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TOP > Techniques > Hidden Unique Rect's.

Solving Techniques 17
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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Hidden Unique Rect's. 2

Below is also a hidden unique rectangle. The X’d out [6] can be removed as a candidate from [R4C3]. (The 8s in the same row form a strong link)

If the [68] in the upper left [R2C1] is an [8], then [R2C3] becomes a [6], so the X’d out [6] in [R4C3] can’t be entered there.

If the upper left [R2C1]’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 [R4C1], it will be an [8]. Furthermore, [R2C3] will also be an [8]. If [R4C3] 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.


Names of cells in Sudoku


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