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# Solving Techniques 19 Aligned Pair Exclusion

Please have a look below. We have the blue cells [4,8][2,8], which are strongly related to the pink cells [2,4][2,5,8].

The possible combinations of the two pink cells are.
[2][2]
[2][5]
[2][8]
[4][2]
[4][5]
[4][8]
The combination of [2][2] is impossible.

The [2][8] combination can’t be used because A9’s candidate is [2,8].

The [4,8] combination can’t be used because B1’s candidate is [4,8]. Hence we have,
[2][2]
[2][5]
[2][8]
[4][2]
[4][5]
[4][8]
and [8] can’t be entered in C1.

As seen above, the Aligned Pair Exclusion technique, considers all possible combinations between two cells to narrow down the candidates.

## Aligned Pair Exclusion 2

Here is another sample. Lets examine the pink cells in the diagram above. The combinations are
[1][3]
[1][4]
[1][9]
[3][3]
[3][4]
[3][9]
[8][3]
[8][4]
[8][9]

If the pink cells are [1][3], then the blue cells in the same box will be [7][7], which won’t work out.

If the pink cells are [1][4], then the blue cell in E3’s candidate will be [1,4], which won’t work out.

If the pink cels are [3][8], the candidates in the blue cell, I3, will be [3,8], which won’t work out.
[1][3]
[1][4]
[1][9]
[3][3]
[3][4]
[3][9]
[8][3]
[8][4]
[8][9]
Hence, a [3] can’t be entered to the right of the pink boxes.

## Aligned Pair Exclusion 3

Here is another sample. Lets examine the pink cells in the diagram above. The combinations are:
[4][3]
[4][7]
[5][3]
[5][7]
[7][3]
[7][7]

If the pink cells are [4][7], then the same box’s blue cells will become [1][1], which won’t work out.

If the pink cells are [5][7], then the blue cell in C8’s candidates will be [5,7] which won’t work out.
[4][3]
[4][7]
[5][3]
[5][7]
[7][3]
[7][7]
Therefore, a [7] can’t be entered below the pink cells, so a [3] is confirmed here.

## Aligned Pair Exclusion 4

Here is another sample. Lets examine the pink cells in the diagram above. The combinations are:
[1][1]
[1][6]
[1][8]
[9][1]
[9][6]
[9][8]

If the pink cells are [1][8], the candidates in the blue cell, A1, will be [1,8], which won’t work out.

If the pink cells are [9][8], the candidates in the blue cell, F2, will be [8,9], which won’t work out.
[1][1]
[1][6]
[1][8]
[9][1]
[9][6]
[9][8]
Hence, an [8] can’t be entered below the pink cells.

## Aligned Pair Exclusion 5

Here is another sample. Lets examine the pink cells in the diagram above. The combinations are:
[1][4]
[1][5]
[1][7]
[2][4]
[2][5]
[2][7]
[7][4]
[7][5]
[7][7]

If the pink cells are [1][4], the candidates for the blue cell, I2, will be [1,4], which won’t work out.

If the pink cells are [1][5], the candidates for the blue cell, H2, will be [1,5], which won’t work out.

If the pink cells are [1][7], the candidates in both the blue cells A3 and C3 will be [9], which won’t work out.
[1][4]
[1][5]
[1][7]
[2][4]
[2][5]
[2][7]
[7][4]
[7][5]
[7][7]
Hence, a [1] can’t be entered to the left of the pink cells.

reference: sudokuwiki.org

## Names of cells in Sudoku

 A1 A2 A3 A4 A5 A6 A7 A8 A9 B1 B2 B3 B4 B5 B6 B7 B8 B9 C1 C2 C3 C4 C5 C6 C7 C8 C9 D1 D2 D3 D4 D5 D6 D7 D8 D9 E1 E2 E3 E4 E5 E6 E7 E8 E9 F1 F2 F3 F4 F5 F6 F7 F8 F9 G1 G2 G3 G4 G5 G6 G7 G8 G9 H1 H2 H3 H4 H5 H6 H7 H8 H9 I1 I2 I3 I4 I5 I6 I7 I8 I9