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Marty R.



Joined: 12 Feb 2006
Posts: 5181
Location: Rochester, NY, USA

PostPosted: Tue Mar 28, 2006 9:10 pm    Post subject: Help? Reply with quote

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 XY-Wings, 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:
7--18----
------8--
-----7-32
5----89--
-6--2--8-
--15----6
31-7-----
--2------
----69--5
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David Bryant



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

PostPosted: Wed Mar 29, 2006 1:07 am    Post subject: Try DIC technique in a pinch Reply with quote

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 double-implication chains. They're hard to find, but they're generally in there somewhere.

In this case we can follow a "6-star 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. Smile
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David Bryant



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

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

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 double-implication 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 two-valued 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: 5181
Location: Rochester, NY, USA

PostPosted: Wed Mar 29, 2006 6:00 pm    Post subject: Reply with quote

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. Laughing
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David Bryant



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

PostPosted: Wed Mar 29, 2006 9:50 pm    Post subject: "Position" vs "value" Reply with quote

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 value-oriented chains, or as using value-oriented 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 value-oriented. That's why I stressed the idea of positional logic in the discussion of the "6-star constellation."

I hope that's clear enough! dcb
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Marty R.



Joined: 12 Feb 2006
Posts: 5181
Location: Rochester, NY, USA

PostPosted: Thu Mar 30, 2006 5:26 pm    Post subject: Reply with quote

Quote:
I hope that's clear enough!


I think that it is. Thanks again David.
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