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Haven't been this stumped in a while. Help, please

 
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daykart



Joined: 22 Nov 2005
Posts: 10

PostPosted: Thu Dec 15, 2005 10:46 pm    Post subject: Haven't been this stumped in a while. Help, please Reply with quote

I am sure the key is staring me in the face, but I can not find a move.
Hint, please.

_ _ _ 7 _ 8 6 _ 4
8 _ _ _ 4 _ 5 _ 9
_ _ _ 5 _ 9 _ 3 8

_ 1 _ _ 8 _ 2 _ _
_ _ 7 1 5 4 _ _ _
_ _ _ _ 3 _ _ 4 _

3 4 _ _ _ _ _ _ _
1 _ 5 _ 9 _ _ _ _
_ _ 2 _ _ 5 _ _ _

r1c1: 5,9 c2:3,5,9 c3: 3,9 c5: 1,2 c8: 1,2
r2c2: 2,6,7 c3: 1,6 c4: 2,3,6 c6: 1,2,3,6 c8: 1,2,7
r3c1: 2,4,6,7 c2: 2,6,7 c3: 1,4 6 c5: 1,2,6 c7: 1,7
r4c1: 4,5,6,8 c3: 3,4,6,9 c4: 6,9 c6: 6,7 c8: 5,6,7,9 c9: 3,5,6,7
r5c1: 2,6,9 c2: 2,3,6,8,9 c7: 3,8,9 c8: 6,8,9 c9: 3,6
r6c1: 5,6,9 c2: 5,6,8,9 c3: 6,8,9 c4: 2,6,9 c6: 2,6,7 c7: 1,7,8,9 c9: 1,5,6,7
r7c3: 6,8,9 c4: 2,6,8 c5: 1,2,6,7 c6: 1,2,6 c7: 1,7,8,9 c8: 1,5,6,7,8,9 c9: 1,2,5,6,7
r8c2: 6,7,8 c4: 2,3,4,6,8 c6: 2,3,6 c7: 3,4,7,8 c8: 6,7,8 c9: 2,3,6,7
r9c1: 6,7,9 c2: 6,7,8,9 c4: 3,4,6,8 c5: 1,6,7 c7: 1,3,4,7,8,9 c8: 1,6,7,8,9
c9: 1,3,4,6,7

I have been at this too long to be stuck here. I do not see where I can eliminate.
Thanks
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David Bryant



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

PostPosted: Fri Dec 16, 2005 12:15 am    Post subject: Puzzle has multiple solutions Reply with quote

Well, it's no wonder you can't make progress, Daykart. This puzzle has 27 solutions!

Just for the record, here are two possible "solutions."
Code:
953728614   593718624
871346529   821346579
624519738   764529138
419687253   419687253
237154896   237154986
586932147   658932741
348271965   346271895
165893472   175893462
792465381   982465317

Where did you find this puzzle? You need to be careful about your authors -- there are a bunch of very sloppy "composers" out there. dcb
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daykart



Joined: 22 Nov 2005
Posts: 10

PostPosted: Fri Dec 16, 2005 1:23 am    Post subject: Thanks David, but... Reply with quote

How did you determine so fast that there were multiple solutions?

What was the next number or numbers that you KNEW had to go and where did you place them??
I mean I know r1c1 c2 c3 had to be a combo of 5 3 9, but if you are telling me that the solution does not demand a definite position for these, how did you figure that out?

Thanks

Daykart
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Fri Dec 16, 2005 9:37 am    Post subject: Reply with quote

Hi,

I have lost myself a lot of time with so called "Sudoku"s which do not have unique solutions.

BE AWARE THAT THERE ARE SUCH SITES IN THE INTERNET, NOT WARNING YOU THAT THEY PUBLISH PUZZLES WITH MULTIPLE SOLUTIONS.

You have 2 options:
- a quick and clean or
- a long and durty
- a wise

The quick and clean, is to use a program. I suggest even for this page to include one that is JUST telling us (using even brute force) that this puzzle has multiple solutions. Or an option to the existing one.

The long and durty, is to find out by yourself. You will need "try and error" technique. Which is durty, durty, durty Laughing bad boy Evil or Very Mad

Or you can ask for help. For example in a forum.

