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Error whe Applying Unique Rectangle Type I

 
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NewUrbanBlues

Joined: 22 Oct 2006
Posts: 36
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PostPosted: Sun Jan 07, 2007 6:49 pm    Post subject: Error whe Applying Unique Rectangle Type I Reply with quote

Hello

I hit an error when using the Unique Rectangle Type I

Here is the board

7 53 4 | 6 1 59 | 8 39 2
53 6 9 | 53 8 2 | 7 4 1
1 8 2 | 7 39 4 | 39 5 6
----------------------------------------
2 579 6 | 8 4 3 | 1 79 59
359 4 1 | 59 2 7 | 6 8 359
8 3579 57 | 1 59 6 | 2 379 4
-----------------------------------------
6 1 57 | 4 359 589 | 39 2 78
59 2 8 |359 7 1 | 4 6 39
4 79 3 | 2 6 89 | 5 1 78

There is a Unique Rectngle Type I with R3C5 - R3C7 - R7C5 - R7C7. According to the UR Type 1 rule, I can remove the candidate 5 from the cell R7C5....

Here is the board solution:
734615892
569382741
182794356
256843179
341927685
897156234
615438927
928571463
473269518

Clearly R7C5 is 3 ... Oops UR Type 1 removes 3 and 9 ...

Ok, there could be other thinhs to do, as an XWings. I wonder why the UR Type 1 rule gives me a false result !!!!!!

Thanks for any clues explaining this ...

Thierry
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daj95376

Joined: 05 Feb 2006
Posts: 349
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PostPosted: Sun Jan 07, 2007 7:27 pm    Post subject: Reply with quote

You made the classic error of using Unique Rectangles -- spanning more than one chute!!! A UR Type 1 has all cells in the same chute; i.e., two of three boxes. Your cells span two chutes and four boxes!

Code:
 *-----------------------------------------------------------*
 | 7     35    4     | 6     1     59    | 8     39    2     |
 | 35    6     9     | 35    8     2     | 7     4     1     |
 | 1     8     2     | 7    *39    4     |*39    5     6     |
 |-------------------+-------------------+-------------------|
 | 2     579   6     | 8     4     3     | 1     79    59    |
 | 359   4     1     | 59    2     7     | 6     8     359   |
 | 8     3579  57    | 1     59    6     | 2     379   4     |
 |-------------------+-------------------+-------------------|
 | 6     1     57    | 4    #359   589   |*39    2     78    |
 | 59    2     8     | 359   7     1     | 4     6     39    |
 | 4     79    3     | 2     6     89    | 5     1     78    |
 *-----------------------------------------------------------*


Last edited by daj95376 on Sun Jan 07, 2007 7:32 pm; edited 1 time in total
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Ruud
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Joined: 17 Sep 2005
Posts: 708
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PostPosted: Sun Jan 07, 2007 7:31 pm    Post subject: Reply with quote

For more info: http://www.sudopedia.org/wiki/Unique_Rectangle

Ruud
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