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George Woods
Joined: 28 Mar 2006 Posts: 296 Location: Dorset UK

Posted: Tue May 02, 2006 10:20 am Post subject: Tuesday 2 May 


Sorry folks can't see it Help
Get to this crunch point
078 050 010
500 041 000
106 072 035
850 406 100
064 517 980
701 008 564
007 185 206
085 060 701
610 704 358
Solve gives a hint 2 in r9c3, and I agree that a 9 here eventually creates a crash BUT I can't see any "logical" reason. I know this is probably a blind spot, but can't afford to waste more than an hour! 

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Steve R
Joined: 24 Oct 2005 Posts: 289 Location: Birmingham, England

Posted: Tue May 02, 2006 11:27 am Post subject: Tuesday 2 May 


George
I think I must have strayed in this puzzle because taking flight was the only way forward I could see.
In both the first and fifth rows there are just two cells for 2: column 1 or column 9. These rows between them ensure that the 2 in box 7 cannot occupy the first column.
I look forward to learning what I missed or whether perhaps the rules have changed to include Xwings.
Steve 

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

Posted: Tue May 02, 2006 11:28 am Post subject: XWing on the "2"s 


There's an XWing on the "2"s, in row 1 and row 5 (cols 1 & 9). So there's either a "2" at r1c1 and a "2" at r5c9, or else there's a "2" at r1c9 and a "2" at r5c1. Either way there cannot be a "2" at r8c1, leaving r9c3 as the only possible spot for a "2" in the bottom left 3x3 box.
There's also a swordfish on the "9"s (in columns 1, 6, and 8  rows 1, 7, & 8) which allows you to set a "2" at r1c9, but the XWing is certainly easier to spot.
So far as I'm aware, this XWing (or swordfish) cannot be avoided  at least, I can't find a simpler clue. I think that's a first for the Daily Sudoku! dcb 

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keith
Joined: 19 Sep 2005 Posts: 3297 Location: near Detroit, Michigan, USA

Posted: Tue May 02, 2006 5:49 pm Post subject: 


I agree.
I get to a stage where there are two unique rectangles and an Xwing. I believe there is no "simpler" way to the solution.
Keith 

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eddieg
Joined: 12 Jan 2006 Posts: 47 Location: San Diego, CA USA

Posted: Tue May 02, 2006 8:00 pm Post subject: 


Help, I don't get the '2' in R9C3 as stated above by David Bryant. I still have the possiblity of R8C3 being a '2' as well as R9C3. Anybody see where I am going wrong?
078 050 010
500 041 000
106 072 005
850 000 100
064 517 980
700 008 564
000 180 206
080 060 001
610 000 358 

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Steve R
Joined: 24 Oct 2005 Posts: 289 Location: Birmingham, England

Posted: Tue May 02, 2006 8:31 pm Post subject: Tuesday 2 May 


Eddie
You haven’t gone wrong but you do need to go a little further.
Have you identified the cells occupied by the pair (68) in row 2? Once this is done, it should be straightforward to develop the puzzle to the position posted by George at the beginning of this thread and so get to grips with the comments which followed.
Steve 

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eddieg
Joined: 12 Jan 2006 Posts: 47 Location: San Diego, CA USA

Posted: Tue May 02, 2006 8:51 pm Post subject: 


Thanks for the response Steve. I was overlooking exactly what you pointed out. 

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Marty R.
Joined: 12 Feb 2006 Posts: 5717 Location: Rochester, NY, USA

Posted: Tue May 02, 2006 9:03 pm Post subject: 


I might as well put my 2¢ in. After the initial elimination techniques, I noticed multiple XWing patterns, but they couldn't eliminate any candidates that I could see. There were also a couple of unique rectangles which I was unable to do anything with. I didn't look for swordfish yet, since it's such a hassle.
There was a "23" in r5c9 that looked promising as a starting cell for a forcing chain; the chain starting with the "2" left a "deadly pattern" and solving the cell with the "3" broke the puzzle wide open. 

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jabejochke
Joined: 16 Mar 2006 Posts: 21 Location: Reading

Posted: Tue May 02, 2006 9:37 pm Post subject: 


I was exactly at the point George outlined in the initial comments.
I hadn't yet moved to Xwings, Swordfish, etc.  and I try not to. But the comments made by each contributor referenced the logic and not the name  hence, I learned from those exchanges  and the solution makes sense.
This specific puzzle was referenced as 'very hard'. As it turned out, it was for me. But I had been sailing along on this one, while struggling with the May 1st puzzle. In reading the comments on the May 1st, the light suddenly dawned on me and I also understood the results to that one to.
Both puzzles were 'very hard' for me. And it really does not matter how they are classified. The important thing is that I can have the chance to ask for help when I hit the wall or offer help when needed.
I continue to learn a lot from the participants at this site.
Thanks,
Jack 

