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Louise56
Joined: 21 Sep 2005 Posts: 94 Location: El Cajon, California USA

Posted: Sat Oct 22, 2005 5:24 pm Post subject: Need advanced technique advice for hard puzzle 


I found this puzzle in the San Diego Union Tribune. I put in 0's where there were empty spaces
008 090 000
050 820 700
000 001 060
300 000 070
702 304 801
010 000 005
070 400 000
004 062 080
000 080 600
I used all the regular techniques until I got stuck. Then found two xwings. There was an xwing of 3's at r3c2, r3c7 and r8c2, r8c7. There was an xwing of 2's at r1c8, r1c9 and r7c8, r7c9. Then I got stuck again. My top middle 3x3 box looked like this:
7/9/36
8/2/36
5/1/1
I guessed that the 3 would go in the top row, simply because the 7 and 9 are large numbers compared to the 8 and 2. This guess turned out to be correct. David and Someone have posted about "Nishio" and "Coloring." I'm not sure what those are, but would you use those techniques to finish the puzzle? What would be the next step. This is how far I got. Thanks!
048 790 000
050 820 700
007 541 068
385 219 476
762 354 891
419 678 235
876 435 000
004 062 087
000 087 600 

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

Posted: Sat Oct 22, 2005 6:29 pm Post subject: The same puzzle was in the RMN! 


Hi, Louise!
This exact same puzzle was in the Rocky Mountain News in Denver this morning. It is far and away the toughest puzzle I have yet seen in that newspaper (which I only get on Saturdays because of the way the two papers in Denver operate  I get the Denver Post Sunday  Friday).
Anyway, "Nishio" or "Coloring" won't work on this one  or at least, I couldn't get them to work. You have in fact reached the crucial stage where the "XYWing" technique is required to make more progress. To understand that, you need to be looking at the full matrix of possibilities.
Code:  1/6 4 8 7 9 3/6 1/5 . 2/3
. 5 1/3 8 2 3/6 7 1/4 .
2/9 . 7 5 4 1 3/9 6 8
3 8 5 2 1 9 4 7 6
7 6 2 3 5 4 8 9 1
4 1 9 6 7 8 2 3 5
8 7 6 4 3 5 1/9 1/2 2/9
. 3/9 4 1/9 6 2 3/5 8 7
. 2/9 1/3 1/9 8 7 6 . . 
Here the cells marked with a dot all have three possibilities as the puzzle stands, and none of them are important for finding the solution. The really critical step here is eliminating the possibility of a "2" at r1c1  we can see that the "2" in row 1 must fall in r1c8 or r1c9, because those are the only two cells where a "2" can fit in the top right 3x3 box.
The "XYWing" formation appears in r1c1, r2c3, r1c6, & r2c6. Think about r2c3 for a moment. If it contains a "1" then r1c1 = 6. If it contains a "3" then r2c5 = 6. Either way, r1c6 cannot be a "6," so it has to be a "3".
Maybe you weren't really guessing, Louise! dcb
PS I sometimes find it easier to spot the "XYWing" in reverse. In this case, if r1c6 = 6 then r2c6 = 3 and r1c1 = 1. But then the square r2c3 cannot be completed. It's the same logic, but backwards.
Last edited by David Bryant on Sat Oct 22, 2005 7:43 pm; edited 1 time in total 

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Louise56
Joined: 21 Sep 2005 Posts: 94 Location: El Cajon, California USA

Posted: Sat Oct 22, 2005 7:00 pm Post subject: Re: The same puzzle was in the RMN! 


David Bryant wrote:  PS I sometimes find it easier to spot the "XYWing" in reverse. In this case, if r1c5 = 6 then r2c5 = 3 and r1c1 = 1. But then the square r2c3 cannot be completed. It's the same logic, but backwards. 
This explanation makes the most sense to me (although I think you meant to say column 6 instead of column 5). The XYWing is still a little fuzzy, but this really helps! Thanks David. I had the same numbers you did except in r9c8 I had a 4/5 and in r9c9 a 3/4. I really was guessing though. If I used my same logic on the bottom middle 3x3 box, I would have put a 9 in r8c4 instead of r9c4 because the 6 and 2 add up to much less than the 8 and 7, and I would have been wrong. On these very hard puzzles, I check my answers as I go along just to be sure I'm not making a dumb mistake, so after I guessed a 3 in r1c6, I checked before I went any farther! Next time I get stuck like this, I'll look for an XY. 

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