Asymmetrical Puzzle?

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Asymmetrical Puzzle?

Postby bradles » Mon Feb 27, 2006 2:07 am

Code: Select all
 *-----------*
 |.39|.6.|4..|
 |.8.|294|3.7|
 |4.7|813|59.|
 |---+---+---|
 |8..|326|971|
 |..3|.7.|..4|
 |671|948|253|
 |---+---+---|
 |3..|.8.|125|
 |..8|.52|.3.|
 |..2|.3.|.4.|
 *-----------*

 
 *-----------------------------------------------------------*
 | 12    3     9     | 57    6     57    | 4     18    28    |
 | 15    8     56    | 2     9     4     | 3     16    7     |
 | 4     26    7     | 8     1     3     | 5     9     26    |
 |-------------------+-------------------+-------------------|
 | 8     45    45    | 3     2     6     | 9     7     1     |
 | 29    29    3     | 15    7     15    | 68    68    4     |
 | 6     7     1     | 9     4     8     | 2     5     3     |
 |-------------------+-------------------+-------------------|
 | 3     469   46    | 467   8     79    | 1     2     5     |
 | 79    14    8     | 14    5     2     | 67    3     69    |
 | 579   1569  2     | 16    3     19    | 78    4     89    |
 *-----------------------------------------------------------*


Hi all,

I am having trouble with this puzzle. I am up to a point where even simple sudoku has no hint available. I entered the puzzle into simple sudoku, including the numbers I had solved, and it warned me that this puzzle is asymmetrical. Does that mean it could go either way or something?

Does anyone have any idea how to progress from here. I started trying to force chains on r1c1 but didn't get anywhere with it.

Brad
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Postby TKiel » Mon Feb 27, 2006 2:15 am

Brad,

Symmetry is generally an aesthetic thing, but it also helps one to catch errors when entering a starting grid, since many puzzles have symmetrical grids. If you entered cells that weren't part of the starting grid, the program may tell you that it isn't symmetrical, but that has nothing to do with whether the puzzle has more than one solution, which most programs will tell you is an invalid puzzle.

Is it possible for you to post the original starting grid?

Tracy
Last edited by TKiel on Sun Feb 26, 2006 11:45 pm, edited 1 time in total.
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Postby bradles » Mon Feb 27, 2006 2:18 am

TKiel wrote:Is it possible for you to post the origional starting grid?

Code: Select all
 *-----------*
 |.3.|...|4..|
 |...|29.|3..|
 |4.7|.1.|...|
 |---+---+---|
 |8..|3.6|.71|
 |...|...|...|
 |67.|9.8|..3|
 |---+---+---|
 |...|.8.|1.5|
 |..8|.52|...|
 |..2|...|.4.|
 *-----------*

Thanks Tracy
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Postby bradles » Mon Feb 27, 2006 2:28 am

I had to try forcing chains from r1c1 being either a 1 or a 2. Starting with r1c1 = 2 made a long chain that eventually couldn't go any further. Re-starting with r1c1=1 made another long winded chain that eventually lead to having two 7s in row 8 so r1c1 couldn't = 2 therefor must =1.

I had to use a graphics program to visualise this and mark it up. It's got me beat how you'd see this if you were using pencil and paper. How do people do this when they are using pencil and paper??

Brad
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Postby TKiel » Mon Feb 27, 2006 3:43 am

Brad,

Thanks for the starting grid. I got to the same spot as you and am now floundering. As for how people do it with pencil and paper, I have no idea. I also use Simple Sudoku and I have a hard time doing it with that. When I get to the point where I have to search for an un-obvious forcing chain, I basically surrender.

But I know somebody will provide a logical solution.

Tracy

P.s. I don't think Simple Simple gives hints for any techniques beyond an xyz-wing.
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Postby emm » Mon Feb 27, 2006 4:01 am

This is from Sudoku Susser.

Found a 7-link Simple Forcing Chain. If we assume that square R1C1 is <2> then we can make the following chain of conclusions:

R1C9 must be <8>, which means that
R9C9 must be <9>, which means that
R8C9 must be <6>, which means that
R8C7 must be <7>, which means that
R8C1 must be <9>, which means that
R5C1 must be <2>, which means that
R1C1 must be <1>.

Since this is logically inconsistent, R1C1 cannot be <2>

Take heart - this is the comment - "3282 links were considered before finding this chain":!:
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Postby Carcul » Mon Feb 27, 2006 11:44 am

Hi Bradles.

Bradles wrote:Does anyone have any idea how to progress from here. I started trying to force chains on r1c1 but didn't get anywhere with it.


The following nice loop:

[r8c1]=7=[r8c7]=6=[r5c7]=8=[r5c8]-8-[r1c8]-1-[r1c1]-2-[r5c1]-9-[r8c1],

which implies r8c1<>9 and that solve the puzzle.

