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Saturday Puzzle Jan 14

 
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keith



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

PostPosted: Sat Jan 14, 2006 1:14 pm    Post subject: Saturday Puzzle Jan 14 Reply with quote

Here is today's puzzle.

Code:


+-------+-------+-------+
| . . 7 | . 9 . | . . . |
| 2 . 6 | . 1 . | . 5 . |
| . 9 . | . . 5 | 7 . 1 |
+-------+-------+-------+
| . . 8 | . 4 . | . . . |
| . 4 1 | . . . | 2 9 . |
| . . . | . 2 . | 8 . . |
+-------+-------+-------+
| 7 . 9 | 1 . . | . 2 . |
| . 1 . | . 7 . | 4 . 8 |
| . . . | . 5 . | 9 . . |
+-------+-------+-------+



I found it easier than most. The puzzle can be solved by identifying a BUG.

Keith
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David Bryant



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

PostPosted: Sat Jan 14, 2006 2:30 pm    Post subject: Not worth 6 stars Reply with quote

Hi, Keith!

I just finished working this puzzle in today's Rocky Mountain News a few minutes ago. The paper gave it six stars for difficulty-- that's hyperbole, imho.

I got it down to 13 empty cells remaining without making any extraneous pencil marks. At that point the puzzle needed three "9"s, five "3"s, and five "6"s. Since there were only two possible ways the "9"s could fit in the puzzle it really wasn't too hard to figure out which one was going to work. dcb

PS I guess the "bug" you're talking about is the 5-pointed figure in r6c4, r6c8, r8c4, r8c6, & r8c8. Is that right? Why do you call it a "bug"?
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Sat Jan 14, 2006 4:41 pm    Post subject: Reply with quote

Hi,

David was reffering to this exclude table:

Code:
1    5    7    8    9    3    6    4    2

2    8    6    4    1    7    3    5    9

4    9    3    2    6    5    7    8    1
 
39   2    8    5    4    69   1    7    36
   
6    4    1    7    3    8    2    9    5

39   7    5    69   2    1    8    36   4
               Aa                  Ba     
               aA                  bB     

7    36   9    1    8    4    5    2    36
     
5    1    2    369  7    69   4    36   8
               baB       Cb        CB   
               bBa       bC        Cb   
     
8    36   4    36   5    2    9    1    7

and from here we can:
- set r8c8 = 3 and/or
- exclude 6 from r6c4

I found a second way to the solution:
also a 5 star constallation with the nodes: r4c6 r4c9 r6c8 r8c8 r8c6
(or a Turbot-Fish)

Code:
1    5    7    8    9    3    6    4    2

2    8    6    4    1    7    3    5    9

4    9    3    2    6    5    7    8    1
 
39   2    8    5    4    69   1    7    36
                         A.             .a
                         aA             bB
   
6    4    1    7    3    8    2    9    5     

39   7    5    69   2    1    8    36   4
                                   .B         
                                   .b     
     
7    36   9    1    8    4    5    2    36
                                        bB
                                        .b
     
5    1    2    369  7    69   4    36   8
                         aB        .b   
                         Ba        .b   
     
8    36   4    36   5    2    9    1    7

and from here we can:
- exclude 6 from r8c8 and/or
- exclude 9 from r4c6

see u,
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keith



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

PostPosted: Sat Jan 14, 2006 8:24 pm    Post subject: A BUG and a remote pair Reply with quote

David and Someone,

In my opinion, the neatest solution to this puzzle is to identify the remote pair in r6c8 and r9c4:

Code:


1    5    7    8    9    3    6    4    2

2    8    6    4    1    7    3    5    9

4    9    3    2    6    5    7    8    1
 
39   2    8    5    4    69   1    7    36
                                        x
   
6    4    1    7    3    8    2    9    5

39   7    5    69   2    1    8    36   4
                                   y
               
7    36   9    1    8    4    5    2    36
     x                                  y
     
5    1    2    369  7    69   4    36   8
                                   x             
     
8    36   4    36   5    2    9    1    7
     y         x



You can find it by connecting the squares whose possibilities are <36>. So, r6c4 cannot be (<3> or) <6>, must be <9>, and the puzzle is solved!

