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19-Jan-2006 has 2 answers

 
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telflonmail
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PostPosted: Thu Jan 19, 2006 11:00 pm    Post subject: 19-Jan-2006 has 2 answers Reply with quote

Hi,

I have done the 19-Jan-2006, [the very hard Smile] and have found it has 2 correct solutions. This was my last move - where the 5 and 7 could be interchanged and everything would be correct.

5 x x x x 7 x x x
x x x x x x x x x
7 x x x x 5 x x x
x x x x x x x x x
x x x x x x x x x
x x x x x x x x x
x x x x x x x x x
x x x x x x x x x
x x x x x x x x x

The 5 and the 7 could be interchanged cleanly to meet suduko. So, which on is the more correct version (or are both) :-)

So, the top left, top middle could be:

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

or:

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

I hope I didn't give away too much - this one was pretty straight forward, as long you worked the definite singles first before keeping score of the doubles and triples and eliminate as you go along.
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David Bryant



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

PostPosted: Thu Jan 19, 2006 11:54 pm    Post subject: Does it have 3 solutions? Reply with quote

telflonmail wrote:
(for thetop left & center 3x3 boxes)
Code:
5 9 4 1 6 7
3 1 6 2 8 4
7 8 2 3 9 5

Huh. That's odd. I worked this one out, too, and this is what I have in that part of the puzzle.
Code:
5 9 4 6 1 7
3 1 6 2 8 4
7 8 2 5 9 3

As you can see, the {5, 7} non-unique rectangle doesn't appear in the solution I found.

Might there possibly be three solutions? Please post your complete solution, and let's compare it with the one Samgj posts in the archives. dcb
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geoff h



Joined: 07 Aug 2005
Posts: 58
Location: Sydney

PostPosted: Fri Jan 20, 2006 7:31 am    Post subject: Reply with quote

Hi there,

Well, I think I have to concur with David on this one - unfortunately it appears that both of telflonmail's solutions are incorrect and that David's solution is the one true solution.

Here's what I had after 34 moves :

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

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

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

Therefore, when considering Row 1, you can see a pair of 5,7 in r1c1 and r1c6. This means you MUST place Nr 1 in r1c5 and then Nr 6 in r1c4. The puzzle is easily solved from there and the first two boxes then read as follows;

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

Which is what David came up with.

Cheers,
Geoff
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telflonmail
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PostPosted: Wed Feb 01, 2006 9:34 pm    Post subject: Reply with quote

my bad! Embarassed

I transcribed two of the givens to the wrong cell when making a larger grid. So kindly ignore above ramble.

Cannot beat a computer generated sudoku Exclamation
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jia
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PostPosted: Thu Feb 09, 2006 9:11 am    Post subject: Reply with quote

Rolling Eyes just one solution Rolling Eyes
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