Regards, Carcul
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Postby ravel » Mon Feb 27, 2006 1:06 pm

A bit shorter:
[r8c1]-9-[r8c9]-6-[r3c9]-2-[r3c2]=2=[r5c2]-2-[r5c1]-9-[r8c1]
ravel
 
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Postby tarek » Mon Feb 27, 2006 2:01 pm

if you would like experimenting with advanced techniques, try:
Code: Select all
*--------------------------------------------------------*
| 12    3     9    | 57    6     57   | 4     18    28   |
| 15    8     56   | 2     9     4    | 3     16    7    |
| 4    *26    7    | 8     1     3    | 5     9     26   |
|------------------+------------------+------------------|
| 8     45    45   | 3     2     6    | 9     7     1    |
| 29   *29    3    | 15    7     15   | 68    68    4    |
| 6     7     1    | 9     4     8    | 2     5     3    |
|------------------+------------------+------------------|
| 3    ^469  ^46   | 467   8     79   | 1     2     5    |
| 79    14    8    | 14    5     2    | 67    3     69   |
| 579  -1569  2    | 16    3     19   | 78    4     89   |
*--------------------------------------------------------*
Eliminating 6 from r9c2(ALS-XZ A=269 in r3c2, r5c2 B=469 in r7c3, r7c2  x=9 z=6)
*-----------------------------------------------*
| 12   3    9   | 57   6    57  | 4    18  %28  |
| 15   8    56  | 2    9    4   | 3    16   7   |
| 4   ^26   7   | 8    1    3   | 5    9   *26  |
|---------------+---------------+---------------|
| 8    45   45  | 3    2    6   | 9    7    1   |
| 29  ^29   3   | 15   7    15  | 68   68   4   |
| 6    7    1   | 9    4    8   | 2    5    3   |
|---------------+---------------+---------------|
| 3    469  46  | 47   8    79  | 1    2    5   |
| 79   14   8   | 14   5    2   | 67   3    69  |
| 579 -159  2   | 6    3    19  | 78   4   %89  |
*-----------------------------------------------*
Eliminating 9 from r9c2(ALS-XY  A=26 in r3c9   B=269 in r3c2,r5c2   C=289 in r9c9,r1c9   x=6 y=2 z=9)
*-----------------------------------------------*
| 12   3    9   | 57   6    57  | 4    18   28  |
| 15   8    56  | 2    9    4   | 3    16   7   |
| 4    26   7   | 8    1    3   | 5    9    26  |
|---------------+---------------+---------------|
| 8   *45   45  | 3    2    6   | 9    7    1   |
| 29   29   3   | 15   7    15  | 68   68   4   |
| 6    7    1   | 9    4    8   | 2    5    3   |
|---------------+---------------+---------------|
| 3   -469  46  | 47   8    79  | 1    2    5   |
| 79  *14   8   | 14   5    2   | 67   3    69  |
| 579 *15   2   | 6    3    19  | 78   4    89  |
*-----------------------------------------------*
r7c2 Must only have 69 as valid Candidates (145 is a Naked Triple in Column 2)
*-----------------------------------------------*
| 12   3    9   | 57   6    57  | 4    18   28  |
| 15   8    56  | 2    9    4   | 3    16   7   |
| 4   *26   7   | 8    1    3   | 5    9   ^26  |
|---------------+---------------+---------------|
| 8    45   45  | 3    2    6   | 9    7    1   |
| 29   29   3   | 15   7    15  | 68   68   4   |
| 6    7    1   | 9    4    8   | 2    5    3   |
|---------------+---------------+---------------|
| 3   %69   46  | 47   8    79  | 1    2    5   |
|-79   14   8   | 14   5    2   | 67   3   ^69  |
| 579  15   2   | 6    3    19  | 78   4    89  |
*-----------------------------------------------*
Eliminating 9 from r8c1(ALS-XY  A=26 in r3c2   B=269 in r8c9,r3c9   C=69 in r7c2   x=2 y=6 z=9)


Tarek
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Postby tso » Tue Feb 28, 2006 3:24 am

bradles wrote:I had to try forcing chains from r1c1 being either a 1 or a 2. Starting with r1c1 = 2 made a long chain that eventually couldn't go any further. Re-starting with r1c1=1 made another long winded chain that eventually lead to having two 7s in row 8 so r1c1 couldn't = 2 therefor must =1.

I had to use a graphics program to visualise this and mark it up. It's got me beat how you'd see this if you were using pencil and paper. How do people do this when they are using pencil and paper??

Brad



I've described one way to do this here.

I used a program in order to make diagrams suitable for posting, but I use this with pen and paper.
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Postby Myth Jellies » Tue Feb 28, 2006 10:14 am

Just for grins and giggles, there is a big old BUG-Lite+3 grid here
Code: Select all
 *-----------------------------------------------------------*
 |*12    3     9     | 57    6     57    | 4    *18   *28    |
 |*15    8    *56    | 2     9     4     | 3    *16    7     |
 | 4    *26    7     | 8     1     3     | 5     9    *26    |
 |-------------------+-------------------+-------------------|
 | 8    *45   *45    | 3     2     6     | 9     7     1     |
 |*29   *29    3     | 15    7     15    |*68   *68    4     |
 | 6     7     1     | 9     4     8     | 2     5     3     |
 |-------------------+-------------------+-------------------|
 | 3    *46+9 *46    | 467   8     79    | 1     2     5     |
 |*79    14    8     | 14    5     2     |*67    3    *69    |
 |*57+9 *59+16 2     | 16    3     19    |*78    4    *89    |
 *-----------------------------------------------------------*

To avoid the BUG-lite, it is pretty easy to show that either r9c1 or r9c6 equals 9, therefore you can remove 9 as a candidate from every other cell in row 9.
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