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Partially Solved Puzzle

 
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daj95376

Joined: 05 Feb 2006
Posts: 431
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PostPosted: Sun Apr 16, 2006 6:30 pm    Post subject: Partially Solved Puzzle Reply with quote

I'm in the process of trying to develop a puzzle generator that generates a filled grid and then produces a difficult puzzle from it. Speed is not a factor!

I'm still early in the development process and keep changing my (un-scientific) methodology. Until today, I haven't been able to generate anything that Simple Sudoku couldn't handle easily. Imagine my surprise when the following puzzle popped out during a test run. It's most likely just an anomaly where my generator stumbled onto a difficult puzzle. In any event, Simple Sudoku partially solves it (using F11) and then said "no hint available".

If someone has a free moment, I'd sure like to know the next technique needed to crack this puzzle. My own experience is limited. Thanks!

Code:
from Simple Sudoku:

 *-----------* "Original"
 |...|.5.|9.6|
 |...|68.|.2.|
 |76.|..4|.5.|
 |---+---+---|
 |..3|..8|..2|
 |1..|...|..9|
 |8..|4..|6..|
 |---+---+---|
 |.2.|7..|.95|
 |.5.|.42|...|
 |9.7|.3.|...|
 *-----------*


 *-----------* "Partially Solved"
 |28.|.5.|9.6|
 |53.|68.|.2.|
 |76.|2.4|853|
 |---+---+---|
 |6.3|..8|..2|
 |1.2|...|.89|
 |8.5|42.|63.|
 |---+---+---|
 |428|7..|395|
 |356|942|..8|
 |917|835|264|
 *-----------*

 
 *-----------------------------------------------------------*
 | 2     8     14    | 13    5     137   | 9     147   6     |
 | 5     3     149   | 6     8     179   | 147   2     17    |
 | 7     6     19    | 2     19    4     | 8     5     3     |
 |-------------------+-------------------+-------------------|
 | 6     479   3     | 15    179   8     | 1457  147   2     |
 | 1     47    2     | 35    67    36    | 457   8     9     |
 | 8     79    5     | 4     2     19    | 6     3     17    |
 |-------------------+-------------------+-------------------|
 | 4     2     8     | 7     16    16    | 3     9     5     |
 | 3     5     6     | 9     4     2     | 17    17    8     |
 | 9     1     7     | 8     3     5     | 2     6     4     |
 *-----------------------------------------------------------*
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vidarino

Joined: 10 Feb 2006
Posts: 38
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Location: Haugesund, Norway

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PostPosted: Sun Apr 16, 2006 7:31 pm    Post subject: Reply with quote

There aren't any trivial techniques that cracks this one, it seems, but the following nice loop does it;
Code:
R2C6-7-R2C9-1-R6C9=1=R6C6=9=R2C6
-> R2C6 <> 7


The notation is thoroughly explained in a post on the Players' forum. (I can look up the direct link if need be.)

Quick and dirty explanation; if R2C6 were 7 it would wipe out all the 9s from column 6.
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Carcul

Joined: 29 Dec 2005
Posts: 50
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Location: Coimbra, Portugal

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PostPosted: Fri Jun 16, 2006 6:35 pm    Post subject: Another Solution Reply with quote

[r5c5](-7-[r4c5|r5c7])-7-[r5c2]-4-[r5c7]-5-[r5c4]-3-[r1c4](-1-[r2c6])-1-
-[r1c3]-4-[r2c3]-{TILA(1): r2c3|r3c3|r3c5|r4c5|r6c6|r6c9|r2c9|},
=> r5c5<>7 and the puzzle is solved.

Carcul
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daj95376

Joined: 05 Feb 2006
Posts: 431
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PostPosted: Fri Jun 16, 2006 9:07 pm    Post subject: Reply with quote

Carcul, Thank You for your solution!

Code:
*-----------------------------------------------------------*
| 2     8     14    | 13    5     137   | 9     147   6     |
| 5     3     149   | 6     8     179   | 147   2     17    |
| 7     6     19    | 2     19    4     | 8     5     3     |
|-------------------+-------------------+-------------------|
| 6     479   3     | 15    179   8     | 1457  147   2     |
| 1     47    2     | 35    67    36    | 457   8     9     |
| 8     79    5     | 4     2     19    | 6     3     17    |
|-------------------+-------------------+-------------------|
| 4     2     8     | 7     16    16    | 3     9     5     |
| 3     5     6     | 9     4     2     | 17    17    8     |
| 9     1     7     | 8     3     5     | 2     6     4     |
*-----------------------------------------------------------*

Since my original posting, I've advanced my solving techniques a little.

Code:
[r3c5]=1 =>                                                 [r7c5]=6
         => [r1c4]=3 => [r1c6]=7 => [r2c6]=9 => [r6c6]=1 => [r7c6]=6

Results in [r3c5]=9 and the puzzle is solved with a cascade of singles.


Last edited by daj95376 on Wed Sep 13, 2006 9:23 am; edited 1 time in total
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Perry

Joined: 13 Jul 2006
Posts: 3
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Location: Geneva

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PostPosted: Fri Jul 14, 2006 4:29 pm    Post subject: Partially Solved Puzzle Reply with quote

Hi,

My program found XY-Chain: r3c5-r1c4-r5c4-r4c4-r6c6
must contain 9 at head or tail, so 9 can be crossed out of
r2c6 and r3c5

Perry
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fermat

Joined: 05 Feb 2006
Posts: 25
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Location: Melbourne

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PostPosted: Sat Jul 15, 2006 12:51 am    Post subject: Re: Partially Solved Puzzle Reply with quote

Perry wrote:
Hi,

My program found XY-Chain: r3c5-r1c4-r5c4-r4c4-r6c6
must contain 9 at head or tail, so 9 can be crossed out of
r2c6 and r3c5

Perry


That should read "r4c5", r3c5 is 9. Wink
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Perry

Joined: 13 Jul 2006
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Location: Geneva

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PostPosted: Mon Jul 17, 2006 3:13 pm    Post subject: Re: Partially Solved Puzzle Reply with quote

You're right, thanks for dorrecting, my apologies for the typo.

Perry
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