What about the BUG? Robert Woodhead says that a puzzle in which each unsolved square has only two possibilities is a "Bivalve Universal Grave" (BUG) and that it is invalid. (It does not have a unique solution.)

Also, if each unsolved square has only two possibilities, then each row, column and block will contain each possibility either zero or twice. (Think about it!)

What does this mean? In the situation above, each unsolved square has only two possibilities, except one: r8c4 is <369>. From the above discussion, r8c4 cannot be <39> for then we have a BUG, so r8c4 must be <6>, and the puzzle is solved!

What do you think? I have a couple of other examples (for puzzles already posted in this forum) and will discuss them later.

Happy puzzling!

Keith
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someone_somewhere



Joined: 07 Aug 2005
Posts: 275
Location: Munich

PostPosted: Sun Jan 15, 2006 5:58 am    Post subject: Reply with quote

Hi,

WONDEFULL!
I had learned something new.
Can you post more examples about the BUG and links about it?

see u,
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keith



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

PostPosted: Sun Jan 15, 2006 3:38 pm    Post subject: BUG me twice! Reply with quote

Someone,

I have put another example in the thread "McCarthy Stone competition".

I found this in the manual for Robert Woodhead's software.

http://www.madoverlord.com/projects/sudoku.t

Here is what he says:

Quote:


BUG Hunting

A particularly interesting situation sometimes occurs when a puzzle is
almost completely solved. If the puzzle reaches a state where all but one
of the unsolved squares has 2 values (“bivalue squares”) (and thus, one
unsolved square has more than two -- the “polyvalue” square), then it is
possible to immediately make a reduction in the polyvalue square.

The way it’s done is very cute. Simply look at the possibilities in the
polyvalue square, and change it to a bivalue square such that each row,
column and block in the puzzle contains each unsolved possibility exactly
twice.

Such a configuration is actually illegal, because it will result in a puzzle that
does not have a single solution! These configurations are called Bivalue
Universal Graves (someone clearly loves acronymns!) or BUGs. The two
remaining possibilities in the polyvalue square are called the BUG
Possibilities.

The Bug Possibilities can be eliminated from the polyvalue square, and the
puzzle should become easily solveable by forces and pins.
It should be noted that it is possible to construct BUGs from puzzles that
have more than one polyvalue. However, it is often very difficult to
figure out what inferences can be made from these BUGs without using
techniques like forcing chains. Finding simple rules for BUG Hunting in
multi-polyvalue puzzles is an ongoing topic of discussion in the Sudoku
research community.

It is my hope to be able to report that BUG hunting is a more powerful
and easily-usable technique in the near future.



This is quite new - it was not in his manual (or software) before about December 31, 2005.

Keith
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David Bryant



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

PostPosted: Mon Jan 16, 2006 10:42 pm    Post subject: Another BUG example Reply with quote

I still have reservations about assuming the existence of a unique solution. But I have to admit that the BUG pattern is very cute. Here's a good example I ran across recently.
Code:
.  .  9  .  .  .  .  .  .
.  2  .  5  .  1  .  .  4
.  .  4  3  .  .  1  .  .
1  .  .  4  .  .  .  .  .
9  8  .  .  .  .  .  4  5
.  .  .  .  .  9  .  .  6
.  .  2  .  .  6  5  .  .
3  .  .  8  .  2  .  7  .
.  .  .  .  .  .  2  .  .

After 38 moves, with 19 cells still unresolved, you will find the BUG pattern. dcb
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keith



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

PostPosted: Mon Jan 16, 2006 11:52 pm    Post subject: Cool Puzzle! Reply with quote

David,

I found this one not very difficult (to get to the BUG). Then, the BUG is <138> and cannot be <18>.

Actually, I think this BUG pattern is more satisfying than some alternatives. In your puzzle one other path to a solution is a forcing chain: Guess a value, reach a contradiction.

Keith
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