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Did I Do This Correctly (Or Just Lucky)?

 
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Wed Dec 26, 2007 9:26 pm    Post subject: Did I Do This Correctly (Or Just Lucky)? Reply with quote
I solved the Super Hard puzzle from BrainBashers dated 12/25/07, but I would like confirmation that I did it correctly. The original puzzle was:

Code:


   +-------+-------+-------+
   | . 1 . | . 9   | . . 4 |
   | . . . | 5 2 . | . . 8 |
   | 7 . . | . . 4 | 1   . |
   +-------+-------+-------+
   | . . 9 | 4 . 3 | . . 5 |
   | . . . | . . . | . . . |
   | 5 . . | 6 . 7 | 3 . . |
   +-------+-------+-------+
   | . . 5 | 9 . . | . . 3 |
   | 9 . . | . 4 8 | . . . |
   | 8 . . | . 7 . | . 2 . |
   +-------+-------+-------+


After the basics, I had:

Code:


   +----------------------+----------------------+----------------------+
   | 23     1      8      | 7      9      6      | 25     35     4      |
   | 346    9      346    | 5      2      1      | 67     367    8      |
   | 7      5      26     | 8      3      4      | 1      69     29     |
   +----------------------+----------------------+----------------------+
   | 26     268    9      | 4      1      3      | 2678   678    5      |
   | 346    3468   7      | 2      5      9      | 468    1468   16     |
   | 5      24     1      | 6      8      7      | 3      49     29     |
   +----------------------+----------------------+----------------------+
   | 1      7      5      | 9      6      2      | 48     48     3      |
   | 9      236    236    | 13     4      8      | 56     156    7      |
   | 8      346    346    | 13     7      5      | 9      2      16     |
   +----------------------+----------------------+----------------------+




I then found what I believe to be a type 3 Unique Rectangle on 48 at r5c78 and r7c78. The two cells in r5 have the extra candidates <16> which form a locked set with the <16> in cell r5c9 which allows me to eliminate a <6> in cells r5c12 and r4c78.

Is this correct ????????

A couple of additional moves concluded the puzzle if my UR is valid.

Ted
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Wed Dec 26, 2007 10:10 pm    Post subject: Reply with quote
Sudoku Susser says:

Quote:
Squares R7C7, R7C8, R5C7 and R5C8 form a Type-3 Unique Rectangle on <48>. Because they share two rows, two columns, and two blocks, if they all had possibilities <48> then the puzzle would have two solutions; you could simply exchange the <4>s with the <8>s in the squares to get the other solution, and their common rows, columns and blocks would still contain one of each value. Since a valid Sudoku can have only one solution, either R5C7 or R5C8 must contain one of the values <16>; if neither does, then the squares form a two-solution configuration. While we don't know which of the squares contains one of the values <16>, the fact that one of them must have one of those values lets us look for naked sets in block 6 and row 5; we can treat R5C7 and R5C8 as if they were a single square with possibilities <16>. Upon close inspection, it is clear that:

(R5C7|R5C8)<16> and R5C9<16> form a naked pair on <16> in block 6. No other squares in the block can contain these possibilities.

R4C7 - can remove <6> from <2678> leaving <278>.
R4C8 - can remove <6> from <678> leaving <78>.

(R5C7|R5C8)<16> and R5C9<16> form a naked pair on <16> in row 5. No other squares in the row can contain these possibilities.

R5C1 - can remove <6> from <346> leaving <34>.
R5C2 - can remove <6> from <3468> leaving <348>.


If you do not use the UR, there is an X-wing and then some kind of chain.

Keith
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
PostPosted: Thu Dec 27, 2007 4:22 am    Post subject: Reply with quote
Quote:


Sudoku Susser says:


Thanks Keith for the response. It not only confirmed that I correctly identified and utilized a type 3 UR, it also raised a new question:

What is Sudoku Susser?

Ted
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Thu Dec 27, 2007 5:12 am    Post subject: Reply with quote
Ted,

Sudoku Susser is the solver written by Robert Woodhead, aka "MadOverlord". You can find it here.

http://www.madoverlord.com/projects/sudoku.t

It is the greatest tool to help you learn how to solve Sudoku. I love it. Also, it comes with a PDF instruction manual that has a wonderful section on solving techniques.

That said, Sudoku Susser does not do some of the techniques that are discussed on this forum: No coloring, W-wings, finned wings, Type 6 UR's, etc.

What I particularly like is the way it gives hints. None of this "R5C6 is <2>" stuff. It says "look for an XY-wing". Or, if you do shift+hint it may say "look for an XY-wing involving R5C7". You can turn the solving heuristics on and off, and change their order.

Since it is the only tool I use, I can't say that SS is better or worse than any other. But, it is all I want.

Keith
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