You found the 3-dt way.

see u,
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David Bryant



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

PostPosted: Fri Dec 16, 2005 2:35 pm    Post subject: Multiple solutions Reply with quote

Daykart wrote:
How did you determine so fast that there were multiple solutions?

Hi, Daykart!

I stared at your puzzle for about 10 minutes, trying to see a pattern. You had kindly provided the list of candidates for each cell, which sped things up a lot for me. Anyway, when I couldn't see any useful clues, I fed the puzzle to a computer program, which informed me that multiple solutions exist.

Daykart wrote:
What was the next number or numbers that you KNEW had to go and where did you place them??


I didn't KNOW where any more numbers had to go. So I just guessed. I focused on the {1, 2} pair appearing in r1c5 & r1c8 -- it was obvious, and offered good possibilities for finding two different solutions. First I tried placing a "1" at r1c8 -- the computer program informed me that 19 solutions were possible. Then I put a "2" at r1c8, and the computer said there were 8 possible solutions.

After that I didn't much care about logical niceties -- I just bashed away at the puzzle using brute force to find two of the 27 possible solutions. (The program I'm using will count the number of possible solutions, but it won't display them all.)

Daykart wrote:
I mean I know r1c1 c2 c3 had to be a combo of 5 3 9, but if you are telling me that the solution does not demand a definite position for these, how did you figure that out?


I just used trial and error (plus the computer program) from the initial placement of either "1" or "2" I had made at r1c8. As it turned out, the particular "solutions" I was able to construct contain the {3, 5, 9} triplet in two different orders. Maybe there are two "solutions" that interchange the "1" and "2" at r1c8 without altering the order of the {3, 5, 9} triplet. I don't know -- and I don't really care.

For me, the important thing is knowing that a puzzle has a unique solution. If it does, then a "logical" route to that unique solution is possible, at least in principle. But when multiple "solutions" exist, the only way to find them is by guessing, and that's no fun. dcb
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Fri Dec 16, 2005 2:45 pm    Post subject: Reply with quote

Hi,

Quote:
For me, the important thing is knowing that a puzzle has a unique solution. If it does, then a "logical" route to that unique solution is possible, at least in principle. But when multiple "solutions" exist, the only way to find them is by guessing, and that's no fun.


100% agree with you.

I am/would start with a program to check, if there is a unique solution, even before dealing with the puzzle, if I don't trust the source that has published it.

Like the german are used to say: "Vertrauen is gut, aber Kontrolle ist besser" - meaning "Confidence is good, but checkup is better".

see u,
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alanr555



Joined: 01 Aug 2005
Posts: 193
Location: Bideford Devon EX39

PostPosted: Sat Dec 17, 2005 1:53 am    Post subject: Reply with quote

Code:

> It is no wonder you can't make progress.
> This puzzle has 27 solutions!

> How did you determine so fast that there were multiple solutions?

> I fed the puzzle to a computer program, which informed me
> that multiple solutions exist. (The program I'm using will count
> the number of possible solutions, but it won't display them all.)

Who publishes this program?
Does it include 'trial and error' in its solution logic?
Other topics on this site suggest that it is almost impossible to
GUARANTEE to find one solution (let alone several!) without
resort to trial and error in some cases.

> For me, the important thing is knowing that a puzzle has
> a unique solution. If it does, then a "logical" route to that
> unique solution is possible, at least in principle. But when
> multiple "solutions" exist, the only way to find them is by
> guessing, and that's no fun.

Agreed, absolutely!!!

> I would start with a program to check, if there is a unique
> solution, even before dealing with the puzzle, if I don't
> trust the source that has published it.

This sounds like a sad overhead. I use the computer as a
print device (DRAW) but after my first couple of months
learning about Sudoku I do not otherwise use the computer
in any way. As SamGJ states in the site introduction (FAQ)
"What's the point?" of devising solvers.

Having said that, the art of COMPILATION is a complete mystery
to me. Are there books on this aspect of Sudoku? I can see that
computers could be helpful with this until one has got to grips
with the processes - including ensuring uniquity!

Alan Rayner  BS23 2QT
 
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