UR with diagonal?

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UR with diagonal?

Postby skjalg » Wed Nov 05, 2008 10:04 am

Start with original puzzle:

Code: Select all
*---+---+---*
|.62|3..|..8|
|3..|...|261|
|.1.|..6|374|
|---+---+---|
|.4.|..7|.3.|
|...|.9.|8..|
|...|4..|5..|
|---+---+---|
|45.|.3.|.8.|
|..8|...|...|
|9..|7.1|.2.|
*---+---+---*


After some rounds I get:
Code: Select all
*---+---+---*
|762|314|958|
|3.4|.7.|261|
|.1.|.26|374|
|---+---+---|
|.4.|.57|.3.|
|...|.9.|84.|
|...|46.|5..|
|---+---+---|
|45.|.3.|.8.|
|..8|.4.|..3|
|936|781|425|
*---+---+---*

*---------------+-----------------+---------------*
| 7    6    2   |  3    1     4   | 9    5    8   |
| 3    89   4   | #59   7    #589 | 2    6    1   |
| 58   1    59  |  89   2     6   | 3    7    4   |
|---------------+-----------------+---------------|
| 68   4    19  |  128  5     7   | 16   3    269 |
| 56   27   1357|  12   9     23  | 8    4    267 |
| 12   89   379 |  4    6     238 | 5    19   279 |
|---------------+-----------------+---------------|
| 4    5    17  |  269  3     29  | 17   8    69  |
| 12   27   8   | #569  4    #59  | 67   19   3   |
| 9    3    6   |  7    8     1   | 4    2    5   |
*---------------+-----------------+---------------*


Do the cells r2c4, r2c6 and r8c4, r8c6 form a UR so that candidate 9 can be removed from the cells with the surplus candidates? If not, what is the better way to proceed?

I appreciate the feedback.

_Skjalg
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Postby eleven » Wed Nov 05, 2008 11:23 am

Are you teasing me because of my typos ?:)

"candidate 5 can be removed from the cells with the surplus candidates"
i.e. r2c4=5 and r9c6=5.

This is easily found, because of the 4 strong links for 5, e.g.
r2c4=9 -> (r2c6=5 & r8c4=5) -> r8c6=9 - deadly pattern.

But this does not solve it yet.
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Postby DonM » Wed Nov 05, 2008 11:54 am

skjalg: This is a classic type 6 UR: Simply put, if you find a UR with extra candidates diagonally opposite each other, if one of the digits of the UR itself forms a perfect x-wing, which is true of the 5 in this case, then that digit, the 5, can be removed from the corners with extra candidates. (Perfect x-wing means that the digit appears nowhere else in the row & column occupied by the UR or, another way of putting it, consists of all strong links, as eleven notes above.)
Last edited by DonM on Wed Nov 05, 2008 2:37 pm, edited 3 times in total.
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Postby ArkieTech » Wed Nov 05, 2008 12:29 pm

eleven wrote:But this does not solve it yet.


Look for a 2 string kite.
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Postby skjalg » Wed Nov 05, 2008 6:35 pm

Are you teasing me because of my typos ?


Well, on this page there is still a typo:
http://www.sudoku9981.com/sudoku-solving/Uniqueness-Test.asp
Uniqueness Test 6

Uniqueness Test 6 is very similar to Uniqueness Test 4, and can be stated as follows:

Suppose exactly two cells in the rectangle contain extra candidates, and they are located diagonally across each other in the rectangle. Suppose the common candidates are U and V, and none of the other cells in the two rows and two columns containing the rectangle contain U. Then V can be eliminated from these two cells.


Which confused me:) . Now, I managed to proceed.

Look for a 2 string kite.

Personaly I used Multi Colour 1 as the last stepping stone.

Again, thanks for the feedback from all of you!

_Skjalg
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Re: UR with diagonal?

Postby RW » Mon Nov 10, 2008 8:14 am

Code: Select all
*---------------+-----------------+---------------*
| 7    6    2   |  3    1     4   | 9    5    8   |
| 3    89   4   | #59   7    #589 | 2    6    1   |
| 58   1    59  |  89   2     6   | 3    7    4   |
|---------------+-----------------+---------------|
| 68   4    19  |  128  5     7   | 16   3    269 |
| 56   27   1357|  12   9     23  | 8    4    267 |
| 12   89   379 |  4    6     238 | 5    19   279 |
|---------------+-----------------+---------------|
| 4    5    17  |  269  3     29  | 17   8    69  |
| 12   27   8   | #569  4    #59  | 67   19   3   |
| 9    3    6   |  7    8     1   | 4    2    5   |
*---------------+-----------------+---------------*

You may use this UR to eliminate 5 from r2c6 and r8c4, as suggested in earlier replies, AND you may also use it to eliminate 9 from r8c4 (can you see why?). This solves the puzzle.

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Postby Luke » Mon Nov 10, 2008 10:37 am

It might have something to do with [89] in r3c4 forcing 9 into r2c6 and a DP.
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Postby RW » Mon Nov 10, 2008 11:57 am

Luke451 wrote:It might have something to do with [89] in r3c4 forcing 9 into r2c6 and a DP.

That's one way of looking at it, though for that you would need to know all the possible candidates in the involved cells. I prefer to look at the grouped link in box 2 or column 6: if r8c4=9 => r2c6=9 (hidden single in box/column). This is a very common UR and it's easy to spot even without pms.

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