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

Posted: Tue Jan 17, 2006 2:51 pm Post subject: Nightmare 


Masochists participating in this forum (and there are a few) might be interested in Ruud van der Werf’s site Sudo Cue. His daily “Nightmare” puzzles are meant for you. If one is neither fish nor fowl, the chains are needed. Today’s (17 January) is not especially difficult by Ruud’s standards but it offers a flavour and you can always try 4 January if it merely serves to whet your appetite.
Sleep well!
Steve 

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

Posted: Tue Jan 17, 2006 3:05 pm Post subject: PS 


I expected the link to appear. Perhaps it will now.
Steve 

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

Posted: Tue Jan 17, 2006 6:25 pm Post subject: A uniquitous puzzle 


Thanks for the link, Steve.
I haven't tried the 4Jan puzzle yet, but I did take a stab at the one for today. It was pretty simple to get through  if I assumed the existence of a unique solution. In fact, I managed to use that assumption twice  on two different "Type4B Unique Rectangles" (a formation that Keith brought to our attention some time ago). dcb 

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

Posted: Wed Jan 18, 2006 12:03 am Post subject: Nightmare 


Yes. An XWing will also do it, without further assumption.
I was unable to solve the fourth of January. Puzzle, which made me think it might be a little harder.
Steve 

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

Posted: Wed Jan 18, 2006 1:12 am Post subject: Jan 4 "Nightmare" 


I must be a masochist, Steve. :)
From the initial "Nightmare" puzzle for Jan 4, 2006
Code:  . 7 2 . 4 . . 6 .
5 . . 9 . 7 . . .
. . . . 6 . . . .
. 5 4 . . . 8 . .
. 9 . . 5 . . 7 .
. . 1 . . . 2 4 .
. . . . 9 . . . .
. . . 1 . 3 . . 6
. 6 . . 7 . 5 9 . 
I was able to arrive, by a number of tricks, at the following position:
Code:  38 7 2 358 4 158 9 6 18
5 138 6 9 138 7 143 1238 2348
4 18 9 238 6 28 13 5 7
67 5 4 2367 123 26 8 13 9
2 9 38 348 5 148 6 7 13
67 38 1 67 38 9 2 4 5
38 2 7 56 9 56 134 138 348
9 4 5 1 28 3 7 28 6
1 6 38 248 7 248 5 9 234 
I found a contradiction by examining r1c9, and assuming that r1c9 = 1.
r1c9 = 1 ==> r3c7 = 3 ==> r2c7 = 4
This leaves the {2, 8} pair in r2c8 & r2c9, and the {1, 3} pair in r2c2 & r2c5.
Also, r3c7 = 3 ==> r3c2 = 1 (only two spots for a "1" in r3) ==> r2c2 = 3. This is the first forcing chain.
r1c9 = 1 ==> r5c9 = 3 ==> r5c3 = 8 ==> r6c2 = 3. This is the second forcing chain.
But now we have two "3"s in column 2. Therefore r1c9 <> 1; r1c9 = 8 and r5c9 = 1 ... the rest of the puzzle is straightforward. dcb
PS As usual with forcing chains, there may be a shorter path to the solution. This is the one I located by concentrating on the preponderance of {3, 8} pairs. 

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

Posted: Wed Jan 18, 2006 8:57 pm Post subject: Jan 4 "Nightmare" 


That’s a neat solution, David.
I stalled a little before the stage shown in your grid. It was only when going through your analysis that I found some wings to get me there. I have since tried Sudo Cue’s solver on the puzzle. The analyser started in the obvious way, found the pair (38) in box (2, 1) and then calmly announced: “R6C5 has Digit 8 as the only remaining candidate.” How it managed to exclude the 3 is beyond me but I have not seen the solver before so there is probably more to it somewhere. In the meantime I shall stick with the solution I can understand. Good stuff!
Steve 

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

Posted: Fri Jan 20, 2006 6:14 pm Post subject: Jan 19 "Nightmare" is a real gem 


The "Nightmare" site is a lot of fun. This puzzle is for Thursday, January 19.
Code:  . . . 9 . . 2 . .
. 1 . 3 . . . . .
2 . 7 . 5 . . 1 .
8 . . 7 . . . 3 .
3 . . . 9 . . . 8
. 4 . . . 8 . . 5
. 5 . . 8 . 9 . 7
. . . . . 1 . 4 .
. . 2 . . 9 . . . 
There are no "6"s in the initial set of clues. Interestingly, the puzzle eventually leads to a position where it is possible to place all nine of the "6"s simultaneously!
Kudos to Ruud van der Werf  this is a beautiful puzzle! dcb 

