No hint on Simple Sudoku

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No hint on Simple Sudoku

Postby caderoux » Thu Mar 16, 2006 5:05 am

http://www.sudocue.net/olddaily.php?id=93&sol=0

Code: Select all
 *-----------*
 |.75|...|...|
 |...|.3.|92.|
 |4..|..7|1..|
 |---+---+---|
 |..3|..9|2..|
 |.6.|...|.5.|
 |..8|1..|7..|
 |---+---+---|
 |..7|5..|..4|
 |.82|.4.|...|
 |...|...|81.|
 *-----------*


What's the deal - why no hints after a certain point? Are there multiple valid solutions?
caderoux
 
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Joined: 15 March 2006

Postby re'born » Thu Mar 16, 2006 5:48 am

caderoux,

I presume that you are using Simple Sudoku. The program only has so many human ready hints available. That is, if the sudoku "requires" more than hidden and naked sets, intersection removal (which it calls locked candidates) x-wings, xy-wings, coloring and multicoloring, eventually, Simple Sudoku will run out of hints. That is not to say that it can't solve it. It already has, just not using the above patterns.

In your puzzle, the candidate grid should be
Code: Select all
 23   7    5|  9    1    268  | 346 3468 368|
 8    1    6|  4    3    5    | 9   2    7  |
 4    23   9| #268 #268  7    | 1   368  5  |
 -----------+-----------------+-------------|
 57  -45   3| #68  #5678 9    | 2   468  1  |
 79   6    1|  238  278  2348 | 34  5    389|
 25   2459 8|  1    56   346  | 7   3469 36 |
 -----------+-----------------+-------------|
 1    39   7|  5    28   28   | 36  369  4  |
 369  8    2|  36   4    1    | 5   7    39 |
 356  35   4|  7    9    36   | 8   1    2  |
 *----------+-----------------+-------------|


Notice that the cells in (3,[45]) and (4,[45]) will form a deadly pattern on <68> if (3,[45])!2 and (4,5)![57] . But (4,2)5 implies (4,5)!5 and it implies that (4,1)7 > (4,5)!7. Moreover, (4,1)7 > (6,1)2 > (1,1)3 > (3,2)2 > (3,[45])!2 . Therefore, (4,2)4.

This does not solve the puzzle completely, but it gets you back to a point where Simple Sudoku can give you hints.
re'born
 
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Postby Carcul » Thu Mar 16, 2006 10:38 am

Hi Caderoux.

Welcome to this forum. Here is a nice loop that also simplifies the puzzle (refer to the grid posted by rep'nA):

[r8c9]=9=[r8c1]-9-[r7c2]=9=[r6c2]=2=[r3c2]-2-[r3c4]=2=[r5c4]=3=[r8c4]-3-[r8c9], => r8c9<>3.

Regards, Carcul
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Postby Carcul » Sat Sep 30, 2006 1:57 pm

And here's a solution:

We have r4c8=6 or r6c2=9, and also r5c4=2 or r1c9/r5c9=3. But

[r4c8]=6|9=[r6c2]-9-[r7c2]=9=[r7c8]-9-[r8c9]-3-[r6c9]-6-[r4c8]

which implies r1c9/r5c9<>3 => r5c4=2 and the puzzle is solved.

Carcul
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Postby ravel » Sat Sep 30, 2006 8:37 pm

Nice solutions. To give a third notation (i like rep'nA's new one [ah, was it aeb ?]):
r5c1=7 => r8c1=9 => r8c4=6 => r4c4=8 => r4c8<>8 => r5c9=8 => r5c1=9
=> r4c1=7
Solves with an xy-wing then.
ravel
 
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Postby re'born » Mon Oct 02, 2006 12:25 pm

ravel wrote:To give a third notation (i like rep'nA's new one [ah, was it aeb ?])


It was aeb. I prefer his notation, and used it for a while trying to inspire others to turn, but, alas, the rXcY notation had pretty much become the standard. Oh well. In any case, nice solution ravel.
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Postby amirzadeh » Tue Oct 10, 2006 7:46 pm

Carcul wrote:Hi Caderoux.

Welcome to this forum. Here is a nice loop that also simplifies the puzzle (refer to the grid posted by rep'nA):

[r8c9]=9=[r8c1]-9-[r7c2]=9=[r6c2]=2=[r3c2]-2-[r3c4]=2=[r5c4]=3=[r8c4]-3-[r8c9], => r8c9<>3.

Regards, Carcul


Trying to follow the notations how did you get r8c9=9 in the first place though. Is that a guess?
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Postby Carcul » Tue Oct 10, 2006 9:25 pm

Amirzadeh wrote:Trying to follow the notations how did you get r8c9=9 in the first place though.


The notation doesn't mean that r8c9=9. [r8c9]=9=[r8c1] is a strong link. Check here for an explanation.

Carcul
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Postby ravel » Tue Oct 10, 2006 10:16 pm

Amirzadeh,

you can read it like this:
r8c9<>9 => r8c1=9 => r7c2<>9 => r6c2=9 => r3c2=2 => r3c4<>2 => r5c4=2 => r8c4=3 => r8c9<>3
i.e, if r8c9 is not 9, then it also cannot be 3, so in any case it is 9
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Postby re'born » Wed Oct 11, 2006 10:29 am

ravel,

There needs to be a sticky note containing just your previous post.

rep'nA
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