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A Super Hard

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Thu Nov 22, 2007 12:42 am    Post subject: A Super Hard Reply with quote

You all might enjoy this one from Menneske:
Code:
Puzzle: M4934597sh(15)
+-------+-------+-------+
| . 8 . | . 6 9 | . 2 . |
| . 6 7 | . . . | 8 5 . |
| . . 2 | 8 . . | 3 . . |
+-------+-------+-------+
| . . . | . 1 . | . . . |
| . . . | 7 3 6 | . . . |
| 9 . . | . 8 . | . . 7 |
+-------+-------+-------+
| . . 9 | . . 1 | 5 . . |
| . 4 5 | . . . | 6 7 . |
| . 7 . | 5 4 . | . 3 . |
+-------+-------+-------+

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Thu Nov 22, 2007 2:06 am    Post subject: Reply with quote

Not familiar with Menneske, but this one proceeded along pretty smoothly. Three moves did it for me.

XY-Wing with coloring
XYZ-Wing
XY-Wing with coloring
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Thu Nov 22, 2007 3:03 am    Post subject: Reply with quote

Marty,

I did the XYZ-wing and a couple of uniqueness things. I ended by finding an XY-wing 13-23-12 in C3R8. Then, coloring on <1> extended it to solve R8C1 as <8>.

Here is the Menneske site.

http://www.menneske.no/sudoku/eng/

The "Very Hard" puzzles seem to have a lot of remote pairs and X-wings. I am finding that the "Super Hard" puzzles with ratings of about 15 are just my speed.

Happy Thanksgiving!

Keith
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS

PostPosted: Thu Nov 22, 2007 3:16 am    Post subject: Super Hard Reply with quote

A three step xy-chain eliminates 1 from R1C3 and the rest is singles.

Earl

PS I am not familiar with "xy-wing with coloring."
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Thu Nov 22, 2007 3:43 am    Post subject: Re: Super Hard Reply with quote

Earl wrote:

PS I am not familiar with "xy-wing with coloring."


Which is why I posted the puzzle! The basics get you to here:
Code:
+----------------+----------------+----------------+
| 5    8    13   | 13   6    9    | 7    2    4    |
| 13   6    7    | 134  2    34   | 8    5    9    |
| 4    9    2    | 8    5    7    | 3    1    6    |
+----------------+----------------+----------------+
| 7    25   6    | 9    1    245  | 24   8    3    |
| 28   12   48   | 7    3    6    | 124  9    5    |
| 9    1235 34   | 24   8    245  | 124  6    7    |
+----------------+----------------+----------------+
| 238  23   9    | 6    7    1    | 5    4    28   |
| 128  4    5    | 23   9    238  | 6    7    128  |
| 6    7    18   | 5    4    28   | 9    3    128  |
+----------------+----------------+----------------+

There are two overlapping XYZ-wings with pivots in R78C1. They take out <2> in R8C1 and <8> in R7C1. The result is:
Code:
+----------------+----------------+----------------+
| 5    8    13A  | 13@a 6    9    | 7    2    4    |
| 13a  6    7    | 134  2    34   | 8    5    9    |
| 4    9    2    | 8    5    7    | 3    1    6    |
+----------------+----------------+----------------+
| 7    25   6    | 9    1    245  | 24   8    3    |
| 28   12   48   | 7    3    6    | 124  9    5    |
| 9    1235 34   | 24   8    245  | 124  6    7    |
+----------------+----------------+----------------+
| 23   23   9    | 6    7    1    | 5    4    8    |
| 18   4    5    | 23@  9    238  | 6    7    12@  |
| 6    7    18   | 5    4    28   | 9    3    12   |
+----------------+----------------+----------------+

Note the seemingly useless XY-wing labelled @. Note also the coloring on <1>, aAa, that says R1C4 and R3C1 have the same value.

The XY-wing says that any cell which sees both R8C9 and R1C4 cannot be <1>. There are no such cells. But, coloring extends this to R8C9 and R3C1, solving R8C1 as <8>. And, solving the puzzle.

Pretty cool, I think!

Keith
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