symbols are only candidates in two cells in the same strip, then they must be the solutions for those two cells: both of them must occur in the strip and they can only occur in these two cells, so one is the solution for one cell and the other is the solution for the other cell. We don't know which candidate is the solution to which cell BUT we do know that any other candidates in those cells can be deleted.

Figure 1. A Hidden Pair example. The sum 16 in 5 cells has the unique combination [1,2,3,4,6] and so the row must contain 4 and 6. These only remain as candidates in two cells, so must be the solution to those cells. Hence, all other candidates in those cells can be removed. The pattern of candidates with green backgrounds means that the candidates with red backgrounds can be deleted.

## Hidden Triple, H3

If the same trio of unique symbols are only candidates in three cells in the same strip, then they must be the solutions for those three cells: all three of them must occur in the strip and they can only occur in these three cells, so each is the solution for one of the three cells. We don't know which candidate is the solution to which cell BUT we do know that any other candidates in those cells can be deleted.

## Naked Pair, N2

If the same pair of symbols are the only candidates for two cells in the same strip, then they must be the solutions for those two cells. Between them they are the only possible solutions for the two cells: if either one is set, the solution to the other cell must be the remaining candidate. We don't know which candidate is the solution to which cell BUT we do know that those candidates cannot occur anywhere else in the same row or column.

Figure 2. A Naked Pair example. Two of the cells in this column have the same two candidates [4,6] remaining as possible solutions. This means that the candidates with red background can be deleted.

## Naked Triple, N3

If the same three symbols are the only candidates for three cells in the same strip, then they must be the solutions for those three cells. Between them they are the only possible solutions for the cells: if either one is set, the solution to the other cells must be one of the remaining candidates, and so on. We don't know which candidate is the solution to which cell BUT we do know that those candidates cannot occur anywhere else in the same row or column.

Figure 3. A Naked Triple example. Three of the cells in this column have the same three candidates [7,8,9] remaining as possible solutions. This means that the candidates with red background can be deleted.

## Naked Quad, N4

If the same four symbols are the only candidates for four cells in the same strip, then they must be the solutions for those four cells. Between them they are the only possible solutions for the cells: if either one is set, the solution to the other cells must be one of the remaining candidates, and so on. We don't know which candidate is the solution to which cell BUT we do know that those candidates cannot occur anywhere else in the same row or column.

## X-Wing, XW

An X-Wing is formed when two columns only have two occurences of a unique symbol S, and for both of these columns these Ss occur on the same two rows. Please see Figure 4.

Figure 4. An X-Wing. The pattern of candidates with the green background means that the candidates with the red background can be deleted.

Focus on the columns in which the candidate 1s have a green background. For the left hand column the remaining sum is 7 - 4 = 3, which has the unique combination [1,2]. The right hand column has remaining sum 6 - 2 = 4, which has the unique combination [1,3]. So both of these columns must contain a 1, and the only possible arrangements are:

```7 6
---
1 3
4 2
2 1

or

7 6
---
2 1
4 2
1 3
```

We don't know which of these arrangements is the solution, BUT both arrangements place a 1 in each of the two rows they intersect. This means that these rows cannot contain a 1 anywhere else. Therefore, the candidate 1s with red backgrounds can be deleted.

Note that the four cells making up the Xwing must be continuously connected via their rows and columns.