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Hidden Unique Rectangles
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|In Figure 1, the cells D3, D7, F3 and F7 (also known as DF37) form a rectangle with a potential deadly pattern on [1/6]. We want to avoid reducing this rectangle to 1/6 in all four cells. There is a bi-value cell at F7, but the other corners contain a clutter of other candidates.
The types of Unique Rectangles that we’ve examined so far simply won’t work here. However, all is not lost because something interesting is going on in the corner opposite to F7. 1 in D3 is part of two strong links in the row and column - that is, 1 occurs only twice in row D and column 3. Our 1 in this rectangle can have only one of two possibilities.
Looking at D3, lets make "Option A" the case where D3 is 1. The pairs or "strong links" remove 1 from in D7 and F3. Option B is where D3 is not a 1. That would put a 1 in D7 and F3.
Hidden Unique Rectangle Type 1: Load Example or : From the Start
|Type 2 Hidden Unique Rectangles
In Figure 2, the cells B1, B3, D1 and D3 (also known as BD13) form a rectangle with a potential deadly pattern on [6/8]. In type 2 we have an identifiable Floor consisting of B1 and B3, both bi-value cells. And the Roof contains a clutter of other candidates. We still want to avoid reducing this rectangle to 6/8 in all four cells.
Type 2 starts with a Naked Pair, 8/6, and we're checking for which strong links exist on the pair candidates. The Naked Pair is obviously a double strong link on both numbers, but candidate 8 has a strong link to the Roof in column 1. From this we can start using the logic of Type 1.
Figure 2, Hidden Unique Rectangle Type 2: Load Example or : From the Start
|Type 2b Hidden Unique Rectangles
In common with Unique Rectangles there is a type B for this strategy, where the floor is across two boxes rather than in the same box.
The yellow cells are the floor with conjugate pairs 1/7. The Deadly Rectangle extends to E3 and H3 (orange) where 1 and 7 are also present among other candidates. The strong link on 1 between E2 and E3 means that a 7 in H3 would create a Deadly Rectangle.
Thanks to Jerry Foil of Virginia, USA for providing the first example. Interestingly this type of Hidden Unique Rectangle is almost twice as common as the Type 1 and three times as common as Type 2.
Hidden Unique Rectangle 2b: Load Example or : From the Start
Klaus Brenner in Germany has created some very beautiful Sudokus like the one on the right. It solves trivially up to the point where a Type 1, Type 2 and Type 2b are used consecutively. In the screen shot the Type 2B is shown with the floor in row H.
HIDDEN UNIQUE RECTANGLE Type 2b: removing 7 at J7 because of HJ47 and one strong link between H4 and J4 on 5
Type 2b Hidden Unique Rectangle: Load Example or : From the Start