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DB Saturday puzzle (March 25)

 
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PostPosted: Sat Mar 25, 2006 6:34 pm    Post subject: DB Saturday puzzle (March 25) Reply with quote

I posted this once, but it seems to have disappeared. A good one.

Code:


Puzzle: DB032506  ******
+-------+-------+-------+
| . . . | . . . | 1 3 . |
| . 2 . | 4 . . | . 9 8 |
| . . . | . 3 1 | 4 5 . |
+-------+-------+-------+
| 8 . . | 3 . 2 | . . 5 |
| . 7 . | . . . | . 1 . |
| 5 . . | 1 . 7 | . . 4 |
+-------+-------+-------+
| . 9 7 | 2 1 . | . . . |
| 3 8 . | . . 4 | . 2 . |
| . 1 5 | . . . | . . . |
+-------+-------+-------+



This is the David Bodycombe puzzle which is not available online.

Keith
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David Bryant



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

PostPosted: Sun Mar 26, 2006 12:45 pm    Post subject: The disappearing Bodycombe puzzle. Reply with quote

Keith wrote:
I posted this once, but it seems to have disappeared. A good one.

Hi, Keith!

I guess that was the "instability" samgj warned us about. I did see your post yesterday, and also had this puzzle in my local newspaper.

Maybe I missed something, but this seems to be the toughest Bodycombe puzzle yet. To get through it I had to do some coloring, then an XY-Wing and an elimination based on a non-unique rectangle. After that an "8-star constellation" and two more XY-Wings finished it off! dcb
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Marty R.



Joined: 12 Feb 2006
Posts: 5159
Location: Rochester, NY, USA

PostPosted: Sun Mar 26, 2006 10:49 pm    Post subject: Reply with quote

Quote:
Maybe I missed something,

David, perhaps you did miss something. After the usual stuff, I started a forcing chain with a "67" that was in r1c9. The "7" resulted in duplicates, so after entering the "6", the puzzle opened up.
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Mon Mar 27, 2006 3:26 am    Post subject: Reply with quote

I found a solution using unique rectangles, XY-wings, and three Double Implication Chains (a first for me). I'll post a solution after I have studied it further.

David, I agree this is about the most difficult DB puzzle to date. There was another one of a similar difficulty in December 2005.

Best wishes,

Keith
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Mon Mar 27, 2006 8:35 am    Post subject: Reply with quote

Hi,
Some comments about using the DIC (Double Implication Chains):
- it depends on your starting Alpha star.
- it depends about how many stars you are willing to follow (how deep you are ready to go). If I start with letter A than I can mark with "a" all that will be excluded, with "B" all that ones that are forced to be, with "b" all the ones excluded by B, with "C" all the ones forced, with "c" all excluded and so on ... with every level some remaining digits from the candidate table are marked as stars with a BIG or SMALL letter. Thorectic I could continue with this till I get a contradiction or I get a star excluded, or I it can happen that I am getting NOWHERE any more. In this last case, I will have to strat with a next ALPHA star.

Starting from this observation, I can be lucky or not in which case I will have to work more.
Now lets prove what I have stated - with this example.

case I.
from the following position I am ready to go any as deep as level "c" from a ALPHA star.

Code:
79   5    4    6789 2    689  1    3    67     
..   .    .    a... .    a..  .    .    Aa     
aB   .    .    .a.b .    ..b  .    .    aA
     
1    2    3    4    57   56   67   9    8     
.    .    .    .    .b   bB   aB   .    .     
.    .    .    .    bB   ..   Ba   .    .
     
79   6    8    79   3    1    4    5    2     
..   .    .    ..   .    .    .    .    .     
Bb   .    .    ..   .    .    .    .    .
     
8    4    1    3    69   2    69   7    5     
.    .    .    .    ..   .    ..   .    .     
.    .    .    .    ..   .    ..   .    .
     
6    7    29   589  4    589  2389 1    39     
.    .    ..   ...  .    ...  .... .    b.     
.    .    ..   ...  .    ...  .... .    ..
     
5    3    29   1    689  7    2689 68   4     
.    .    ..   .    ...  .    .... b.   .     
.    .    ..   .    ...  .    .... ..   .
     
4    9    7    2    1    3568 358  68   36     
.    .    .    .    .    b.b. b..  Bb   Ba     
.    .    .    .    .    .... ...  ..   ..
     
3    8    6    579  579  4    579  2    1     
.    .    .    ...  ...  .    .b.  .    .     
.    .    .    ...  .b.  .    ...  .    .
     
2    1    5    6789 789  3689 3789 4    3679     
.    .    .    Bbbb b..  .b.. bb.. .    baBb     
.    .    .    .... b..  .... .... .    ..a.     

and I can exclude 7 from r9c5. But this ia unfortunate not a breakthrough.
So I will continue (after Hidden Pair 5 7 in r2c5 and r8c5):

Code:
79    5     4     6789  2     689   1     3     67     
bC    .     .     .a.b  .     ..b   .     .     bB
     
1     2     3     4     57    56    67    9     8     
.     .     .     .     aA    Bb    Ba    .     .     

79    6     8     79     3    1     4     5     2     
Bb    .     .     aB     .    .     .     .     .     

8     4     1     3     69    2     69    7     5     
.     .     .     .     C.    .     bC    .     .     

6     7     29    589   4     589   2389  1     39     
.     .     ..    C.b   .     b..   ....  .     ..     

5     3     29    1     689   7     2689  68    4     
.     .     ..    .     ...   .     .b..  C.    .     

4     9     7     2     1     3568  358   68    36     
.     .     .     .     .     .b..  .C.   ..    ..     

3     8     6     579   57    4     579   2     1     
.     .     .     bCb   Ba    .     b.C   .     .     

