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Stumped, Again ...

 
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Ema Nymton



Joined: 17 Apr 2009
Posts: 87

PostPosted: Sat Jun 07, 2014 10:33 pm    Post subject: Stumped, Again ... Reply with quote

.

Is this solvable?

Code:

+------------+----------+----------+
| 9  8   46  | 3  7  5  | 1 46  2  |
| 2  7   146 | 69 14 8  | 5 3   49 |
| 3  5   146 | 69 14 2  | 8 469 7  |
+------------+----------+----------+
| 5  6   3   | 2  9  14 | 7 14  8  |
| 7  14  8   | 5  6  3  | 9 2   14 |
| 14 2   9   | 7  8  14 | 3 5   6  |
+------------+----------+----------+
| 8  19  2   | 4  5  7  | 6 19  3  |
| 14 149 5   | 8  3  6  | 2 7   19 |
| 6  3   7   | 1  2  9  | 4 8   5  |
+------------+----------+----------+

Play this puzzle online at the Daily Sudoku site

If it solvable, what is the step I am overlooking?

Thanks for any help you may be able to provide.

Ema Nymton
~ @ : o ?
.
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arkietech



Joined: 31 Jul 2008
Posts: 1708
Location: Northwest Arkansas USA

PostPosted: Sat Jun 07, 2014 11:24 pm    Post subject: Reply with quote

Code:
 
 *--------------------------------------------------*
 | 9    8    46   | 3    7    5    | 1    46   2    |
 | 2    7    146  | 69   14   8    | 5    3    49   |
 | 3    5    146  | 69   14   2    | 8    469  7    |
 |----------------+----------------+----------------|
 | 5    6    3    | 2    9    14   | 7    14   8    |
 | 7   *14   8    | 5    6    3    | 9    2   *14   |
 |*14   2    9    | 7    8    14   | 3    5    6    |
 |----------------+----------------+----------------|
 | 8    19   2    | 4    5    7    | 6    19   3    |
 |*14   149  5    | 8    3    6    | 2    7    9-1  |
 | 6    3    7    | 1    2    9    | 4    8    5    |
 *--------------------------------------------------*
The 14 pairs shown form a Remote Pair removing 1 from r8c9 and solving the puzzle.
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Ema Nymton



Joined: 17 Apr 2009
Posts: 87

PostPosted: Sat Jun 07, 2014 11:42 pm    Post subject: Reply with quote

.

Thank you. Impressive solution.

Ema Nymton
~ @ : o ?
.
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dongrave



Joined: 06 Mar 2014
Posts: 16

PostPosted: Sun Jun 08, 2014 2:37 pm    Post subject: Reply with quote

I think you can also remove a bunch of the 1's if you 'color' them all in rows 4 through 8. I don't know what the technical solution name is for this (yet) but maybe the experts could tell us. Instead, I applied what's called a proof by contradiction in math terms (i.e. assume that any one the squares r4c8, r5c2, r6c6, r7c2, r8c1, or r8c9 contains a 1 , then chain them until you arrive at a contradiction). What do they call this in Sudoku solving terms - or is this generally not an accepted approach? Thanks, Don.
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dongrave



Joined: 06 Mar 2014
Posts: 16

PostPosted: Sat Jun 14, 2014 6:29 pm    Post subject: Hey! Coloring chains is cool! Reply with quote

I just went back and read more about coloring and I now see how it works! Cool! I can see that in this puzzle if you color the 1's beginning at r7c9 (I used yellow) and then color r5c9 with red, then r5c2 with yellow, r6c1 with red, then r8c1 must be yellow - but it can't be yellow! Cool! I also see now the major difference between this and the 'assume and find contraction' approach in that the 'contradiction' approach truly is trial and error - and it seems to me that one should never have to resort to trial and error to solve a puzzle. I'd appreciate any thoughts. Oh, and please let me know if I'm wrong about the coloring that I've described above. I've been wrong before - so much so that I was thinking of asking for someone to add a 'very embarrassed' Emoticon (like maybe a bag over the head)! Thanks, Don.
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Marty R.



Joined: 12 Feb 2006
Posts: 5119
Location: Rochester, NY, USA

PostPosted: Sat Jun 14, 2014 9:59 pm    Post subject: Re: Hey! Coloring chains is cool! Reply with quote

dongrave wrote:
I just went back and read more about coloring and I now see how it works! Cool! I can see that in this puzzle if you color the 1's beginning at r7c9 (I used yellow) and then color r5c9 with red, then r5c2 with yellow, r6c1 with red, then r8c1 must be yellow - but it can't be yellow! Cool! I also see now the major difference between this and the 'assume and find contraction' approach in that the 'contradiction' approach truly is trial and error - and it seems to me that one should never have to resort to trial and error to solve a puzzle. I'd appreciate any thoughts. Oh, and please let me know if I'm wrong about the coloring that I've described above. I've been wrong before - so much so that I was thinking of asking for someone to add a 'very embarrassed' Emoticon (like maybe a bag over the head)! Thanks, Don.


Don, I assume you had a typo and started with r8c9. Coloring got its name from using colors, but it isn't necessary. In a Simple Coloring chain, you use a series of strong links, such as exists with the 1s. Using your four cells, you can say T-F-T-F, or Plus-Minus-Plus-Minus, just to use two examples.

The important consideration is that the chain has an even number of cells, thus the start and end of the chain have opposite "polarity" and any cell seeing both the start and end cells cannot contain the value since one or the other must be true.
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