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Marty R.
Joined: 12 Feb 2006 Posts: 5500 Location: Rochester, NY, USA

Posted: Tue Mar 28, 2006 9:10 pm Post subject: Help? 


The below puzzle is similar to a number of puzzles that I encounter; i.e., the basic techniques of pairs, triples, etc., and locked candidates leave me at an impasse while numerous cells still contain four, five and six candidates. These cells are too busy for me to proceed to XYWings, rectangles, chains and the like. Following the puzzle with my candidates is the original.
I have two questions:
1) Are there some general guidelines for how to proceed when so many cells have all those candidates?
2) What is the next step for this particular puzzle?
Code:  
7 23459 34569 1 8 23456 346 4569 49 
12469 23459 34569 2349 3459 23456 8 145679 1479 
14689 4589 45689 49 459 7 146 3 2 

5 2347 347 6 1347 8 9 1247 1347 
49 6 3479 349 2 134 5 8 1347 
2489 234789 1 5 3479 34 2347 247 6 

3 1 569 7 45 245 246 2469 8 
69 59 2 8 1345 1345 3467 4679 3479 
48 478 478 23 6 9 123 12 5 
 
Code:  718
8
732
589
628
156
317
2
695 


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

Posted: Wed Mar 29, 2006 1:07 am Post subject: Try DIC technique in a pinch 


Marty R wrote:  I have two questions:
1) Are there some general guidelines for how to proceed when so many cells have all those candidates?
2) What is the next step for this particular puzzle? 
The best suggestion I have in this situation is to try looking for doubleimplication chains. They're hard to find, but they're generally in there somewhere.
In this case we can follow a "6star constellation" to show that r9c8 = 1. The "alpha star" is r9c4.
A. r9c4 = 2 ==> r9c8 = 1.
B. r9c4 = 3 ==> r2c4 = 2 ==> r1c2 = 2 ==> r6c1 = 2 ==> r4c8 = 2 ==> r9c8 = 1.
Notice that the second chain is entirely positional  there are only two places for a "2" in column 4, so if r9c4 <> 2 we must have r2c4 = 2. Similarly for the rest of the links in this chain ... once there's a "2" at r2c4 the only place left for a "2" in box 1 is at r1c2  that forces the "2" in box 4, and that in turn forces the "2" in box 6.
On simple puzzles we sometimes encounter a "spiral" in a single digit ... we can see immediately that there's only one way to place all the remaining instances of a missing digit, and the path unfolds as we follow it. The second leg of this DIC is like that. dcb
PS I'm sorry this doesn't lead any farther right away, Marty  I'll try to find another digit or two when I have some spare time. 

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

Posted: Wed Mar 29, 2006 1:35 am Post subject: This thing is loaded with DIC's 


Hi again, Marty!
I had a little more time  this puzzle is fun! Here's the position after placing a couple of "1"s in the puzzle.
Code:  
7 23459 34569 1 8 23456 346 4569 49 
1 23459 34569 2349 3459 23456 8 45679 479 
4689 4589 45689 49 459 7 1 3 2 

5 2347 347 6 1347 8 9 247 1347 
49 6 3479 349 2 134 5 8 1347 
2489 234789 1 5 3479 34 2347 247 6 

3 1 569 7 45 245 246 2469 8 
69 59 2 8 1345 1345 3467 4679 3479 
48 478 478 23 6 9 23 1 5 
 
Let's try a doubleimplication chain from r9c1.
A. r9c1 = 4 ==> r5c1 = 9.
B. r9c1 = 8 ==> r6c2 = 8 ==> r3c2 = 8 ==> r3c1 = 6 ==> r8c1 = 9.
So now we know that the "9" in column 1 must lie either in r5c1 or r8c1  there are no other possible outcomes. So we can eliminate "9" at r2c1, r3c1, and r6c1.
Try working out from some of the other twovalued cells in this puzzle, Marty ... I'll bet you can find several more DIC's in short order! dcb 

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Marty R.
Joined: 12 Feb 2006 Posts: 5500 Location: Rochester, NY, USA

Posted: Wed Mar 29, 2006 6:00 pm Post subject: 


Thank you very much David. I'm printing out this thread to follow it along a little easier. I was really put off by all those cells with the large number of candidates.
Quote:  Notice that the second chain is entirely positional 
How is a "positional" chain defined? As opposed to a _________chain?
Quote:  this puzzle is fun! 
That is a fact that heretofore had escaped me. 

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

Posted: Wed Mar 29, 2006 9:50 pm Post subject: "Position" vs "value" 


Marty R wrote:  How is a "positional" chain defined? As opposed to a _________chain? 
I think we've had part of this discussion before, Marty  right here.
Anyway, there are in general two ways to place a single value into a particular cell.
 The value may be the sole candidate in that cell  digit x has to go there because the other 8 digits already appear in the row + column + box in which that cell lies. I refer to chains that contain links based on this idea as valueoriented chains, or as using valueoriented logic.
 The cell may be the only one in this row, or column, or box, in which value x can possibly fit. This is often referred to as a "unique" cell (unique in column, unique in row, or unique in box)  I think Keith says such a cell is "pinned" to be x (or maybe x is "pinned" in that cell?). I refer to chains containing links based on this idea as positional chains, or as using positional logic.
Your observation that there were too many cells with 4, 5, & 6 candidates in this puzzle for "forcing chains" to be useful was apparently rooted in the notion that chains are always valueoriented. That's why I stressed the idea of positional logic in the discussion of the "6star constellation."
I hope that's clear enough! dcb 

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Marty R.
Joined: 12 Feb 2006 Posts: 5500 Location: Rochester, NY, USA

Posted: Thu Mar 30, 2006 5:26 pm Post subject: 


Quote:  I hope that's clear enough! 
I think that it is. Thanks again David. 

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