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What is it?

 
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

PostPosted: Mon Jun 01, 2009 2:58 pm    Post subject: What is it? Reply with quote

Code:
 *-----------*
 |...|3.5|.7.|
 |1.5|.87|...|
 |...|.1.|.8.|
 |---+---+---|
 |97.|...|..8|
 |.56|...|71.|
 |2..|...|.49|
 |---+---+---|
 |.6.|.5.|...|
 |...|29.|1.4|
 |.9.|7.6|...|
 *-----------*

 *--------------------------------------------------------------------*
 | 6      48     89     | 3      2      5      | 49     7      1      |
 | 1      234    5      | 469    8      7      | 2349   239    36     |
 | 7      234    39     | 469    1      49     | 23459  8      356    |
 |----------------------+----------------------+----------------------|
 | 9      7      4      | 1      6      2      | 35     35     8      |
 | 38     5      6      | 489    34     49     | 7      1      2      |
 | 2      1      38     | 5      7      38     | 6      4      9      |
 |----------------------+----------------------+----------------------|
 |*348    6      2      |*48     5      1      | 389    39     7      |
 | 5     *38     7      | 2      9     *38     | 1      6      4      |
 |*348    9      1      | 7      34     6      | 2358   235    35     |
 *--------------------------------------------------------------------*
if r8c2=8 then r7c4=4 r7c1=3 r9c1=8 => r8c2<>8

I got this puzzle from the playr.co.uk web site. Solved it by the above logic but would like some help from the wing and extension experts. Or maybe a remote pair guru.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Mon Jun 01, 2009 4:36 pm    Post subject: Reply with quote

Quote:
if r8c2=8 then r7c4=4

Dan, I'm having trouble with this. It looks like if r8c2=8, then r7c4 must=8. Question
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

PostPosted: Mon Jun 01, 2009 4:47 pm    Post subject: Reply with quote

Marty R. wrote:
Quote:
if r8c2=8 then r7c4=4

Dan, I'm having trouble with this. It looks like if r8c2=8, then r7c4 must=8. Question

Marty,

You are right. r8c2 cannot be an 8. I need a slick trick here. Or am I missing something? Confused
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Mon Jun 01, 2009 5:20 pm    Post subject: Reply with quote

This needs some kind of chain. You might try R9C1 = 8 => R5C1 = 8 via the 34 pair in C5.

Keith
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Mon Jun 01, 2009 7:03 pm    Post subject: Reply with quote

what I see is

a w-wing (3) r4c7=r9c9 via col 8
another w-wing (4) r1c7=r3c6 via col 3

AND a sort of grouped m-wing involving the marked cells in col 1, which sets r9c789<>3.

How?

if r9c5<>3 then r9c5=4 then (strong link (4) in col 1) r7c1=4 then r7c78=3 which means at least one of r9c5 and r7c78 must be "3"

In fact, if you apply the 2 w-wings, the (regular, not grouped) m-wing (3) r9c5=r7c8 (via col 1) appears.

_________

edit: in case anybody wonders about the m-wing reference, this is how I think:

any time a bi-value cell (in this case r9c5 {3,4}) "sees" a strong link in one of the two candidates of the bi-value (r7c1 and r9c1 in "4"), check for a strong link in the other candidate (here: "3") and coming out of the other end of the (first) strong link (that would be r7c1). In dan's grid this strong link (3) is between r7c1 and r7c78. r9c5 and r7c78 are the two pincers of the wing, r9c789 the victim cells

P.S. If you don't like to use the term m-wing, just call it the "nataraj gun" Cool www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2908"


Last edited by nataraj on Mon Jun 01, 2009 7:20 pm; edited 1 time in total
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Mon Jun 01, 2009 7:16 pm    Post subject: Reply with quote

There are some XY-Chains, but none of them seem to advance the solution much.

There are three chains that crack this puzzle. One produces [r7c1]<>3, the second produces [r9c1]<>8, and the third is a generalized M-Wing for [r7c7]<>8.

[Correction: nataraj's grouped M-Wing is chain #4.]
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

PostPosted: Mon Jun 01, 2009 8:24 pm    Post subject: Reply with quote

nataraj wrote:
any time a bi-value cell (in this case r9c5 {3,4}) "sees" a strong link in one of the two candidates of the bi-value (r7c1 and r9c1 in "4"), check for a strong link in the other candidate (here: "3") and coming out of the other end of the (first) strong link (that would be r7c1). In dan's grid this strong link (3) is between r7c1 and r7c78. r9c5 and r7c78 are the two pincers of the wing, r9c789 the victim cells
Thanks, I like having a "gun" handy for some of these puzzles. Smile
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