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help me Help Me!!

Postby marland » Mon May 01, 2006 4:58 pm

Hi I like to think that im a good sudokuplayer but im getting stuck more often.

really need help with this one THANKS

3 7 2 | . . . | 4 6 .
4 . . | 7 . . | . 8 2
9 8 1 | 4 2 6 | 3 5 7
-------+-------+-------
8 . 3 | 6 4 5 | 2 7 .
2 . 7 | . . . | 6 . 5
. . . | 2 7 9 | 8 . 3
-------+--------+------
7 3 9 | 8 1 4 | 5 2 6
5 . 8 | . . 2 | 7 . 4
. 2 4 | . . 7 | . 3 8
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Postby Sped » Mon May 01, 2006 5:20 pm

Code: Select all
 *-----------------------------------------------------------*
 | 3     7     2     | 159   589   18    | 4     6     19    |
 | 4     56    56    | 7     359   13    | 19    8     2     |
 | 9     8     1     | 4     2     6     | 3     5     7     |
 |-------------------+-------------------+-------------------|
 | 8     19    3     | 6     4     5     | 2     7     19    |
 | 2     149   7     | 13    38    138   | 6     149   5     |
 | 16    1456  56    | 2     7     9     | 8     14    3     |
 |-------------------+-------------------+-------------------|
 | 7     3     9     | 8     1     4     | 5     2     6     |
 | 5     16    8     | 39    369   2     | 7     19    4     |
 | 16    2     4     | 59    569   7     | 19    3     8     |
 *-----------------------------------------------------------*

You'll notice that the 1s in box 5 are restricted to row 5. That allows you to exclude 1s from r5c2 and r5c8. Resulting in:

Code: Select all
 
 *-----------------------------------------------------------*
 | 3     7     2     | 159   589   18    | 4     6     19    |
 | 4     56    56    | 7     359   13    | 19    8     2     |
 | 9     8     1     | 4     2     6     | 3     5     7     |
 |-------------------+-------------------+-------------------|
 | 8     19    3     | 6     4     5     | 2     7     19    |
 | 2     49    7     | 13    38    138   | 6     49    5     |
 | 16    1456  56    | 2     7     9     | 8     14    3     |
 |-------------------+-------------------+-------------------|
 | 7     3     9     | 8     1     4     | 5     2     6     |
 | 5     16    8     | 39    369   2     | 7     19    4     |
 | 16    2     4     | 59    569   7     | 19    3     8     |
 *-----------------------------------------------------------*


If you color on 1s you get massive eliminations which bust the puzzle wide open:

Code: Select all
 *-----------------------------------------------------------*
 | 3     7     2     | 159   589   18    | 4     6     19A   |
 | 4     56    56    | 7     359   13A   | 19B   8     2     |
 | 9     8     1     | 4     2     6     | 3     5     7     |
 |-------------------+-------------------+-------------------|
 | 8     19A   3     | 6     4     5     | 2     7     19B   |
 | 2     49    7     | 13    38    138   | 6     49    5     |
 | 16A   1456  56    | 2     7     9     | 8     14A   3     |
 |-------------------+-------------------+-------------------|
 | 7     3     9     | 8     1     4     | 5     2     6     |
 | 5     16A   8     | 39    369   2     | 7     19B   4     |
 | 16B   2     4     | 59    569   7     | 19A   3     8     |
 *-----------------------------------------------------------*


Conjugate pairs of 1s are marked A and B above. The As share a group in box 4 and in row 6. So the As cannot be 1s. Eliminate 1s from all the A cells and set all the B cells to 1.

It's all singles after that.

An alternative solution would be the XY chain:

9-(r9c7)-1-(r9c1)-6-(r6c1)-1-(r4c2)-9-(r4c9)-1-(r1c9)-9

which eliminates the 9 in r2c7, reducing the puzzle to singles.
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Posts: 126
Joined: 26 March 2006

Postby re'born » Mon May 01, 2006 9:11 pm

Code: Select all
 *-----------------------------------------------------------*
 | 3     7     2     | 159   589   18    | 4     6     19    |
 | 4    *56   *56    | 7     359   13    | 19    8     2     |
 | 9     8     1     | 4     2     6     | 3     5     7     |
 |-------------------+-------------------+-------------------|
 | 8     19    3     | 6     4     5     | 2     7     19    |
 | 2     149   7     | 13    38    138   | 6     149   5     |
 | 16   *1456 *56    | 2     7     9     | 8     14    3     |
 |-------------------+-------------------+-------------------|
 | 7     3     9     | 8     1     4     | 5     2     6     |
 | 5     16    8     | 39    369   2     | 7     19    4     |
 | 16    2     4     | 59    569   7     | 19    3     8     |
 *-----------------------------------------------------------*


Or you could note the UR in cells r2c23 and r6c23. This allows you to eliminate 5 and 6 from r6c2 and from here the puzzle is all singles.
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Postby underquark » Mon May 01, 2006 9:49 pm

And the 56 56 in box one knocks out the 5 in r2c6
And the 138 triple in box 5 knocks out the other 1s in r5
etc.?
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Postby Sped » Mon May 01, 2006 10:50 pm

underquark wrote:

And the 56 56 in box one knocks out the 5 in r2c6

I think you mean the 5 in r2c5

And the 138 triple in box 5 knocks out the other 1s in r5

Yes it does.

