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UR Type 5???

 
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Mon Aug 14, 2006 7:00 pm    Post subject: UR Type 5??? Reply with quote

Ran across this today, and I thought I'd get your take on it:

Code:
8 6  4    1 7 2  9   3 5
3 5  27   9 4 6  278 1 28
9 17 127  3 5 8  27  6 4


If r3c2 = <1> ==> r2c3, r3c3 = <27>
If r3c2 = <7> ==> r2c3 = <2> ==> r3c3 = <7>

In either case (based on UR theory in the first case), r2c7 cannot = <2>, and the 2 can be eliminated as a candidate for that cell.

Using that same logic, you can also eliminate the 7 as a candidate from r3c3.

Unfortunately, neither of those tidbits solved the puzzle (it's today's Brian Basher's Super Hard, turned ninety degrees so it is easier to see the UR), but I thought it was interesting.

I assume this isn't new, but I haven't run across it before, and it seems like it would happen fairly often and occasionally be useful.

Any thoughts?
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keith



Joined: 19 Sep 2005
Posts: 3179
Location: near Detroit, Michigan, USA

PostPosted: Mon Aug 14, 2006 7:13 pm    Post subject: UR Type 5 Reply with quote

AZ,

You are correct, and it is actually called a type 5. It is very rare; can you post the original puzzle? Take a look at

----- Unique Rectangles http://www.sudoku.com/forums/viewtopic.php?p=29105#29105
---------- Types 1-4 http://www.setbb.com/phpbb/viewtopic.php?p=2441
----------------------- http://www.sudoku.com/forums/viewtopic.php?t=2000
---------- Diagonal and X-wing types http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?p=2894#2894

which are links taken from Mike Barker's list of solution techniques:

http://www.sudoku.com/forums/viewtopic.php?p=21804#21804

Keith
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Mon Aug 14, 2006 8:54 pm    Post subject: UR 5 Reply with quote

It is today's (August 14) Super Hard at brainbashers.com. I didn't post it because it didn't help solve the puzzle, and I finally found an xy-wing that brought the puzzle down all at once, but here it is:

006402900
040080050
900050004
400708001
068000540
700503002
600030009
070090010
009607400

It is in boxes 3 and 9.

It seems like it wouldn't be that rare to find that pattern in two boxes with trips remaining, but I certainly never looked for it before. I suppos some would argue that it is like forcing chains in a UR format. Rolling Eyes
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keith



Joined: 19 Sep 2005
Posts: 3179
Location: near Detroit, Michigan, USA

PostPosted: Mon Aug 14, 2006 10:07 pm    Post subject: Well, not Type 5 Reply with quote

AZ,

I was incorrect, this is not a Type 5 (which is a diagonal form of Type 2). It is a Type 7 or greater, look at:

http://www.sudoku.com/forums/viewtopic.php?t=4088

Type 6 is a UR on an X-wing, see

http://www.sudoku.com/forums/viewtopic.php?t=3709&start=0

The classifications into types do not much matter to me. Rather, it is the idea of blending UR's with strong links. You say:

Quote:
I suppos some would argue that it is like forcing chains in a UR format.


which I think is exactly correct. The neat thing is, the UR gives you set of cells to look for a short chain, and the criterion is to avoid the non-unique pattern.

By the way, I get to this point:

Code:
+-------------+-------------+-------------+
| 15  15  6   | 4   7   2   | 9   3   8   |
| 2   4   37  | 139 8   19  | 17  5   6   |
| 9   8   37  | 13  5   6   | 127 27  4   |
+-------------+-------------+-------------+
| 4   25  25  | 7   6   8   | 3   9   1   |
| 3   6   8   | 129 12  19  | 5   4   7   |
| 7   9   1   | 5   4   3   | 8   6   2   |
+-------------+-------------+-------------+
| 6   125 245 | 128 3   45  | 27  278 9   |
| 58  7   245 | 28  9   45  | 6   1   3   |
| 18  3   9   | 6   12  7   | 4   28  5   |
+-------------+-------------+-------------+


Did you notice FOUR UR's? There is a Type 4 R25C46, a Type 2 R78C36, yours R37C78, and another R47C23. You don't need all of them to get here:

Code:
+-------------+-------------+-------------+
| 15  15  6   | 4   7   2   | 9   3   8   |
| 2   4   37  | 39  8   19  | 17  5   6   |
| 9   8   37  | 13  5   6   | 12  27  4   |
+-------------+-------------+-------------+
| 4   2   5   | 7   6   8   | 3   9   1   |
| 3   6   8   | 29  12  19  | 5   4   7   |
| 7   9   1   | 5   4   3   | 8   6   2   |
+-------------+-------------+-------------+
| 6   15  24  | 128 3   45  | 27  78  9   |
| 58  7   24  | 28  9   45  | 6   1   3   |
| 18  3   9   | 6   12  7   | 4   28  5   |
+-------------+-------------+-------------+


This is a BUG+1: R7C4 must be <2>.

Otherwise your XY-wing <128> in R89 says R8C1 is not <8>. It solves the puzzle without any of the UR's!

Still, I think, a nice example of uniqueness arguments!

Keith
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Tue Aug 15, 2006 4:46 pm    Post subject: Uniqueness theory Reply with quote

I did note the potential URs, but the xy-wing jumped out at me as I was looking at them and it solved the puzzle.

If only the puzzle didn't have the xy-wing solve -- it would be unique in my (limited) experience, and my solve on the R37C78 would have in fact been criotical. (I get discouraged when I think I've found a strong solve, and it turns out there was a simpler way to do it.)

I realize now that uniqueness theory has always been critical to my solving techniques for seriously difficult puzzles. It is that imbalance, the lack of symetry, the sense that a certain group of numbers just can't quite fit into the allotted space, that points the way -- almost invariably -- to a significant and helpful solution.

Thanks for breaking the puzzle down, Keith.
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