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XY-Wing Example #1

 
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
PostPosted: Fri Oct 07, 2005 11:35 pm    Post subject: XY-Wing Example #1 Reply with quote
This is a continuation from "A Very Tough Minimal Sudoku."

Someone_Somewhere wrote:
Hi,

Here one that needs XY-wing technique:

000010780
500009000
000000040
026000000
000600003
074080000
000003002
080040010
600500000

...


Funny, I got all the way through this one without resorting to the "XY-Wing" technique at all. The first move was extremely hard to find, though. Here's a description of the first couple of moves ... I wouldn't want to spoil the fun for everybody else, but the very first move (at least, the one I found) is a real killer.

1. We can place a "7" in r8c9 after analyzing column 9. The pair {4, 8} can't fit in any of r1c9, r2c9, r3c9, r6c9, or r8c9 because of {4, 8} pairs in the top right 3x3 box, in row 6, and in row 8. So the {4, 8} pair must fit in r6c9 & r9c9; since "7" already appears in the top right 3x3 box, and in row 6, the only spot left for a "7" in column 9 is at r8c9.

2. It is clear that the "3" in the middle center 3x3 box must appear in row 4. So there must be a "3" at r6c1.

3. The next move is in row 2, and it uses logic similar to my reasoning in step 1. Can anybody else spot it?
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
PostPosted: Sat Oct 08, 2005 12:33 am    Post subject: Oops! I made a mistake. Reply with quote
I went back over this puzzle, and I just realized that I made a mistake when I put a "3" at r6c1. I must have looked at it cross-eyed, or something. Anyway, it was a lucky mistake, because as it eventually turns out, that is indeed the right place to put the "3" in column 1. But my reasoning was incorrect.

This is one tough puzzle! dcb

PS The second example someone_somewhere posted under the "very tough minimal sudoku" topic is identical to this one. So I'm moving on to example #3.
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich
PostPosted: Sat Oct 08, 2005 6:12 am    Post subject: Reply with quote
Hi,

So the bottom line is that you did NOT make it without XY-wing?

see u,
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
PostPosted: Sat Oct 08, 2005 1:37 pm    Post subject: Can't do it without a "XY-Wing" Reply with quote
Yes, you're right. After some 35 moves I reach a position that's impervious to other techniques. Will write more later ... right now it's time for breakfast! dcb

PS Thanks for a _great_ puzzle. It kept me scratching my head for quite a while, even with the lucky mistake I made the first time around.
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
PostPosted: Sat Oct 08, 2005 8:15 pm    Post subject: Now I see the "XY-Wing" Reply with quote
OK, I finally found the "xy-wing" in this puzzle. After 34 moves I arrived at the following position:

Code:

  2   3/6   9   3/4   1   4/5   7    8   5/6
  5    4    8    7   3/6   9    .   2/3  1/6
  7   3/6   1    8    .    2    .    4    .

*1/3*  2    6    .  *3/5*  7    .   5/9   8
  8    9    5    6    2   1/4  1/4   7    3
*1/3*  7    4   3/9   8  *1/5*  .    .    .

  4    5    7    1    9    3    8    6    2
  9    8    3    2    4    6    5    1    7
  6    1    2    5    7    8   3/9  3/9   4


The "xy-wing" formation appears in the cells marked with "*". We see that r6c1 must be a "3", because whichever value (3 or 5) we place at r4c5, a "1" is seen to be impossible at r6c1. Once the "3" is placed in this spot, the rest of the puzzle presents no unusual difficulties.

Coincidentally, this "3" is the value I placed in the right spot by a happy accident on my first time through. I'm still not sure exactly how that happened -- beginner's luck, I suppose. dcb Smile
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich
PostPosted: Sun Oct 09, 2005 5:57 am    Post subject: Reply with quote
Yup David,

It is the XY-wing of that Sudoku!

Good work.
see u,
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