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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.

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.

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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.

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.

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.

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 |

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