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next number

 
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peter newman



Joined: 29 May 2006
Posts: 3

PostPosted: Wed Jun 14, 2006 5:53 pm    Post subject: next number Reply with quote

can anybody give me the next number and why

7x53x96x2
3xx5xx79x
4x9x8x351
x4x1xx5x7
853674129
1x7x5xxxx
231x6x9x5
xx8x35x1x
5x4xx1xx3
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keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Wed Jun 14, 2006 9:18 pm    Post subject: Some progress Reply with quote

Here is the position you posted, after clearing hidden pairs, etc:

Code:

+----------------+----------------+----------------+
| 7    18   5    | 3    14   9    | 6    48   2    |
| 3    18   26   | 5    14   26   | 7    9    48   |
| 4    26   9    | 27   8    267  | 3    5    1    |
+----------------+----------------+----------------+
| 69   4    26   | 1    29   38   | 5    38   7    |
| 8    5    3    | 6    7    4    | 1    2    9    |
| 1    29   7    | 289  5    238  | 48   3468 468  |
+----------------+----------------+----------------+
| 2    3    1    | 478  6    78   | 9    478  5    |
| 69   679  8    | 2479 3    5    | 24   1    46   |
| 5    679  4    | 2789 29   1    | 28   678  3    |
+----------------+----------------+----------------+

There is a Unique Rectangle in R46C68. You can eliminate <8> from R6C68.

There are strong links on <9> in C15. You can eliminate <9> from R9C2 and R8C4. (Either R8C1 or R9C5 is <9>.)

Then, there is an XY-wing on <267> which removes <7> from R9C4.

Then, it seems, you have to look for chains.

Keith
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Thu Jun 15, 2006 12:01 am    Post subject: Reply with quote

From Keith's grid, colouring on digit 2 excludes 2 from r6c6, which creates a naked pair that allows a placement in r6c7. After that it's all singles.
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Thu Jun 15, 2006 4:03 am    Post subject: Reply with quote

Quote:
Then, there is an XY-wing on <267> which removes <7> from R9C4.


Keith, I'm missing something here, unless 679 counts as a 67. ??
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keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Thu Jun 15, 2006 10:36 am    Post subject: Reply with quote

The <9> in R9C2 is eliminated in the previous step (coloring on the <9>'s).

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Thu Jun 15, 2006 3:41 pm    Post subject: Reply with quote

keith wrote:
The <9> in R9C2 is eliminated in the previous step (coloring on the <9>'s).

Keith


Oops, sorry, I missed that. Thanks.
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peter newman



Joined: 29 May 2006
Posts: 3

PostPosted: Thu Jun 15, 2006 6:08 pm    Post subject: Reply with quote

TKiel wrote:
From Keith's grid, colouring on digit 2 excludes 2 from r6c6, which creates a naked pair that allows a placement in r6c7. After that it's all singles.


So is this the solution, if so please explain colouring i.e. why 2's excluded.

Pete.
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keith



Joined: 19 Sep 2005
Posts: 3173
Location: near Detroit, Michigan, USA

PostPosted: Thu Jun 15, 2006 9:09 pm    Post subject: Coloring Reply with quote

Starting from here (the same as above, but I have labeled some cells):
Code:

+----------------+----------------+----------------+
| 7    18   5    | 3    14   9    | 6    48   2    |
| 3    18   26b  | 5    14   26a  | 7    9    48   |
| 4    26a  9    | 27   8    267  | 3    5    1    |
+----------------+----------------+----------------+
| 69   4    26   | 1    29   38   | 5    38   7    |
| 8    5    3    | 6    7    4    | 1    2    9    |
| 1    29b  7    | 289  5    238c | 48   3468 468  |
+----------------+----------------+----------------+
| 2    3    1    | 478  6    78   | 9    478  5    |
| 69   679  8    | 2479 3    5    | 24   1    46   |
| 5    679  4    | 2789 29   1    | 28   678  3    |
+----------------+----------------+----------------+

a and b label conjugate pairs (or strong links) in R2, B1, and C2. In each of these there are only two candidates for <2>. Notice how these links form a chain from R1C6 to R6C2. In the solution, either all the cells labeled a are <2>, OR all the cells labeled b are <2>.

So, the cell labeled c, R6C6, cannot be <2>.

Nice observation, Tracy!

Keith
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