The New Sudoku Players' Forum

[caderoux]

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?

[re'born]

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.

[Carcul]

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

[Carcul]

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

[ravel]

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.

[re'born]

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.

[amirzadeh]

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?

[Carcul]

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

[ravel]

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

[re'born]

ravel,

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

rep'nA