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Techniques for tough puzzles

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Tue Jan 01, 2008 10:16 pm    Post subject: Techniques for tough puzzles Reply with quote

I've learned a number of new techniques lately, such as W- and M-Wings, XY-Chains, pincer coloring, ERs, Medusa and others, but most of them require strong links and bivalue cells. What I am wondering is how you generally approach a puzzle that's loaded with polyvalue cells and won't budge? I've tried everything I know except the ocean dwellers.

Here is one example of such a puzzle. If you'd like to see the original, you're looking at it since not one cell has been solved.

Code:

+-----------------+-------------------+-----------------+
| 137  6    1237  | 13478  5   1478   | 2347  2378 9    |
| 37   2359 4     | 36789  39  6789   | 23567 1    278  |
| 8    359  13579 | 134679 2   14679  | 3456  3567 47   |
+-----------------+-------------------+-----------------+
| 14   7    158   | 2459   19  3      | 129   28   6    |
| 2    34   136   | 4679   8   4679   | 1379  37   5    |
| 9    358  13568 | 2567   16  2567   | 1237  4    1278 |
+-----------------+-------------------+-----------------+
| 46   2489 289   | 125689 7   125689 | 12456 256  3    |
| 3467 1    2379  | 23569  369 2569   | 8     2567 247  |
| 5    238  2378  | 12368  4   1268   | 1267  9    127  |
+-----------------+-------------------+-----------------+

Play this puzzle online at the Daily Sudoku site
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Steve R



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

PostPosted: Wed Jan 02, 2008 1:13 pm    Post subject: Reply with quote

I rely heavily on conjugates, so much so that Iím usually stuck if I donít see any.

Here r4c7 and r5c7 are conjugate with respect to 9, while r5c7 is also conjugate to r5c3 with respect to 1. Throw in the (19) in r4c5 and I think you can eliminate 1 from r4c1.

More formally, the conjugates suggest a chain:

r4c1 = 1 ==> r4c5 = 9 ==> r4c7 ≠ 9 ==> r5c7 = 9 ==> r5c3 = 1 ==> r4c1 ≠ 1

We all do puzzles in our own way but perhaps this approach will help occasionally.

Steve

PS And youíre right: there is a fish.

3 can be eliminated from r2c2 using the x-wing in columns 1 and 5.
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Wed Jan 02, 2008 4:55 pm    Post subject: Reply with quote

Thank you Steve, I'll try that conjugate approach.

Quote:
3 can be eliminated from r2c2 using the x-wing in columns 1 and 5.

Not sure what happened here. My paper copy has an extra 3 in column 1 but it's not there on the Draw/Play grid. Now I don't know which is right. Question
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Steve R



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

PostPosted: Wed Jan 02, 2008 5:05 pm    Post subject: Reply with quote

We may be at cross purposes but I saw the x-wing as targeting rows 2 and 8 with the fin (r1c1) limiting the elimination to r2c2.

Steve
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Wed Jan 02, 2008 5:39 pm    Post subject: Reply with quote

Steve R wrote:
We may be at cross purposes but I saw the x-wing as targeting rows 2 and 8 with the fin (r1c1) limiting the elimination to r2c2.

Steve

My paper copy has a fourth 3, this one in r7c1. I just now noticed that 3 was a given in r7c9, so that's why the Draw/Play didn't have it. It's amazing how I can stare at something that should jump off the page, but doesn't. Exclamation
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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI

PostPosted: Wed Jan 02, 2008 9:29 pm    Post subject: Reply with quote

Marty, you've caused brief marital disharmony! - I got hooked on this instead of putting up a bookshelf, spending a happy 2 or 3 hours hunting and eventually finding one of my favourite animals, ALS.

Set A: R5 less C7: {1,3,4,6,7,9}
Set B : R4C5 on its own: {1,9}

I'm sure you're familiar with ALS, but in case someone's reading this who isn't, here goes with one way of looking at it.
Only one of A & B can have the 9 in box 5. If it's in A then B is just {1}. If it's in B, then A is {1,3,4,6,7} So there must be a 1 in either R5C3 or R4C5. So that kills the 1s in R4C13. (In general, the linking number, 9 here, is called x, the other one, 1 here, is z.)