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someone_somewhere
Joined: 07 Aug 2005 Posts: 275 Location: Munich

Posted: Sat Jan 21, 2006 12:56 pm Post subject: 


Hi,
I found a Hidden Triple 5 7 8 in r1c8 r2c7 r2c8
and could eliminate 6 from r1c8, r2c7, r2c8.
Sometimes later, I found Hidden Pair 3 8 in r8c3 and r9c2 (in 3x3 Block)
and could eliminate it from r8c3, r8c3.
And then 6 not in r8c1, Nacked Pair 4 6 in r7c3 and r9c1 (same 3x3 Block).
Than I started the "double implication chains from pairs":
6 = r5c3, 6 <> r5c8, 6 = r9c8
6 = r5c3, 6 <> r7c3, 6 = r9c1
which leads to a contradiction for 6 in row 9, concluding:
6 not in r5c3.
6 = r3c7, 6 <> r4c7, 6 <> r5c7, 6<> r6c7, 6 = r5c8
6 = r5c7, 6 <> r3c6, 6 = r5c6
which leads to a contradiction for 6 in row 5, concluding:
6 not in r3c7
A little bit later I found a nice Swordfish on Row for digit 6:
in r6c3 r6c7 r7c3 r7c4 r8c4 r8c7 eliminating it from:
r2c3, r4c3, r4c7, r5c7, r9c7 and r9c4.
and finally a nice XYwing: X=4 Y=9 in r2c3 X=4 Z=6 in r2c5 Y=9 Z=6 in r3c2 leads me to eliminate 6 from r3c6.
I think that is pretty close to David's solution. I did not count the remaining 6's but the the puzzle is solved after dealing with them.
see u, 

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

Posted: Sun Jan 22, 2006 3:03 am Post subject: I didn't notice the XYWing ... 


Someone_Somewhere wrote:  ...finally a nice XYwing: X=4 Y=9 in r2c3 X=4 Z=6 in r2c5 Y=9 Z=6 in r3c2 leads me to eliminate 6 from r3c6. 
Huh. I didn't spot that XYWing, Someone. But I'm pretty sure if you look at the puzzle after you found the Swordfish you'll see the chain of 19 cells that can contain a "6"  and if you just color that chain you'll find a contradiction in r3c2 & r3c6, which allows one to solve 19 cells all at once!
Just in case you're interested, here's what the puzzle looks like after you find the swordfish.
Code:  46 8 3 9 1 7 2 5 46
5 1 49 3 46 2 78 78 469
2 69 7 8 5 46 3 1 469
8 69 19 7 46 5 14 3 2
3 2 5 1 9 46 47 76 8
7 4 16 2 3 8 16 9 5
1 5 46 46 8 3 9 2 7
9 7 8 56 2 1 56 4 3
46 3 2 45 7 9 58 68 1 
The beautiful binary chain of "6"s is apparent  it leads all around the board from r1c9 through r1c1 to r9c1 to r9c8, etc. dcb 

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someone_somewhere
Joined: 07 Aug 2005 Posts: 275 Location: Munich

Posted: Sun Jan 22, 2006 8:53 am Post subject: 


Hi,
The distribution of 6's is relly BEAUTIFULL.
If we eliminate first the one from r2c9 we are left with exact 2 occurences of digit 6 in every block!
It would be a pitty to distroy it with the XYwing, as you pointed.
I am using seldom coloring, as I worked a lot with it and it does not help in a lot of puzzles. So, I found a nice excuse for my "colorblindness".
I prefer now the "double implication chains" that are almost always giving good results. For example, in this case, a "5 star constallation" of 6's with the alpha star in r4c6 and the r4c2, r3c2 and r5c6, r3c6 is giving a contradiction in row 3, so that the aplha could be exploded.
This is equivalent to the coloring for a subset of nodes that is minimal for getting a contradiction.
This is one of the nice coloring examples that I ever have seen.
And it starts with 19 elements in the exclude table. My previous finding was that situations with 17 or 19 elements have the highest chance to give results with the coloring thechnique.
see u, 

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