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Graded "Too Hard" by Daily Sudoku

 
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Korky



Joined: 29 Mar 2006
Posts: 13
Location: Sheffield, UK

PostPosted: Wed Jul 11, 2007 10:36 am    Post subject: Graded "Too Hard" by Daily Sudoku Reply with quote

Can anyone give me a clue? All I can see is that R2C1 can't reduce to 89 (deadly pattern) so must contain either a 3 or 4
Code:

+--------------+----------+----------+
| 1    2    5  | 8 9   7  | 6  3   4 |
| 3489 3489 89 | 5 234 6  | 12 129 7 |
| 6    349  7  | 1 234 34 | 5  29  8 |
+--------------+----------+----------+
| 48   478  2  | 6 1   45 | 9  57  3 |
| 5    34   6  | 7 34  9  | 18 18  2 |
| 39   379  1  | 2 8   35 | 4  57  6 |
+--------------+----------+----------+
| 2    1    4  | 9 7   8  | 3  6   5 |
| 7    5    3  | 4 6   1  | 28 28  9 |
| 89   6    89 | 3 5   2  | 7  4   1 |
+--------------+----------+----------+

Play this puzzle online at the Daily Sudoku site
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keith



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

PostPosted: Wed Jul 11, 2007 11:06 am    Post subject: Reply with quote

Right, so take out <89> from R2C1.

Then, you will find two finned X-wings on <3>, and a finned X-wing on <4> that solve it. All of the eliminations are in boxes 1 and 2.

I suspect the UR reduction is not needed, and after one or two of the finned X-wings, there is an XY-wing I did not use.

Keith
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Korky



Joined: 29 Mar 2006
Posts: 13
Location: Sheffield, UK

PostPosted: Wed Jul 11, 2007 11:11 am    Post subject: Reply with quote

Thanks Keith. I'm working on it.
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Korky



Joined: 29 Mar 2006
Posts: 13
Location: Sheffield, UK

PostPosted: Wed Jul 11, 2007 12:04 pm    Post subject: Reply with quote

Keith, following your clues, one finned x-wing on 3 and another on 4 eliminated both from R2C5 and the puzzle collapsed.
Thanks again!
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Wed Jul 11, 2007 12:19 pm    Post subject: Reply with quote

If you are prepared to assume that the puzzle has a unique solution, there is a quicker way.

9 may be placed in r2c8 using the unique six r258c78.

Steve
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Wed Jul 11, 2007 12:33 pm    Post subject: Reply with quote

A uniqueness triple - first time I've seen that.

Similar to the finned x-wings but maybe easier to spot because they're simple strong links:




Eliminates 3&4 from r3c2.
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Korky



Joined: 29 Mar 2006
Posts: 13
Location: Sheffield, UK

PostPosted: Wed Jul 11, 2007 2:19 pm    Post subject: Reply with quote

I think the unique six is very neat. I'll look for it in future.
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Marty R.



Joined: 12 Feb 2006
Posts: 5164
Location: Rochester, NY, USA

PostPosted: Wed Jul 11, 2007 4:37 pm    Post subject: Reply with quote

Steve R wrote:
If you are prepared to assume that the puzzle has a unique solution, there is a quicker way.

9 may be placed in r2c8 using the unique six r258c78.

Steve

Steve, could you explain the logic for those of us (i.e., me) who are too dense to see it?
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keith



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

PostPosted: Wed Jul 11, 2007 5:31 pm    Post subject: Reply with quote

Marty,

This pattern:
Code:
+----------+----------+----------+
|  .  .  . |  12 .  12|  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+
|  .  .  . |  23 .  23|  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  13 .  13|  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+


is not unique. Try it. Pick <1> in R1C4. Then pick <2>. Both lead to a solution.
The complete situation would have to be something like:
Code:
+----------+----------+----------+
|  .  .  . |  12 .  12|  .  3  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  .  3  . |  .  .  . |
+----------+----------+----------+
|  .  .  . |  23 .  23|  .  1  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  .  1  . |  .  .  . |
+----------+----------+----------+
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  13 .  13|  .  2  . |
|  .  .  . |  .  2  . |  .  .  . |
+----------+----------+----------+


so it is indeed true you can interchange the solutions and still have a single 1,2,3 in each row, column and block.


Something I have seen before:
Code:
+----------+----------+----------+
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+
|  .  12 . |  12 .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  12 . |  .  .  12|  .  .  . |
+----------+----------+----------+
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  12 .  12|  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+



Is the following possible? I don't know.
Code:
+----------+----------+----------+
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+
|  .  12 . |  23 .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  12 . |  .  .  23|  .  .  . |
+----------+----------+----------+
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  13 .  13|  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+


Best wishes,
Keith
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Wed Jul 11, 2007 6:06 pm    Post subject: Reply with quote

I donít think Keithís last pattern has any bearing on the number of solutions. As far as I know there are just three patterns of six cells. One is aligned (in two columns or rows) as in the original puzzle; one is bent (i.e. goes round a corner) as in Keithís penultimate example. The third (skew) is even less useful than the other two:

Code:
+----------+------------+----------+
|  .  .  . |  .   .  .  |  .  .  . |
|  .  .  . |  12  12  . |  .  .  . |
|  .  .  . |  .   .  .  |  .  .  . |
+----------+------------+----------+
|  .  .  . |  .   .  .  |  .  .  . |
|  .  .  . |  .   .  .  |  .  .  . |
|  .  .  . |  .   12 12 |  .  .  . |
+----------+------------+----------+
|  .  .  . |  .   .  .  |  .  .  . |
|  .  .  . |  12  .  12 |  .  .  . |
|  .  .  . |  .   .  .  |  .  .  . |
+----------+------------+----------+

The bent version is not restricted to six cells even in a 9 x 9 grid. If he had wished, and started in the first box rather than the fourth, Keith could have gone round the board with it.

Regards

Steve
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Marty R.



Joined: 12 Feb 2006
Posts: 5164
Location: Rochester, NY, USA

PostPosted: Wed Jul 11, 2007 9:10 pm    Post subject: Reply with quote

Thanks guys.
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jLo



Joined: 30 Apr 2007
Posts: 55

PostPosted: Thu Jul 12, 2007 5:19 am    Post subject: Reply with quote

What about using the W-wing right from the beginning?
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Thu Jul 12, 2007 11:10 pm    Post subject: Reply with quote

Coloring on <3>and coloring on <4> leaves 9 as the only possibility in r3c2.

It occurred to me after I posted that my coloring on 3 & 4 was the same as jLo's W-wing and it turns out that it was. Also turns out the (3,4) pairs in r3c6 & r5c2 are connected by strong links on both 3 and 4.
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Fri Jul 13, 2007 7:38 am    Post subject: Reply with quote

keith wrote:

Is the following possible? I don't know.
Code:
+----------+----------+----------+
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+
|  .  12 . |  23 .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  12 . |  .  .  23|  .  .  . |
+----------+----------+----------+
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  13 .  13|  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+
Yes, the 2's or 3's in boxes 2, 4, 6 or 8 could "fix" it to one solution. This is deadly:
Code:
+----------+----------+----------+
|  .  .  . |  12 .  12|  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+
|  .  12 . |  23 .  . |  .  13 . |
|  .  .  . |  .  .  . |  .  .  . |
|  .  12 . |  .  .  23|  .  13 . |
+----------+----------+----------+
|  .  .  . |  .  .  . |  .  .  . |
|  .  .  . |  13 .  13|  .  .  . |
|  .  .  . |  .  .  . |  .  .  . |
+----------+----------+----------+
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