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GREG N Guest

Posted: Tue May 02, 2006 9:54 pm Post subject: MAY 2 


WHAT THE H*** IS AN XWING OR SWORDFISH. I AM NEW AT THIS SUDOKU STUFF AND I SOLVED THIS PUZZLE BY TRIAL AND ERROR. THE WAY I BROKE IT OPEN WAS THERE COULD EITHER BE A 2 OR 9 IN R9C5 AND I GUESSED 9 WHICH BROKE THE PUZZLE OPEN FOR ME.
PLEASE LET ME KNOW HOW TO SOLVE THIS PUZZLE USING LOGIC ONLY.
THANKS, 

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

Posted: Wed May 03, 2006 12:18 am Post subject: XWings, Swordfishes, etc. 


Hi, Greg!
You really don't have to shout to get someone's attention.
Quite a bit has already been written about the "advanced techniques"  you can read some of that stuff from the links provided in another message.
Here, I'll explain the XWing one more time. I'm assuming you arrived at the position George Woods posted at the beginning of this thread.
Code:  *78 .5. .1*
5** .41 .**
1.6 .72 .35
85* 4*6 1**
*64 517 98*
7*1 **8 564
..7 185 2.6
*85 *6. 7.1
61* 7*4 358 
I have marked every spot where a "2" can be legally placed with an asterisk. We reason as follows.
 There are only two places to fit a "2" in row 1, at r1c1, or at r1c9.
 Similarly, there are only two places to fit a "2" in row 5, at r5c1, or at r5c9.
 If r1c1 = 2, then r5c9 = 2.
 If r1c1 <> 2, then r1c9 = 2, and r5c1 = 2.
 Either way, the "2" in column 1 must appear at either r1c1 or r5c1, and the "2" in column 9 must appear at either r1c9 or r5c9.
 Therefore we cannot possibly have a "2" at r8c1, r2c9, or r4c9.
Now the grid looks like this:
Code:  *78 .5. .1*
5** .41 .*.
1.6 .72 .35
85* 4*6 1*.
*64 517 98*
7*1 **8 564
..7 185 2.6
.85 *6. 7.1
61* 7*4 358 
We see that the only spot left for a "2" in the bottom left 3x3 box is at r9c3, and the "9" you found by trial and error [in r9c5] follows immediately.
A "swordfish" is similar to an XWing, but instead of involving 4 cells at the corners of a rectangle it involves 6, 7, 8, or 9 cells at the vertices of a 3 x 3 pattern (sort of like tictactoe). The "complete" swordfish always has nine cells in it, but as many as three of those can be cells that are already resolved, leaving a skeleton that is still useful.
The logic is exactly the same as an XWing ... in the three columns and rows occupied by the swordfish cells, the target digit must lie within the pattern, and the target digit can be eliminated from cells outside that pattern.
The swordfish on "9"s appears as follows.
Code:  x78 *5x .1*
5.. .41 ...
1.6 .72 .35
85. 4.6 1..
.64 517 98.
7.1 ..8 564
x*7 185 2x6
x85 *6x 7x1
61. 7.4 358 
Here I have marked the "corners" of the swordfish with the letter x, and I have used an asterisk to mark the four cells from which the digit "9" can be eliminated. In particular, this pattern allows one to set r1c9 = 2, and that breaks the rest of the puzzle wide open. dcb 

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keith
Joined: 19 Sep 2005 Posts: 3297 Location: near Detroit, Michigan, USA

Posted: Wed May 03, 2006 12:34 am Post subject: Tutorial 


After using all the techniques required in every previous Daily Sudoku, we get to here. Now what?
Code: 
++++
 249 7 8  369 5 39  46 1 29 
 5 239 239  68 4 1  68 27 279 
 1 49 6  89 7 2  48 3 5 
++++
 8 5 239  4 239 6  1 27 237 
 23 6 4  5 1 7  9 8 23 
 7 239 1  29 239 8  5 6 4 
++++
 349 349 7  1 8 5  2 49 6 
 249 8 5  239 6 39  7 49 1 
 6 1 29  7 29 4  3 5 8 
++++

There is a unique rectangle on <39> in R18 C46. R1C4 and R8C4 cannot be <9>.
There is a unique rectangle on <49> in R78 C18. R1C1 cannot be <2>.
There is a unique rectangle on <27> in R24 C89. R2C9 and R4C9 cannot be <2>.
There is an Xwing on 2 in R15. All other possibilities of <2> in C1 C9 can be removed.
There is an Xwing on <9> in R49. All other possibilities of <9> in C3 C5 can be removed.
If you still think something is fishy, you can look (in the grid above) for:
A swordfish on <9> in R158.
A swordfish on <9> in C168.
A swordfish on <2> in R158.
A jellyfish on <2> in C2358.
A jellyfish on <9> in R3469
and (TaDaa!)
A squirmbag on <2> in C23458.
An interesting situation!
Keith 

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TKiel
Joined: 22 Feb 2006 Posts: 292 Location: Kalamazoo, MI

Posted: Wed May 03, 2006 2:06 am Post subject: 


Simple and multiple colouring on digit 2 solves it from where George Woods posted the grid. Don't know if that's easier or harder than Xwings and fish. 

