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Example with "hidden pair", "X-wing" and
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David Bryant

Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sun Oct 02, 2005 11:33 pm    Post subject: Re: Oops! Reply with quote

Louise56 wrote:

Hi David,

The one I did from USA today was the Sept 30 one, which is the same one you and Someone worked on. I can't remember all my steps, I'll have to go back. I did an X wing three times as I remember. The X Wing numbers were all four fairly close to each other, but that helped me elimate others. I'll go through it again and write a solution. Can you tell me what a "Nishio" is?

"Nishio" is a technique for determining where a particular number has to go by a form of proof by contradiction, or reductio ad absurdem. In its pure form it looks at a certain number (say a "4") and asks "If I put a '4' here, can I place all the rest of the '4's in this grid?" People also use this term to refer to other proofs by contradiction.

Some players object to the reductio technique because they think it's trial and error. In a way it is, but I don't see any reason not to use it if the resulting chain of inferences that leads to a contradiction is not too long -- say ten or twelve steps, as a practical limit. One might make a wild guess in one cell and find a contradiction after making 25 or 30 more moves, but that wouldn't really be much fun. And it would require a lot of backtracking, to boot.

Here are a couple of Web resources with more information about "Nishio":

Have a great day! dcb Smile
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Joined: 21 Sep 2005
Posts: 94
Location: El Cajon, California USA

PostPosted: Mon Oct 03, 2005 2:40 am    Post subject: Reply with quote

someone_somewhere wrote:
Hi Louise,

The Sudoku from USATODAY is extreme interesting.
I am wondering how you solved it with the X-wing technique.

From here only some coloring, multicoloring, nisho, etc can help.
Or someone else . . . ?


I went through the puzzle again, this time writing down my moves and I couldn't get it! I got to the same point you did. I must have accidently solved it the first time, perhaps by accidently erasing a number which wasn't supposed to be there! I willl keep looking at it, but if you and David couldn't get past this point, I'm sure I won't be able to. Has anyone else out there done this puzzle (USA Today online Sept 30) without using any guessing? If so, please give us your solution. When I was working on the solution, I noticed my X wings were the same as using row or column pairs. It was just another way to solve. Looking for pairs in rows or columns is probably faster and neater. Oh well, for a brief period of time I felt very smart!
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