2     1     5     6789  89    3689  3789  4     3679     
.     .     .     ...b  ..    ....  ....  .     ..b.     

Contradiction on column: 9 in r4c7 (level='C') and I can
excluded 7 from r2c5
This time I am lucky and this is breaking the puzzle.
Note that for this case I was willing to analyze up to level "C".

case II. I am to bored and willing to get only up to level "b".
With such a strategy, and starting with the APLHA stars from r1c1 first on the row and than r2c1 ... I will need 6 times to use the DICs !!!

1. starting from APLHA 6,7 in r1c9 - 7 not in r9c5 (level='b')
Hidden Pair 5 7 in r2c5 and r8c5 (in Column)
2. starting from APLHA 7,9 in r3c4 - 7 not in r8c7 (level='b')
3. starting from APLHA 6,7 in r1c9 - 3 not in r9c7 (level='b')
4. starting from APLHA 6,9 in r4c7 - 9 not in r5c4 (level='b')
5. starting again from same ALPHA stars - 9 not in r9c5 (level='b')
6. starting from 7,9 in r1c1 - 9 not in r9c9 (level='b')
and this is finally breaking the puzzle.

So, it can happen that starting from one ALPHA star if I work deep enough and get not bored, and if I am lucky, the puzzle can be broken.
I am thinking now of using an additional technique (thank you David for it): instead of starting from pairs of an ALPHA star, to start from a DOUBLE star - meaning to start from 2 different cells that can have several candidates each. But to choose the same digit in each one, by the criteria that only one of each can hold that digit in the final solution.

hope that I could contribute ...
see u,
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Tue Mar 28, 2006 12:59 am    Post subject: Double meanings Reply with quote

Someone,

Thank you very much for the detailed explanation. Now, I undersatnd your Double Implication Chains (DIC) and Constellations. (I think!)

As I see it, your technique involves choosing a value in a square (that has only two possibilities?) and then following the dual implications of values that other squares can and cannot have.

There is another "Dual Implication" technique. This is to start from a square that has only two possible values, and then to track the implications of each value.

For example, look at R6C8 = <68> as the Alpha square. (It is a confusing coincidence that this square has the same possibilities as its row and column numbers!)

Then R6C8 = <6>, R4C7 = <9>, and R5C9 = <3>.

And, R6C8 = <8>, R7C8 = <6>, and R7C9 = <3>.

So, no matter the value of R6C8, there is a <3> in C9, and R9C9 is not <3>.

There are a number of such eliminations which can be made in this puzzle. I am still studying it.


---------------
Someone and David,

I am not so sure about the proposed double star technique (as stated and as I understand it). If you start with the same value in two related squares, that is already a contradiction. If you start with the same value in two unrelated squares and then reach a contradiction, what can you conclude?

Best wishes,

Keith
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David Bryant



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

PostPosted: Tue Mar 28, 2006 4:38 pm    Post subject: Ruud's "template" elimination Reply with quote

Keith wrote:
I am not so sure about the proposed double star technique (as stated and as I understand it). If you start with the same value in two related squares, that is already a contradiction. If you start with the same value in two unrelated squares and then reach a contradiction, what can you conclude?

I'll try to clarify this for you, Keith.

I first ran into this "double-star" idea as a "template" elimination on some of Ruud's "nightmare" puzzles. This is (sometimes) similar to "coloring." Let's say, for instance, that there are only two ways to fit a "5" in column 5. One may be able to obtain information by first supposing that there's a "5" in the first spot and seeing where that leads. Then suppose that the "5" is in the other possible position. If it leads to some result that's the same as what one obtained with the "5" in its first location, then that result must be valid, because it holds no matter where the "5" actually goes.

Here's an actual illustration from the "nightmare" puzzle for March 27, 2006, where the following position arises after making a few "obvious" moves.
Code:
 489    7   12589 1589    6   1289+  459   249    3
 469  12469 1259    3   1257  1279    8   24679  256
  3    269  2589- 5789  2578    4   5679    1    256
  1    34     7     2    34     5    69    69     8
  5     8     6    179   17    179    2     3     4
 49   2349   239   48    348    6     1     5     7
 78     5    138    6   12478 1278-  347   247    9
7869+  169    4   1578  12578   3    567   267  1256
  2    136   13   1457    9    17   34567   8    156

Here the "double-star" lies in column 6.

-- If r1c6 = 8 then r1c3 = 8 (only place left for an "8" in top left 3x3 box).
-- If r7c6 = 8 then r8c1 = 8 (only place left for an "8" in bottom left 3x3 box).
-- In each case there cannot be an "8" at r1c1, nor at r7c3.

Interestingly, we can also view this as an application of the "coloring" method, as indicated by the +/- signs in the grid above. It's also pretty easy to translate this into the language of Nishio:

r1c1 = 8 ==> r7c6 = 8 ==> no way to fit an "8" in bottom left 3x3 box.
r6c3 = 8 ==> r1c6 = 8 ==> no way to fit an "8" in top left 3x3 box.

Calling this a "double-star" rather than "Nishio" probably doesn't add anything. But the technique of working in the other direction (from the pair of possible locations in column 6) makes this pattern easier to find than the classic "Nishio" would be, I think. dcb
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Tue Mar 28, 2006 4:58 pm    Post subject: Reply with quote

Hi David,

That is exact what I had in mind, and that you have suggested in one of the last emails.

Instead of starting from an ALPHA star with 2 digits, we could also start from a "double" star. So it is quite easy to find such double stars.
I have to look in the candidate table on rows, on columns and in the boxes and than I can start the DIC from them.

This is real an real enhancement to the DIC that I have used till now!
Thank you David for all your pacience to expain it so clear. Of course that everyone should start using it in order to find out that there are a couple of nice cases that where not explained (by intention).

see u,
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