But you're still left with coloring on 1s, the XY chain or the UR thing.

I vote for rep'nA's solution with unique rectangles. It's the simplest and easiest solution that reduces the puzzle to singles.
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Postby TKiel » Mon May 01, 2006 11:31 pm

Sped wrote:I vote for rep'nA's solution with unique rectangles. It's the simplest and easiest solution that reduces the puzzle to singles.


True, but only if one knows how to use the UR to make the exclusions. Perhaps a bit much in this case when naked pairs and triples were underutilized.

Tracy
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Postby QBasicMac » Tue May 02, 2006 12:06 am

Marland hasn't replied so I'll try too

Either r9c1=1 or c8c2=1
r9c1=1 --> r9c9=1 --> r4c9=1 --> r4c2<>1
r8c2=1 --> r4c2<>1
Puzzle solved

Mac
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Postby Steve R » Tue May 02, 2006 2:01 am

Another elementary approach is to note that there are only two places for 1 in row 4 (columns 2 and 9) and in row 8 (columns 2 and 8). As column 2 can accommodate only a single 1, at least one of r4c9 and r8c8 must contain1, which means that r6c8 contains 4.

Steve
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Postby re'born » Tue May 02, 2006 2:13 am

Steve R wrote:Another elementary approach is to note that there are only two places for 1 in row 4 (columns 2 and 9) and in row 8 (columns 2 and 8). As column 2 can accommodate only a single 1, at least one of r4c9 and r8c8 must contain1, which means that r6c8 contains 4.

Steve


Steve,

Nice find. The pattern is an example of a skyscraper, a special case of multicoloring. It also implies that r5c8 is not a 1.
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Postby tarek » Tue May 02, 2006 10:31 am

you can always use the finned x-wing
Code: Select all
*--------------------------------------------------------*
| 3     7     2    | 159   589   18   | 4     6     19   |
| 4     56    56   | 7     39    13   | 19    8     2    |
| 9     8     1    | 4     2     6    | 3     5     7    |
|------------------+------------------+------------------|
| 8     19    3    | 6     4     5    | 2     7     19   |
| 2     49    7    | 13    38    138  | 6     49    5    |
|*16    1456  56   | 2     7     9    | 8    *14    3    |
|------------------+------------------+------------------|
| 7     3     9    | 8     1     4    | 5     2     6    |
|*5    -16    8    | 39    369   2    | 7    *19    4    |
|#16    2     4    | 59    569   7    | 19    3     8    |
*--------------------------------------------------------*
Eliminating 1 From r8c2 (Finned XWing in Columns 18)


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Postby marland » Tue May 02, 2006 4:21 pm

Thanks to all.

:D

I must admitt I only understand the steve way yet. Ill take it home and study it.
- I had some trouble understanding how the A's in box 4 and row 6 cannot be 1s. (because they share a group?)
- I have to find out what the UR is (Unconditional Response??)

anyway, thanks

Marland
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Postby Sped » Tue May 02, 2006 6:58 pm

marland wrote:Thanks to all.

:D


- I had some trouble understanding how the A's in box 4 and row 6 cannot be 1s. (because they share a group?)
- I have to find out what the UR is (Unconditional Response??)

anyway, thanks

Marland

That's right. The A's share a group. So if the A's are 1s there'd be two 1s in the same box, which is impossible. So all the As have their 1s eliminated, and all the Bs get set to 1.

UR stands for "Unique Rectangle" It's a neat trick that presents itself from time to time. There is a sticky post on the Advanced solving methods forum that has links explaining URs, coloring, and other methods.
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Postby ravel » Tue May 02, 2006 9:00 pm

I have already answered this UR question elsewhere:

This site explains types 1-4 very good, see also the original thread here.
See here for type 5.
Currently there is a discussion about other types here.
flagitious and Hans first introduced it in this thread (July 05).
Last edited by ravel on Wed May 03, 2006 3:30 am, edited 1 time in total.
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Postby Crazy Girl » Tue May 02, 2006 9:55 pm

edit: no longer relevant
Last edited by Crazy Girl on Thu May 04, 2006 8:01 am, edited 1 time in total.
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Postby ravel » Wed May 03, 2006 7:31 am

Thanks Crazy, i corrected it.
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