## UR with diagonal?

Post the puzzle or solving technique that's causing you trouble and someone will help

### UR with diagonal?

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
skjalg

Posts: 7
Joined: 21 October 2008

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.
eleven

Posts: 1901
Joined: 10 February 2008

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.
DonM
2013 Supporter

Posts: 475
Joined: 13 January 2008

eleven wrote:But this does not solve it yet.

Look for a 2 string kite.
dan

ArkieTech

Posts: 3000
Joined: 29 May 2006
Location: NW Arkansas USA

Are you teasing me because of my typos ?

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
skjalg

Posts: 7
Joined: 21 October 2008

### Re: UR with diagonal?

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.

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

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

Luke
2015 Supporter

Posts: 435
Joined: 06 August 2006
Location: Southern Northern California

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.

RW
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006