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David
Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK
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 Posted: Tue Aug 29, 2006 10:41 am Post subject: 29 August V Hard |
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| This seemed a bit of a struggle for me, so perhaps I missed something obvious. Did anyone solve it without using a UR ? |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Tue Aug 29, 2006 11:42 am Post subject: |
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| Alternatively to the UR there is an x-wing in 4. |
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David
Joined: 02 Jun 2006
Posts: 58
Location: Bedford, UK
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| Posted: Tue Aug 29, 2006 1:27 pm Post subject: |
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| Thanks, I will have another look. |
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mazin
Joined: 05 Aug 2006
Posts: 2
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| Posted: Tue Aug 29, 2006 9:33 pm Post subject: |
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What is a UR?
I am at
6 / / / 3 / 9 / /
/ 9 / 2 / 7 3 8 /
/ 4 3 / / / 5 2 /
9 / 4 / 7 / / 1 /
3 / / 1 / 4 / / 9
/ 3 6 / / 2 / 9 /
2 5 9 6 / 8 / 3 /
/ 1 / / 9 / / / 2
I know from the Hint on Draw / Play that a 6 goes in Ig, but why?
Could someone explain?
Thank you!
I am at the stage where I can use the basis steps to solve the straightforward puzzles, but I need some examples of how to eliminate numbers from cells where the obvious methods leave multiple options. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Tue Aug 29, 2006 9:40 pm Post subject: |
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Mazin,
The puzzle you posted has only 8 rows.
UR is a Unique Rectangle.
Keith |
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George Woods
Joined: 28 Mar 2006
Posts: 304
Location: Dorset UK
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| Posted: Tue Aug 29, 2006 11:25 pm Post subject: |
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| The xwing in 4 rows 2 and 8 allow the naked pair 47 to be found in row 7, forcing 8 to lie in box 7 on row 9 so 7 is forced to be on row 8 of box 9 so r9c7 can be neither 8 nor 7 - so must be 6! |
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Bill Denholm
Joined: 24 Mar 2006
Posts: 17
Location: Mountain View, California
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| Posted: Tue Aug 29, 2006 11:43 pm Post subject: |
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Keith,
I know X-Wings, but URs are new to me. Are they the same thing with different names?
Bill |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Wed Aug 30, 2006 12:18 am Post subject: "UR"s are not X-Wings ... |
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Hi, Bill!
The only thing an X-Wing and a "Unique Rectangle" have in common is that each must have four corners.
Keith has written an excellent explanation of Unique Rectangles. Try reading this one on the Daily Sudoku forum, and also this one over on another forum. dcb |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Aug 30, 2006 12:29 am Post subject: The perfect straight man! |
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Bill,
Unique Rectangles are not the same as X-wings. However, they often occur in the same puzzle.
In particular, the Daily Sudoku "very hard" puzzles now usually "require" an X-wing to solve. But, the solver and ratings do not consider UR's.
You can learn about UR's here:
http://www.sudoku.com/forums/viewtopic.php?p=29105#29105
If you have any questions, please ask! Here, or privately.
Best wishes,
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Aug 30, 2006 2:01 am Post subject: The same thing? |
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dcb wrote:
| Quote: | | The only thing an X-Wing and a "Unique Rectangle" have in common is that each must have four corners. |
Except, when they share the same four corners!
http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?p=2894#2894
David is absolutely correct: An X-wing relies only on the basic Sudoku premise: Each row, column, and block contains only one occurrence of nine symbols.
Th UR and other uniqueness arguments bring in the additional condition: The given set of initial clues has a unique solution.
What I happened into was the observation that the overlay of an X-wing and a UR can solve the rectangle. This has led to a class of techniques which overlay strong links on uniqueness patterns. (cf: Type 4 UR.)
It is, I think, incredibly cool stuff, because it is useful to pencil & paper solvers (like me), and it has also led computer programs to solve some of the hardest Sudokus.
Anyway, if you are a pencil and paper solver, I think a most important thing to learn is: An X-wing is two strong links that line up at both ends.
Then, you can learn what happens when the two strong links only line up at one end. Good things can happen!
