Undeadly UR Patterns

Advanced methods and approaches for solving Sudoku puzzles

Undeadly UR Patterns

Postby Bud » Sat Aug 30, 2008 5:10 pm

Until recently I have always been pro UR and thought the UR pattern was deadly. I have cracked countless puzzles using this technique. I started working a number of the Sudoku9981 expert and extreme puzzles. On 2 out of hundreds of these puzzles, I came across type 1 UR patterns and when I applied the technique I quickly ran into a contradiction. At first I assumed that the puzzles did not have a unique solution, but I used other techniques to solve at least one of these and a unique solution did exist with a UR pattern. I thought about logical arguments for why the pattern is called deadly. Certainly the candidates in the pattern can be interchanged and the row and columns are still valid, but ahat about the boxes? Shouldn't one investigate if these are interchangeable in the boxes also before using this technique? Now I only use this technique as a last resort and I check the boxes where the cells are before I use it. Has anyone else encountered these undeadly UR patterns in puzzles they have worked. The puzzle that I have worked is Sudoku9981 Expert Book 26 #8. The Type 1 UR pattern in a partially worked puzzle is in row 3 and 7 and columns 6 and 7. Three of the cells in the rectangular pattern have 35 as candidates and the other has 357. Here is the partially worked pattern. To get to this point in the puzzle I used a 3 x-wing, a 9 2-string kite and a 4 2-string kite. I have not shown the candidates in the cells marked -. Setting r7c7 = 7 as the type 1 UR rule suggests leads to a contradiction. The undeadly 35 UR pattern exists but the puzzle has a unique solution. I did not use the information obtained from the random contradiction to finish solving this puzzle because that would be trial and error.

| - 3 - | - - - | 2 - - |
| - 6 5 | 2 - 4 | - - 1 |
| 7 1 2 | 6 8 35 | 35 4 9 |

| 5 9 - | - - 6 | - 7 2 |
| 1 2 - | - - 8 | - 9 - |
| - 7 6 | 5 2 9 | - - 3 |

| 6 8 1 | 9 4 35 | 357 2 - |
| - 4 9 | - - 7 | - - 8 |
| - 5 7 | 8 - - | 9 - 4 |
Last edited by Bud on Sat Aug 30, 2008 6:06 pm, edited 8 times in total.
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Postby daj95376 » Sat Aug 30, 2008 6:16 pm

There have been posts in the past by people who misunderstood the constraints on a UR pattern and wanted to know why a UR Type 1 failed to work. It turned out that they didn't have a valid pattern.

If you still think that you've encountered an exception, maybe you can share a real example with us.
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Postby DonM » Sat Aug 30, 2008 7:29 pm

I seem to remember someone bringing up that premise some time ago (not sure where) and it turned out that when an example was given, the alleged UR was in the same box, not across 2 boxes.
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Re: Undeadly UR Patterns

Postby daj95376 » Sat Aug 30, 2008 11:00 pm

Bud wrote:The Type 1 UR pattern in a partially worked puzzle is in row 3 and 7 and columns 6 and 7.

You made the classic mistake of having the UR reside in four boxes. A UR exists in: two rows, two columns, and two boxes.
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Postby ab » Sun Aug 31, 2008 7:35 am

DonM wrote:I seem to remember someone bringing up that premise some time ago (not sure where) and it turned out that when an example was given, the alleged UR was in the same box, not across 2 boxes.

I made a similar mistake here:
http://forum.enjoysudoku.com/viewtopic.php?t=3957
it's across four boxes:!:
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Postby udosuk » Wed Sep 03, 2008 12:47 am

The stranger thing to me is your example at that state could be solved with singles and naked pairs but you were still looking for that incorrect UR pattern.:!:
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