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

Posted: Sun Oct 01, 2006 2:22 pm Post subject: Question on type 2 UR's 


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: 5486 Location: Rochester, NY, USA

Posted: Sun Oct 01, 2006 5:37 pm Post subject: 


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: 3260 Location: near Detroit, Michigan, USA

Posted: Sun Oct 01, 2006 6:04 pm Post subject: Re: Question on type 2 UR's 


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)
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
Keith 

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

Posted: Mon Oct 02, 2006 6:55 pm Post subject: 


Thanks for the replies guys, that helps 

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keith
Joined: 19 Sep 2005 Posts: 3260 Location: near Detroit, Michigan, USA


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