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DB Saturday Puzzle - May 20, 2006

 
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keith



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

PostPosted: Sat May 20, 2006 11:55 am    Post subject: DB Saturday Puzzle - May 20, 2006 Reply with quote

This is a great puzzle to solve with pencil and paper! With an "advanced" twist at the end.

Code:

Puzzle: DB052006  ******
+-------+-------+-------+
| 6 . . | . 5 4 | . . . |
| . 2 . | . . . | . . . |
| 3 . 4 | 2 7 6 | . . . |
+-------+-------+-------+
| . . . | 8 . . | 1 4 6 |
| . 1 . | . . . | . 8 . |
| 8 5 2 | . . 1 | . . . |
+-------+-------+-------+
| . . . | 9 8 2 | 5 . 4 |
| . . . | . . . | . 7 . |
| . . . | 6 1 . | . . 3 |
+-------+-------+-------+


Keith
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Marty R.



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

PostPosted: Sat May 20, 2006 5:06 pm    Post subject: Re: DB Saturday Puzzle - May 20, 2006 Reply with quote

keith wrote:
This is a great puzzle to solve with pencil and paper!

Is there another way? I've never tried a computer program. Wink

Quote:
With an "advanced" twist at the end.


Being a lousy mind reader, I'm not sure what you mean by that term.

My take: this puzzle practically seemed to solve itself while filling in cells with their candidates. When that process was done, the vast majority of the cells were solved or occupied with pairs and triples.

At this point, I guessed that the solution could be had via three or four different techniques. However, I noticed the potential for a technique (which I learned from this forum) which, to the best of my knowledge, I've only used two or three times, so I used that one. That solved one cell which was enough to finish it off.

Later, after some discussion, I'll be interested to find out if the technique I used was the "advanced" twist you mentioned.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat May 20, 2006 8:41 pm    Post subject: Reply with quote

I agree with you Marty, the puzzle did seem to solve itself. I found three techniques that would finish it off, two of which are essentially the same and make the same exclusion. I think Keith referred to the third.
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keith



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

PostPosted: Sat May 20, 2006 10:23 pm    Post subject: Easier than usual? Reply with quote

The puzzle is, I think, relatively easy. I solved it with no pencil marks to this point:

Code:

+-------------+-------------+-------------+
| 6   7   89  | 1   5   4   | 3   29  28  |
| 15  2   15  | 3   9   8   | 4   6   7   |
| 3   89a 4   | 2   7   6   | 89b 5   1   |
+-------------+-------------+-------------+
| 9   3   7   | 8   2   5   | 1   4   6   |
| 4   1   6   | 7   3   9   | 2   8   5   |
| 8   5   2   | 4   6   1   | 7   3   9   |
+-------------+-------------+-------------+
| 7   6   3   | 9   8   2   | 5   1   4   |
| 12  89b 189 | 5   4   3   | 6   7   28  |
| 25  4   589 | 6   1   7   | 89a 29  3   |
+-------------+-------------+-------------+

(All the moves so far involve only naked or hidden singles.)

Solution 1:
Now, notice the remote naked pair <89>, in the chain labeled "a", "b". Thus, R9C3 is not <89>, it must be <5>.

Edit: I see R1C3 is also <89> and could be labeled "b". It achieves the same reduction.

Solution 2:
If you do not see the above, you may notice the interaction: R9 is the only place for <9> in B9. Thus, R9C3 is not <9>. Then, all the unsolved cells have only two candidates, except R8C3 has three candidates.

This is a BUG pattern; R8C3 must be <8>. (If it is not <8>, it is <19>. Then, all unsolved squares have two candidates, and each candidate occurs twice, and only twice, in each row, column, and block. This pattern does not have a unique solution.)

These two I found by hand. Looking at this with Sudoku Susser, there are a number of techniques (coloring, forks, chains) that essentially make the same reductions as the remote pair.

Marty and Tracy: What did you do at the end?

Best wishes,

Keith
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Marty R.



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

PostPosted: Sat May 20, 2006 11:30 pm    Post subject: Reply with quote

I used the remote pairs. After reading some of the replies, I erased it and did it again to see what options I could find. The first time I missed the locked "9s" in row 9, but noticed it the second time around.

In addition to the remote pairs, I saw coloring on the "8" would do the job, as well as a forcing chain which could probably be based in any unsolved cell.

I did not notice the BUG pattern, and if I did, I wouldn't have known what to do with it.

Quote:
This is a BUG pattern; R8C3 must be <8>. (If it is not <8>, it is <19>. Then, all unsolved squares have two candidates, and each candidate occurs twice, and only twice, in each row, column, and block. This pattern does not have a unique solution.)


