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Question on type 2 UR's

 
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David



Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK

PostPosted: Sun Oct 01, 2006 2:22 pm    Post subject: Question on type 2 UR's Reply with quote

Can somebody answer me this question;


123 1235

12 12

For the above example, is it possible to exclude the number 3 from any other cells on the top row ?
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Marty R.



Joined: 12 Feb 2006
Posts: 5178
Location: Rochester, NY, USA

PostPosted: Sun Oct 01, 2006 5:37 pm    Post subject: Reply with quote

I am hardly a rectangle expert, but it looks like the exclusion could be made if in the top row, all the possibilities for "3" are confined to that row.
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Sun Oct 01, 2006 6:04 pm    Post subject: Re: Question on type 2 UR's Reply with quote

David wrote:
Can somebody answer me this question;

123 1235

12 12

For the above example, is it possible to exclude the number 3 from any other cells on the top row ?

No. The solution could be (for example)
Code:
 1   5

 2   1

and <3> must lie somewhere else in the row.

Some exclusions may be possible:

If there is a candidate pair <35> in some cell in the top row, you can eliminate <35> from the remaining cells in the row. The same holds true if the top cells are in the same 3x3 box, and there is a canidate pair <35> in the box. Here is the argument:
Code:
123   1235  35  .  .  .

12     12

To ensure uniqueness, either <1> or <2> must be missing in the solution of the first two cells in the row. One of them must be <3> or <5>, so the three cells contain all the possible occurrences of <35> in the row.

The same logic applies if you have something like
Code:
123   1235  345  45.  .  .

12     12

The first four cells contain all the occurrences of <345>.

The other type of reduction occurs if the only occurrences of <1> (or <2>) in the top line are on the corners of the rectangle. Then, <2> (or <1>) can be eliminated from the top two cells of the rectangle.

If <1> is a strong link in the top line, you get
Code:
13   135  .  .  .

12   12


Keith
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David



Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK

PostPosted: Mon Oct 02, 2006 6:55 pm    Post subject: Reply with quote

Thanks for the replies guys, that helps
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Mon Oct 02, 2006 9:09 pm    Post subject: Guide to UR's Reply with quote

Of course, there is this excellent guide ...

http://www.sudoku.com/forums/viewtopic.php?p=29105#29105

Keith
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