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Hidden Pairs/Triples/Quads

Like the naked pairs, this method involves looking for pairs like [1,2][1,2], in cases where these pairs are hidden. Since they are hidden numbers, they are harder to find, but when you find them, [1,2] can be eliminated as candidates from other cells.

Lets have a look at the center-right box. 4,5,6 in column 9 are [1,2,5,6][1,2,5,6][1,2,6].

In [R3C9]’s [5,8,9], a 1, 2, or 6 can’t be entered.

Also, in [R8C9]’s [5,8,9], a 1, 2, or 6 can’t be entered.

It appears that a 1 might fit in [R9C9], but since 1 can only go in row [7] in column [7], it is impossible.

Hence, a triple of [1,2,6] arises in 4,5,6 of column 9.

Therefore, [1,2,6] can’t be entered in the other cells of this box. Hence, a [5] in [R5C8] and a [3] in [R6C8] are confirmed.

[1] in [R7C7] is also confirmed.

It’s not quite hidden, but a triple of 1,7,8 arises between [R4C4], [R5C4] and [R8C4]. The 1 will have to be in either [R4C4] or [R5C4], so it will not be in [R5C6] or [R6C6].

Hence, 1 in [R9C6] is confirmed.

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As seen in the diagram below, if 1,2 is in the upper left and upper middle, and there is also 1,2 in column 7, [R1C8] and [R1C9] in the upper right box will become [1,2][1,2]

Since a [1,2] pair is now in the upper right box, 1 and 2 can’t be entered in the other cells.

Quads are made up of four numbers in the same way, but we couldn’t find a specific example for this. It will appear as if there are many candidates, but if a number can’t be entered in any of the other cells, this technique will work.

It is a bit difficult, but it is an effective technique when you get stuck.

R1C1 | R1C2 | R1C3 | R1C4 | R1C5 | R1C6 | R1C7 | R1C8 | R1C9 |

R2C1 | R2C2 | R2C3 | R2C4 | R2C5 | R2C6 | R2C7 | R2C8 | R2C9 |

R3C1 | R3C2 | R3C3 | R3C4 | R3C5 | R3C6 | R3C7 | R3C8 | R3C9 |

R4C1 | R4C2 | R4C3 | R4C4 | R4C5 | R4C6 | R4C7 | R4C8 | R4C9 |

R5C1 | R5C2 | R5C3 | R5C4 | R5C5 | R5C6 | R5C7 | R5C8 | R5C9 |

R6C1 | R6C2 | R6C3 | R6C4 | R6C5 | R6C6 | R6C7 | R6C8 | R6C9 |

R7C1 | R7C2 | R7C3 | R7C4 | R7C5 | R7C6 | R7C7 | R7C8 | R7C9 |

R8C1 | R8C2 | R8C3 | R8C4 | R8C5 | R8C6 | R8C7 | R8C8 | R8C9 |

R9C1 | R9C2 | R9C3 | R9C4 | R9C5 | R9C6 | R9C7 | R9C8 | R9C9 |

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