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Huw Llewellyn Guest

Posted: Wed May 03, 2006 10:19 am Post subject: Sudoku 2nd May 2006 


I try my hand at the Sudoku problems on this website and after a lot of practice, have managed to solve all bar the occasional Very Hard puzzle. The one on 2nd May was all but impossible!! I thought I was doing well to get to the point of needing a Swordfish! I can understand Greg N's frustration. Thanks to David Bryant for his help. I am perplexed by these "in" terms for special moves, and Swordfish and X wings are completely new to me. This has put back my proper work by hours and hours. 

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keith
Joined: 19 Sep 2005 Posts: 3297 Location: near Detroit, Michigan, USA


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Marty R.
Joined: 12 Feb 2006 Posts: 5717 Location: Rochester, NY, USA

Posted: Wed May 03, 2006 3:48 pm Post subject: 


Quote:  There is a unique rectangle on <39> in R18 C46. R1C4 and R8C4 cannot be <9>.
There is a unique rectangle on <49> in R78 C18. R1C1 cannot be <2>.
There is a unique rectangle on <27> in R24 C89. R2C9 and R4C9 cannot be <2>. 
Keith, I see a fair number of similar rectangles, but I can't do anything with them. For example, take the "39" rectangle. It's obvious that either r1c4=6 or r8c4=2, but I don't see enough because nothing seems locked. How do you deduce that both r1c4 and r8c4 cannot be "9"? 

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

Posted: Wed May 03, 2006 4:09 pm Post subject: Forcing chains are present. 


Marty R wrote:  How do you deduce that both r1c4 and r8c4 cannot be "9"? 
It's really two separate deductions, using forcing chains in column 4.
Code:  ++++
 249 7 8  369 5 39  46 1 29 
 5 239 239  68 4 1  68 27 279 
 1 49 6  89 7 2  48 3 5 
++++
 8 5 239  4 239 6  1 27 237 
 23 6 4  5 1 7  9 8 23 
 7 239 1  29 239 8  5 6 4 
++++
 349 349 7  1 8 5  2 49 6 
 249 8 5  239 6 39  7 49 1 
 6 1 29  7 29 4  3 5 8 
++++ 
A. r1c4 = 9 ==> r6c4 = 2 ==> r8c4 = 3 (the "deadly pattern" results)
B. r8c4 = 9 ==> r3c4 = 8 ==> r2c4 = 6 ==> r1c4 = 3 ("deadly pattern" again) 

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Marty R.
Joined: 12 Feb 2006 Posts: 5717 Location: Rochester, NY, USA

Posted: Wed May 03, 2006 4:40 pm Post subject: 


Quote:  It's really two separate deductions, using forcing chains in column 4. 
Thank you David, that's very helpful. I never thought in terms of what are the things that would leave the "deadly pattern." Also thanks to Keith who I know would have answered had you not beat him to the punch. 

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ravel
Joined: 21 Apr 2006 Posts: 536

Posted: Wed May 03, 2006 5:24 pm Post subject: 


Marty,
its a type 4 UR, because there are only the two 3's in column 4. So Davids chains can be written shorter:
r1c4=9 => r8c4=3 (=> r8c6=9 => r1c6=3 )
r8c4=9 => r1c4=3 (=> r1c6=9 => r8c6=3 )
Whenever you have a UR with a naked pair [39 above] in one row (column) and one of the numbers is strongly linked [the 3] in the other row (col), where there can be additional candidates, you can eliminate the second number from the UR corners in that row (col) [the 9]. 

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RogerC
Joined: 08 Oct 2005 Posts: 14 Location: High Wycombe, Bucks, England

Posted: Fri May 05, 2006 7:15 am Post subject: Simple and multiple colouring 


This is the hardest puzzle I have attempted  and the most fascinating discussion I have ever read!! Thanks to all the contributors; I have learned a lot.
There is one post I that I still haven't grasped yet from TKeil:
Quote:  Simple and multiple colouring 
Can you explain, please, Tracy?
Roger 

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