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Aug 30, 2006 6:02 pm Post subject: An explanation |
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In this puzzle you get here while there are still basic moves to do.
| Code: | +-------------------+-------------------+-------------------+
| 6 12789 12578 | 4589 3 159 | 179 47 147 |
| 15 19 15 | 2 1456 7 | 3 8 146 |
| 178 4 3 | 89 168 169 | 5 2 167 |
+-------------------+-------------------+-------------------+
| 9 28 4 | 358 7 356 | 268 1 568 |
| 3 278 2578 | 1 568 4 | 2678 567 9 |
| 1578 6 1578 | 589 2 59 | 4 57 3 |
+-------------------+-------------------+-------------------+
| 12478 3 6 | 457 145 125 | 178 9 14578 |
| 1247 5 9 | 6 14 8 | 17 3 147 |
| 1478 178 178 | 3457 9 135 | 1678 4567 2 |
+-------------------+-------------------+-------------------+ |
Th Unique Rectangle on <15> is in R26C13. It can be treated as either a Type 3 or Type 4. In any event, the net result is R5C3 is <5>.
If you do all the basic moves, you get to:
| Code: | +----------------+----------------+----------------+
| 6 278 278 | 458 3 15 | 9 47 147 |
| 15 9 15 | 2 46 7 | 3 8 46 |
| 78 4 3 | 89 68 169 | 5 2 167 |
+----------------+----------------+----------------+
| 9 28 4 | 358 7 356 | 268 1 58 |
| 3 278 2578 | 1 568 4 | 2678 567 9 |
| 15 6 1578 | 589 2 59 | 4 57 3 |
+----------------+----------------+----------------+
| 478 3 6 | 457 145 2 | 18 9 58 |
| 2 5 9 | 6 14 8 | 17 3 47 |
| 478 1 78 | 3457 9 35 | 68 456 2 |
+----------------+----------------+----------------+ |
The UR is now much more obvious as a Type 1. But, not so fast! All of the following are available:
Type 1: Remove <15> from R6C3.
Type 3: Remove <278> from R5C3.
Type 4: Remove <5> from R6C13.
The X-wing on <4> is in R28. It takes out <4> from R1C9 and R7C5.
Keith |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Tue Sep 05, 2006 3:16 pm Post subject: UR and X-Wing in 05 Sep Daily Sudoku |
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| David Bryant wrote: | | The only thing an X-Wing and a "Unique Rectangle" have in common is that each must have four corners. |
Here's a very cute example (the Daily Sudoku for Tuesday, 05 Sep) containing both a "UR" and an X-Wing that reach the same conclusion. The really interesting thing is that both patterns can be found in the initial puzzle, before any additional values are entered.
| Code: | *-----------*
|...|..9|..1|
|...|..7|.23|
|.71|.4.|6..|
|---+---+---|
|69.|...|...|
|..4|...|2..|
|...|...|.15|
|---+---+---|
|..7|.6.|84.|
|54.|9..|...|
|3..|7..|...|
*-----------* |
-- Because of the "3" and the "5" appearing in box 7, and also in column 9, it's apparent that the hidden pair {3, 5} lies in r7c46.
-- Because of the "3" in box 3, and also in column 1, it's apparent that the value "3" must lie in r3c4 or r3c6.
-- Applying the "UR" logic we see that "5" cannot appear in either r3c4 or r3c6, because the "deadly pattern" would then result. So the "5" in row 3 must appear at r3c8 (or else the solution would not be unique).
OK, that's the "UR" What about the X-Wing?
-- The "3"s in r3c4 or r3c6, and in r7c4 or c6, combine with the {7, 9} pair in both box 2 and box 8 to create the "hidden triple" {3, 7, 9} in the center column of box 5 -- that is, in c5r4-6.
-- The placement of the "1" in column 3 and in row 6 reveals that the "1" in row 5 must lie in box 4. Similarly, the placement of the "6" in column 6 and in row 4 reveals that the "6" in row 5 must lie in box 6.
-- Combining this information with the hidden triple, we see that none of the values {1, 3, 6, 7, 9} can lie in either r5c4 or r5c6. This leaves the hidden pair {5, 8} in those two cells, because the values "2" and "4" are already entered in row 5.
But now there's an X-Wing apparent in rows 5 and 7, consisting of the two hidden pairs {5, 8} and {3, 5} -- this eliminates the possibility of a "5" at r3c4 and r3c6, implying that r3c8 = 5, as before. dcb |
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