Next move please - Sudoku black belt 11/15/06

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Next move please - Sudoku black belt 11/15/06

Postby mayres » Fri Jul 20, 2007 4:20 am

I have an uneasy feeling that I am missing something very obvious, but I hope not. Can someone please give me the logic for the next step in this puzzle - found in a sudoku a day puzzle collection - not sure of publisher at this point.

Start of puzzle like this....
Code: Select all
 *-----------*
 |.26|5..|...|
 |...|3..|.4.|
 |5..|..6|2..|
 |---+---+---|
 |..3|..8|.6.|
 |..7|.9.|4..|
 |.6.|4..|3..|
 |---+---+---|
 |8.9|2..|..6|
 |.5.|..7|...|
 |...|..5|78.|
 *-----------*


I am now at this point
Code: Select all
  *--------------------------------------------------------------------*
 | 3      2      6      | 5      147    149    | 8      179    179    |
 | 7      19     18     | 3      128    129    | 6      4      5      |
 | 5      149    148    | 17     178    6      | 2      179    3      |
 |----------------------+----------------------+----------------------|
 | 1249   14     3      | 17     5      8      | 19     6      1279   |
 | 12     8      7      | 6      9      3      | 4      5      12     |
 | 19     6      5      | 4      127    12     | 3      179    8      |
 |----------------------+----------------------+----------------------|
 | 8      7      9      | 2      14     14     | 5      3      6      |
 | 6      5      14     | 8      3      7      | 19     2      149    |
 | 14     3      2      | 9      6      5      | 7      8      14     |
 *--------------------------------------------------------------------*

Thanks - mike
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Postby udosuk » Fri Jul 20, 2007 4:45 am

An X-Wing on 1s will solve it.

http://www.sudopedia.org/wiki/X-Wing
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Postby wintder » Fri Jul 20, 2007 4:58 am

The "original" is not valid.

The markup does have a solution, as listed above.
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Postby udosuk » Fri Jul 20, 2007 9:17 am

wintder wrote:The "original" is not valid.

My guess is Mike has mistakenly omitted the 3 in r3c9:
Code: Select all
 *-----------*
 |.26|5..|...|
 |...|3..|.4.|
 |5..|..6|2.3|
 |---+---+---|
 |..3|..8|.6.|
 |..7|.9.|4..|
 |.6.|4..|3..|
 |---+---+---|
 |8.9|2..|..6|
 |.5.|..7|...|
 |...|..5|78.|
 *-----------*
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Postby mayres » Sat Jul 21, 2007 3:49 am

udosuk - you are ABSOLUTELY correct! I don't think you "guessed" at all.:)
I'd like to ask a few questions about the x-wing you suggested. I have read about the x-wing in various places and want to make certain I have the correct principle as it applies to this puzzle and others.
Are we talking about r5c1, r5c9, r9c1, and r9c9?
If this be the case I'm wondering what the logic is in this puzzle for example. From what I can understand by reading the example given in this thread it appears that the next step is to eliminate all the "1's" from the other cells in columns 1 and 9. Is this correct? I'm having a challenge understanding why at this step a 1 cannot be in r4c1 or r4c9? What is the logic versus just taking them out because of the x-wing present?
Is the principle that there must be the same number in all four corners with not other repeats of the number in the row, but the other number can be anything? Is it necessary for any of the four pairs to be identical? Does it only work with pairs?
Thanks to any words of wisdom you can provide to help in further understanding. Also, is it OK to continue to ask these kinds of questions here or should I be doing it somewhere else?
mike
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Postby udosuk » Sat Jul 21, 2007 5:17 am

mayres wrote:udosuk - you are ABSOLUTELY correct! I don't think you "guessed" at all.:)
Mike, you are ABSOLUTE correct about this bit too.:D

mayres wrote:I'd like to ask a few questions about the x-wing you suggested. I have read about the x-wing in various places and want to make certain I have the correct principle as it applies to this puzzle and others.
Are we talking about r5c1, r5c9, r9c1, and r9c9?
Yes. These are the 4 cells relevant to this move.

mayres wrote:If this be the case I'm wondering what the logic is in this puzzle for example. From what I can understand by reading the example given in this thread it appears that the next step is to eliminate all the "1's" from the other cells in columns 1 and 9. Is this correct?
Totally correct.

mayres wrote:I'm having a challenge understanding why at this step a 1 cannot be in r4c1 or r4c9? What is the logic versus just taking them out because of the x-wing present?
An easy way to see the logic is to visualise what would happen if r4c1=1. Then the 1s on r5 & r9 will be forced to be on r5c9 and r9c9 respectively. Thus we're forced to have two 1s on c9, a contradiction. Therefore r4c1 must not be 1.

mayres wrote:Is the principle that there must be the same number in all four corners with not other repeats of the number in the row, but the other number can be anything? Is it necessary for any of the four pairs to be identical? Does it only work with pairs?
The pairs aren't important here. Just focus on the digit 1. The main point is there are exactly two 1s on the same columns on each of row 5 & row 9. Other digits can be completely ignored for this move. As a guide, take a look at the following board. All the information you need to know is in there.:idea:
Code: Select all
  .  .  .  |  .  1  1  |  .  1 -1
  .  1  1  |  .  1  1  |  .  .  .
  .  1  1  |  1  1  .  |  .  1  .
-----------+-----------+-----------
 -1  1  .  |  1  .  .  |  1  . -1
 #1  .  .  |  .  .  .  |  .  . #1
 -1  .  .  |  .  1  1  |  .  1  .
-----------+-----------+-----------
  .  .  .  |  .  1  1  |  .  .  .
  .  .  1  |  .  .  .  |  1  . -1
 #1  .  .  |  .  .  .  |  .  . #1

mayres wrote:Thanks to any words of wisdom you can provide to help in further understanding. Also, is it OK to continue to ask these kinds of questions here or should I be doing it somewhere else?
This is a good place to ask these kinds of questions. Whenever we have the time (and the mood:) ) we'll be glad to provide help to beginners and bring them up to speed. I do think there are other similar forums on the Internet for these questions but as long as you're comfortable here feel free to ask any questions you want.
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Postby mayres » Sat Jul 21, 2007 7:16 am

THANKS so much for taking the time to help me along. I REALLY appreciate it. Have a GREAT weekend! mike
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re: X-wing

Postby Pat » Sun Jul 22, 2007 1:30 pm

    as recently as 2006.Nov.22, we had a request to explain X-wing -- implying that the existing descriptions are inadequate -- thus causing me to try explaining it by example --
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