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 stevegnet
 Joined: 24 Jan 2010  Posts: 4  :  Location: essex,UK  Items 

Posted: Sun Jan 24, 2010 12:25 pm Post subject: Minimum (given numbers) before guessing? 


Hi all, hope this quetion is in the right forum? (if not can a MOD move)
What is the minimum number of (given numbers) a Sudoko puzzle needs to have to be completed without having to guess a number in a position to be able to continue?
I know 17 is the minimum numbers required for a unique completion.
The reason I ask is I started a puzzle which had 27 numbers given at start. I progressed to finding another 13 numbers IE: 41 in total so far.
Have penciled in all combinations of remaining numbers.
I have used a couple of internet solvers to prove the numbers can work to complete. A couple of solvers when I entered the initial 27 numbers stopped when they got to where I am with the further 13 numbers?.
Hope this makes sense and thanks in advace for any replies....Steve
Initial numbers are:
352
4316
87
723
5698
23
549
4675
14
with numbers I have found:_
638752
431865
8547
723
563741928
423
549
4675
154 

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 JasonLion
 Joined: 16 Nov 2008  Posts: 61  :  Location: Silver Spring, MD  Items 

Posted: Sun Jan 24, 2010 2:01 pm Post subject: 


That puzzle has a unique solution. After filling in 14 digits fairly easily it suddenly requires some fairly complex solving techniques. I would use a finned XWing and a WWing, though there are other ways to do it. After that it gets simple again. 

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 lkSudoku
 Joined: 16 May 2009  Posts: 60  :   Items 

Posted: Sun Jan 24, 2010 4:49 pm Post subject: Re: Minimum (given numbers) before guessing? 


stevegnet wrote:  What is the minimum number of (given numbers) a Sudoko puzzle needs to have to be completed without having to guess a number in a position to be able to continue?

The difficulty of a puzzle is not determined by the number of givens usually
There were some discussions about the guessing and difficulty, and it seems that there can always be a logical technique but it becomes more difficult at times, see http://www.setbb.com/sudoku/viewtopic.php?t=1728&mforum=sudoku for an example discussion
stevegnet wrote:  I know 17 is the minimum numbers required for a unique completion.

17 is the minimum givens puzzles with unique solution found so far, there is no proof as far as I know that there is no 16 givens puzzle, it just was not found yet 

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 daj95376
 Joined: 05 Feb 2006  Posts: 349  :   Items 

Posted: Sun Jan 24, 2010 6:32 pm Post subject: Re: Minimum (given numbers) before guessing? 


stevegnet wrote:  What is the minimum number of (given numbers) a Sudoko puzzle needs to have to be completed without having to guess a number in a position to be able to continue?
I know 17 is the minimum numbers required for a unique completion.

Here's the answer as I understand your question.
Most known puzzles with 17 givens are solvable through Singles. I would qualify that as without having to guess on those puzzles.
Another answer might be 72 givens. That leaves nine Naked Singles and you are guaranteed not to need to guess for every possible puzzle that can be constructed this way. 

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 stevegnet
 Joined: 24 Jan 2010  Posts: 4  :  Location: essex,UK  Items 

Posted: Sun Jan 24, 2010 7:22 pm Post subject: 


OK thanks for the replies,
I am new to this and have completed a number of sudoku puzzles recently. I didn't realise just how involved and complicated a "SIMPLE??" puzzle could be I guess. . I have been pulling my hair out for the past week trying to see a logical answer to this puzzle. I keep leaving it and coming back trying with a fresh mind.
Having since looked up a few of these weird names of strategies suggested and even more confused would it be possible for someone on here to work out the next number in the above puzzle so I can try to see why without guessing??
Thanks again Steve.........very confused. 

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 hobiwan
 Joined: 11 Feb 2008  Posts: 83  :   Items 

Posted: Tue Jan 26, 2010 5:58 pm Post subject: 


Assuming you arrived at this state:
Code:  ....
 6 3 19  8 7 5  2 149 14 
 4 279 79  3 1 29  8 6 5 
 8 129 5  269 69 4  7 139 13 
:++:
 7 189 2  569 3 689  16 145 146 
 5 6 3  7 4 1  9 2 8 
 19 189 4  569 2 689  3 157 167 
:++:
 123 5 178  4 68 2368  16 1378 9 
 1239 4 6  29 89 7  5 138 123 
 239 2789 789  1 5 23689  4 378 2367 
'''' 
One possibility to continue is the Finned XWing JasonLion mentioned:
Code:  ....
 6 3 19  8 7 5  2 149 14 
 4 279 79  3 1 29  8 6 5 
 8 129 5  269 69 4  7 139 13 
:++:
 7 189 2  569 3 689  16 145 146 
 5 6 3  7 4 1  9 2 8 
 19 189 4  #569 2 *689  3 157 *167 
:++:
 123 5 178  4 68 2368  16 1378 9 
 1239 4 6  29 89 7  5 138 123 
 239 2789 789  1 5 *23689  4 378 *2367 
''''
Finned XWing: 6 r69 c69 fr6c4 => r4c6<>6 
The following WWing is also present in the puzzle (together with the Finned XWing) and it leads to all Singles:
Code:  ....
 6 3 19  8 7 5  2 149 14 
 4 279 79  3 1 #29  8 6 5 
 8 129 5  269 #69 4  7 139 13 
:++:
 7 189 2  569 3 689  16 145 146 
 5 6 3  7 4 1  9 2 8 
 19 189 4  569 2 689  3 157 167 
:++:
 123 5 178  4 68 2368  16 1378 9 
 1239 4 6  #29 #89 7  5 138 123 
 239 2789 789  1 5 23689  4 378 2367 
''''
WWing: 2/9 in r2c6,r8c4 connected by 9 in r38c5 => r3c4,r79c6<>2 


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 stevegnet
 Joined: 24 Jan 2010  Posts: 4  :  Location: essex,UK  Items 

Posted: Sat Mar 20, 2010 2:42 pm Post subject: 


Well after coming back to this puzzle after about 2 months now each week it seems I have finally completed it. I did however try to understand these various named strategies posted to no avail. I would like to thank those who replied....THANK YOU!!!
Here's my logical? approach to it:
The 2's in box 1 eliminate the 2 at r8c2
The 1,2, 3's in box 7 column 1 eliminate the 9's in box 7 column 1
Therefore the remaining 9 in column 1 is in r6c1
The rest is straight forward from there on........Well it worked for me 

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 stevegnet
 Joined: 24 Jan 2010  Posts: 4  :  Location: essex,UK  Items 

Posted: Sat Mar 20, 2010 3:30 pm Post subject: 


Ooops! over looked the possibility of the 1 in r7c3 which puts the spanner in the works to my theory even if result was correct?.
Back to the drawing board. 

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