(And, perhaps surprisingly, it's fairly easy thereafter.)
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Thu Jan 03, 2008 2:11 am    Post subject: Reply with quote

Steve's chain also removes <1> from r4c3. So, it has the same result as Victor's ALS.

For those interested, Steve's chain in Eureka notation is:
(1)r4c13-(1=9)r4c5-(9)r4c7=(9-1)r5c7=(1)r5c3-(1)r4c13; r4c13<>1
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Thu Jan 03, 2008 2:37 am    Post subject: Reply with quote

After those <1>s are removed, the puzzle only requires a c15 X-Wing on <3> and then, after considerable simplification, one XY-Wing.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Thu Jan 03, 2008 11:21 pm    Post subject: Reply with quote

Getting back to Marty's original question about attacking tough puzzles, I posted another approach, using this puzzle as an example, in a new thread.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Sun Jan 13, 2008 8:00 pm    Post subject: Reply with quote

I had a go at this one and couldn't get any further. Is this a Sudoku.com Very Hard puzzle? I don't recall any of these that couldn't be completed without a wing, UR or ER. I never got into chains - borderline guessing I say - in fact my reference guidelines suggest the ALS method could be considered a form of guessing. So there !!

Marty: One question: Using the Draw/Play and the Sweep functions - how did you remove the redundant 1's from Box 5 and the 6's from Box 7.
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Sun Jan 13, 2008 10:34 pm    Post subject: Reply with quote

cgordon wrote:
I had a go at this one and couldn't get any further. Is this a Sudoku.com Very Hard puzzle? I don't recall any of these that couldn't be completed without a wing, UR or ER. I never got into chains - borderline guessing I say - in fact my reference guidelines suggest the ALS method could be considered a form of guessing. So there !!

Marty: One question: Using the Draw/Play and the Sweep functions - how did you remove the redundant 1's from Box 5 and the 6's from Box 7.


Craig, I don't know where this puzzle was from, but I'm positive it wasn't from this site.

As to your question about how I removed redundant candidates using Draw/Play: not sure if you're asking about the logic I used or the mechanics of Draw/Play. If it's the former, I don't know. If it's the latter, you remove (or add) candidates by clicking in the cell, then typing the number(s) you want removed (or added) while holding down either the Ctrl or Alt key.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Mon Jan 14, 2008 1:06 am    Post subject: Reply with quote

Quote:
If it's the latter, you remove (or add) candidates by clicking in the cell, then typing the number(s) you want removed (or added) while holding down either the Ctrl or Alt key.


Thanks Mate: I am actually extremely clever but could never have figured that out in a million years. Should this Site be more user friendly?

Actually, I wrote my own Mickey Mouse computer program for showing the possibilities for EACH number. Awesome for spotting PATTERNS -which help with the UR's and ERs.

I often think that the preparatory work for a Sudoku is like initially turning over the pieces in a jig-saw puzzle. The more the computer can help - the better.
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Mon Jan 14, 2008 4:49 am    Post subject: Reply with quote

Quote:
Thanks Mate: I am actually extremely clever but could never have figured that out in a million years.

You're welcome. It's explained, not as directly as it could be, in the Draw/Play help section.
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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI

PostPosted: Wed Jan 16, 2008 1:22 pm    Post subject: Reply with quote

Cgordon says:
Quote:
my reference guidelines suggest the ALS method could be considered a form of guessing.


Don't think that's true, but this puzzle has caused me some sudoku heart-searching. I spent a long time looking for ALS, which was the the only technique I'd learned beyond the sorts of thing most contributors here can cope with, like W-wings, ERs, etc. I do think Steve's method is much better, but my mind doesn't seem to work that way - I mean that I can see how he did it, but not really how he knew how to to do it.

Anyway, I'm trying to learn how to do this kind of stuff, and have had some limited success, but it doesn't come easily.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Thu Jan 17, 2008 8:42 am    Post subject: Reply with quote

If ALS solutions in general are guessing, then so are XY Wings and XYZ Wings, since both of these are just forms of the "xz" ALS technique. If one were to forgo the former as "guessing," then consistency would demand that one forgo the latter. Me, I don't see that any of it is guessing in any way whatsoever.
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