So, when you spot a BUG pattern, do you just have to eyeball the grid to see what would create the non-unique solution or is there some sort of guideline? Also, is a BUG pattern ever required to solve a puzzle, or does one use it because it's fun to spot and use? At first thought, it would seem that a puzzle with all two-candidate cells but one would have other solutions.

Finally, you referred to a "fork" technique, a term I've never seen.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sun May 21, 2006 1:18 pm    Post subject: Reply with quote

Keith,

I used the BUG+1 pattern to solve it, then looking back at it noticed the colouring and the remote pair (grouped colouring). I thought you were referring to the BUG+1 pattern as your 'twist' at the end.

Marty,

In the BUG+1 pattern all unsolved cells have two candidates except for one cell which has three. One of the values in that cell occurs three times in each row, box and column of which that cell is a member. That is the value that must be assigned to that cell to avoid the BUG pattern.
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keith



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

PostPosted: Sun May 21, 2006 2:45 pm    Post subject: "Fork" Reply with quote

Marty,

Some call the following a "fork". It is two strong links that line up at one end. (Almost an X-wing.) In this puzzle, it is uses exactly the same cells as the remote pair. Apply it first for <8>, then for <9>.

Code:

. . . | . . . | . . .
* . * | . C . | . . .
. A . | * | * | . . .
--|---+---|---+------
. | . | . | . | . . .
. | . | . | . | . . .
. | . | . | . | . . .
--|---+---|---+------
. | . | . | . | . . .
. B . | . D . | . . .
. . . | . . . | . . .

In this picture, A and B are the only cells in C2 that contain a particular candidate. Similarly, C and D are the only cells in C5 that have the candidate. You can make eliminations of the candidate in the cells marked "*".

If A is true you can make the eliminations. If A is false, B is true, D is false, and C must be true, and you can make the eliminations. There are various names for this (none of which I made up).

The diagram is taken from

http://www.sudoku.com/forums/viewtopic.php?t=3326

In the puzzle of this thread, the fork uses exactly the same cells as the remote pair. Apply it first for <8>, then for <9>.

Here is more on the BUG pattern:

http://www.sudoku.com/forums/viewtopic.php?t=2352

In our puzzle, block 7 comes down to:
Code:

+-------------+
| 7   6   3   |
| 12  89  189 |
| 25  4   58  |
+-------------+

If <189> has <1> as a candidate, there will be two <1>'s in the block. If it has <9> as a candidate, there will be two <9>'s. To break the BUG pattern, <189> must be <8>.

Maybe Tracy's explanation is better.

I have encountered this a few times. I would argue that, because of all the strong links, coloring will probably solve this pattern every time.

Keith
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Marty R.



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

PostPosted: Sun May 21, 2006 9:35 pm    Post subject: Reply with quote

Thanks, Tracy and Keith. I have seen numerous "forks" that haven't helped. At first glance, it would appear that "A" and "C" need to be in the same band/stack for elimination possibilities.

It also appears that "BUG" and "BUG+1" both refer to the same pattern.
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keith



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

PostPosted: Sun May 21, 2006 9:57 pm    Post subject: Reply with quote

Marty,

Tracy is being more precise.

The BUG pattern is where every unsolved cell has two candidates. It is not unique.

The BUG+1 pattern is where one cell has three candidates, all the other unsolved cells have two. You have to avoid the BUG.

Actually, I am not a fan of this. If you do not clear all naked and hidden singles first (or, if you do not check that each candidate occurs only twice in each row, column, or box, which is the same thing), The BUG+1 reduction cannot be applied. I have been burned a couple of times.

Keith
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Marty R.



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

PostPosted: Mon May 22, 2006 12:25 am    Post subject: Reply with quote

Gotcha. You do something with the BUG+1 to prevent the BUG.

By the way, are you two Michiganders relieved that your Pistons finally woke up and realized they weren't supposed to lose to the Cavs?
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keith



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

PostPosted: Mon May 22, 2006 3:17 am    Post subject: Reply with quote

Whether they win it all or not, I think this Pistons team is one of the greatest ever. Did you watch game 1 against the Cavs? An awesome display. How this series went to 7 games is beyond me.

Keith
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Marty R.



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

PostPosted: Mon May 22, 2006 3:37 pm    Post subject: Reply with quote

I probably saw a piece of game 1, as I have for most of the games. I lack the patience to watch whole games, but I tend to catch the last few minutes and watch highlights, as I want to keep abreast of what's happening. I'd be watching the whole game if there was a home team for me. I watch Buffalo Bills games and Syracuse U. basketball games because they are de facto home teams for Rochester.

But Detroit has certainly shown over the last few years how successful the team concept can be.
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