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TOP > Techniques > Hidden Unique Rect's.

Hidden Unique Rect's.

This is a method of finding hidden unique rectangles.

Below, the [6] in the [156] is X’d out. It can be eliminated as a candidate.

If the upper left blue [156] cell is a [1], then [6] can’t be a candidate for this cell.

A problem arises when the blue [156] is any number other than [1]. The yellow parts become candidates for [1].

Then the lower right blue cell would be a [6], since it is a [16]. In this case, too, if the upper left, blue cell is a [6]…

we eventually arrive at the following diagram.

But lets step back. The four blue cells create a unique rectangle with [16][16], leading to multiple solutions. Therefore, in this case, the blue cell to the upper left is a [5] and not a [6].

**Hence, this [6] can be removed as a candidate. Otherwise, we are left with a Sudoku problem which doesn’t work. **

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Below is also a hidden unique rectangle. The X’d out [6] can be removed as a candidate from D3. (The 8s in the same row form a strong link)

If the [68] in the upper left B1 is an [8], then B3 becomes a [6], so the X’d out [6] in D3 can’t be entered there.

If the upper left B1’s [68] is a [6], we have a problem. In this case, there are only two [8]’s in the same row, so even if there are many candidates for D1, it will be an [8]. Furthermore, B3 will also be an [8]. If D3 is a [6], we have a unique triangle where [6] and [8] are interchangeable.

**It will hence, not work as a Sudoku problem, and [6] can be removed as a candidate. **

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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