Unique rectangle help

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Unique rectangle help

Postby Dickd23344 » Fri Jul 08, 2016 12:44 am

New to the forums, so hey.

I'm starting to solve diabolical puzzles without help more frequently. I've noticed you encounter many more unique rectangles with these. I know how to solve many of them but one thing I can't seem to figure out with the more cluttered ones.

When you've spotted the unique rectangle and you see there are two opposing cells in the rectangle with the two candidates in question for the rectangle which angle do you choose to eliminate one of the candidates?

See the picture for reference:

Why would I eliminate the 9 from A8 as opposed to H7?

Any help would be great!
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Re: Unique rectangle help

Postby Leren » Fri Jul 08, 2016 7:39 am

Code: Select all
*--------------------------------------------------------------*
| 2     1     3      | 4     8     7      | 6     5     9      |
| 5     48    7      | 1     6     9      | 48    2     3      |
| 68    46    9      | 5     3     2      | 1     7     48     |
|--------------------+--------------------+--------------------|
| 378   37    1      | 9     2     5      | 47    6     48     |
| 4     89    6      | 7     1     3      | 5     89    2      |
| 79    2     5      | 8     4     6      | 79    3     1      |
|--------------------+--------------------+--------------------|
|*39-1  39    4      | 6     5     8      | 2    *1-9   7      |
|*1-9   5     2      | 3     7     4      | 89   *89-1  6      |
| 67    67    8      | 2     9     1      | 3     4     5      |
*--------------------------------------------------------------*

There are actually 4 Unique Rectangle eliminations available in the Yellow cells, which I've marked with * in my diagram.

The reason is that there is an X Wing of 1's in the 4 cells, which provides extra inferences.

So, for example, if the top left hand * cell was 1, the top right hand and bottom left hand * cells would both obviously be 9.

What might not be so obvious, is that because these cells are 9, they are not 1, and that forces the bottom right hand * cell to be 1 (because there are two 1's in Row 8 and Column H it's forced to be 1 twice !)

So you end up with an exposed Deadly Pattern like so, in two boxes.

Code: Select all
1   9

9   1

Similar arguments apply for the other three eliminations. With Unique Rectangles, it's often a good idea not to make the first elimination you see, but check for all the possibilities, and then make all the eliminations that are possible.

This is a Type 6 Unique Rectangle, which you can read about here.

Hope this helps, Leren

PS for the benefit of others on this forum, here is the puzzle status in line format : 2134876595.7169.23..953217...1925.6.4.67135.2.25846.31..46582.7.52374..6..8291345

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Re: Unique rectangle help

Postby eleven » Fri Jul 08, 2016 12:08 pm

Dick,

yes, look at the UR description, but
especially for pencil&paper players, who do no fill in all the pencilmarks, it is often better to look at the cells OUTSIDE the UR-cells, where the 2 digits could be to prevent a deadly pattern.

In this case the 1 is an x-wing and cannot be elsewhere, so the 9 must be somewhere outside in these units (houses).

If the 9 is not in r78c1 (A78), it must be in r6c1 (only 9 left in column 1) and r7c2 (left in box 7).
If it is not in r78c8, it must be in r5c8 and r8c7.

One of these 2 cases must be true.
So you can say, that 9 must be in r6c1 or r5c8, and it must be in r7c2 or r8c7.

Now the 9 in r5c2 sees both r6c1 and r5c8, and can be eliminated, same for 9 in r6c7.
The 9 in r8c1 both sees r7c2 and r8c7, and can be eliminated, same for 9 in r7c8.

[Edit:] Corrected typo and notation.
Last edited by eleven on Fri Jul 08, 2016 9:31 pm, edited 1 time in total.
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Re: Unique rectangle help

Postby Leren » Fri Jul 08, 2016 8:56 pm

eleven wrote : If the 9 is not in r78c2 (GH1)

Hi eleven, you have a typo here. I think you meant r78c1.

Also Dick appears to be using spreadsheet notation in his question, so he would presumably refer to r78c1 as A78, although the phone picture refers to Column 1, so why he refers to columns by letters is unknown.

On Alan Stuart's site rows are referred to by letters and columns by numbers, so r78c1 would indeed be GH1. Don't you just love all this non-standardization ?

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Re: Unique rectangle help

Postby eleven » Fri Jul 08, 2016 9:28 pm

Leren,

thanks for pointing out the typo.

Apart from the rc notation the chess notation (A1 left/bottom to I9 right top) was somewhat natural for me.
Now i remember, that Sudoku Explainers alternative was A1 left/top to I9 right/bottom, which only confused me.

I did not understand, what Dick meant with "Why would I eliminate the 9 from A8 as opposed to H7?"
I thought, maybe he counted A to I top down, and had a typo.
But with this numeration it makes sense. So i also change GH1 to A78.
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Re: Unique rectangle help

Postby SteveG48 » Sun Jul 10, 2016 2:29 pm

Dickd23344 wrote:Why would I eliminate the 9 from A8 as opposed to H7?

Any help would be great!


Hi, Dick. The simple answer is that it makes no difference. Eliminating the 9 in either of those corners quickly determines that you have a 1 in both of those corners. 9 is eliminated in both.
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