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arkietech
Joined: 31 Jul 2008 Posts: 1834 Location: Northwest Arkansas USA
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Posted: Mon Jun 01, 2009 2:58 pm Post subject: What is it? |
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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
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Posted: Mon Jun 01, 2009 4:36 pm Post subject: |
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Quote: | if r8c2=8 then r7c4=4 |
Dan, I'm having trouble with this. It looks like if r8c2=8, then r7c4 must=8. |
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arkietech
Joined: 31 Jul 2008 Posts: 1834 Location: Northwest Arkansas USA
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Posted: Mon Jun 01, 2009 4:47 pm Post subject: |
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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. |
Marty,
You are right. r8c2 cannot be an 8. I need a slick trick here. Or am I missing something? |
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keith
Joined: 19 Sep 2005 Posts: 3355 Location: near Detroit, Michigan, USA
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Posted: Mon Jun 01, 2009 5:20 pm Post subject: |
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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
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Posted: Mon Jun 01, 2009 7:03 pm Post subject: |
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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" 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
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Posted: Mon Jun 01, 2009 7:16 pm Post subject: |
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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
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Posted: Mon Jun 01, 2009 8:24 pm Post subject: |
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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. |
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