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Constellations, etc.

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5161
Location: Rochester, NY, USA

PostPosted: Sun Mar 26, 2006 12:06 am    Post subject: Constellations, etc. Reply with quote

David (Bryant), I dredged up this post of yours from late November from this thread, http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=302&highlight=constellation

I started the puzzle and routinely got to the position shown below, or something very close to it. I then did the remote pairs (69) chain starting at r3c6. I've never before used this word--conjugate--but I think that describes the relationship between r3c6 and r9c3. That then solves r9c6 with a "5" and everything fell into place after that.

I still have trouble with constellations, implications, BUGs, etc., yet I continue to solve puzzles (not as many as I'd like) with different techniques, some of which I've learned here, such as the remote pairs I used for this puzzle, other than what I see described in the forum.

That said, I'm not sure of the purpose of this post, except that sometimes there are discussions of techniques that seem more complicated than what's needed for me to solve a puzzle. Please don't anyone take that as a negative, because that's the last kind of comment I'd make to a group that has been so helpful to me.

Quote:
I could kick myself -- I totally overlooked the "X-Wing" pattern in columns 3 & 5 ... with that, the "XY-Wing" pattern is relatively easy to spot. Good catch, someone!

Anyway, here's the "5 Star Constellation" I was talking about. Without noticing the X-Wing on "6" I had arrived at the following candidate table.
Code:

  2    5   6/9   1/6/9   6/8   1/8    4    7    3
  4   6/9   8     3/7    3/7    2     5    1   6/9
  7    3    1      4      5    6/9    8    2   6/9

  3    1    7     5/6     4    5/6    2    9    8
  6    8    5      2      9     7     3    4    1
  9    2    4     1/3    3/8   1/8    6    5    7

  5    7    2      8      1     3     9    6    4
  1   6/9   3     6/9     2     4     7    8    5
  8    4   6/9  5/6/7/9  6/7  5/6/9   1    3    2


The "Constellation" is in r8c4 (the "alpha star"), r4c4, r9c6, r4c6, and r3c6. One chain leads from r8c4 through r4c4 and r4c6 to r3c6 -- if r8c4 = 6 then r4c4 = 5, r4c6 = 6, and r3c6 = 9. The other chain leads from r8c4 through r9c6 & r4c6 to r3c6 -- if r8c4 = 9 then we have the {5, 6} pair in r4c6 & r9c6, so that r3c6 = 9 once again.

Interestingly, I found that I could also apply the "single chain" method starting from r8c4 -- assuming that r8c4 = 9 I deduce that r3c6 = 9 via r9c6 & r4c6, as before. But then there's a chain of {6, 9} pairs leading around the puzzle (r3c9, r2c9, r2c2, r8c2) that forces a contradiction, because it forces r8c2 = 9 (can't have two "9"s in the same row). dcb
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sun Mar 26, 2006 12:38 am    Post subject: It was a discussion ... Reply with quote

Marty R wrote:
... I'm not sure of the purpose of this post ...

Purpose? I guess I like to talk. Smile

More seriously, my friend someone_somewhere had (in November) just recently started to explain his ideas about "double-implication chains." I was trying to learn how to apply that technique, so when I hit a puzzle where I had figured out a "constellation," I posted it on the board. I think working through examples is a good way to learn new techniques.

If you dig back farther in the forum you'll find a whole lot of discussion of other techniques, like X-Wing, and Swordfish, and XY-Wing, etc. Most of it was pretty desultory, but it helped me (and some others too, maybe) learn a lot of stuff about sudokus when I was just starting in on them. dcb
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Marty R.



Joined: 12 Feb 2006
Posts: 5161
Location: Rochester, NY, USA

PostPosted: Sun Mar 26, 2006 1:40 am    Post subject: Re: It was a discussion ... Reply with quote

David Bryant wrote:
Marty R wrote:
... I'm not sure of the purpose of this post ...

Purpose? I guess I like to talk. Smile

Actually, David, in looking at the above response, I realize that I didn't make it clear that I was wondering about the purpose of MY post, not yours. Sorry about that misunderstanding, but I'd never make a rude comment like that about someone else's post. Your post was legitimately explaining some logic.
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