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DB Saturday Puzzle - July 29, 2006

 
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Sat Jul 29, 2006 12:29 pm    Post subject: DB Saturday Puzzle - July 29, 2006 Reply with quote

More difficult than usual?

Code:
Puzzle: DB072906  ******
+-------+-------+-------+
| . 9 . | 5 3 . | 4 . 8 |
| . . . | . . . | . 9 1 |
| . . 5 | . . 6 | . . 3 |
+-------+-------+-------+
| . . . | 9 . . | . 1 7 |
| . . . | . . . | . . . |
| 6 1 . | . . 8 | . . . |
+-------+-------+-------+
| 5 . . | 7 . . | 9 . . |
| 3 8 . | . . . | . . . |
| 9 . 1 | . 2 3 | . 8 . |
+-------+-------+-------+


Keith
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Sat Jul 29, 2006 1:36 pm    Post subject: My solution Reply with quote

I get it to here:

Code:
+----------------+----------------+----------------+
| 1    9    27a  | 5    3    27b  | 4    6    8    |
| 27b  36   36   | 8    47   247  | 5    9    1    |
| 8    4    5    | 1    9    6    | 27   27   3    |
+----------------+----------------+----------------+
| 24   235  238  | 9    6    45   | 238  1    7    |
| 247a 2357 89   | 23   1    457c | 68   24   69   |
| 6    1    79   | 23   47   8    | 23   5    49   |
+----------------+----------------+----------------+
| 5    26   246  | 7    8    1    | 9    3    246  |
| 3    8    247  | 6    5    9    | 1    47   24   |
| 9    67   1    | 4    2    3    | 67   8    5    |
+----------------+----------------+----------------+


Note the hidden triple <689> in R5.

There is an interesting UR in R78C39. R8C9 cannot be <4>, it must be <2>, but this does not solve the puzzle.

Coloring on <7> (either "a" or "b" is <7>) eliminates <7> from R5C6 ("c") and the puzzle is solved.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5064
Location: Rochester, NY, USA

PostPosted: Sat Jul 29, 2006 4:00 pm    Post subject: Reply with quote

Quote:
Note the hidden triple <689> in R5.


Keith, just to clarify terminology: when I was learning the most basic stuff, this would have been a naked triple, or just plain triple. I thought hidden meant it had to be somewhat disguised by having other candidates in one or more of the cells.
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Marty R.



Joined: 12 Feb 2006
Posts: 5064
Location: Rochester, NY, USA

PostPosted: Sat Jul 29, 2006 5:17 pm    Post subject: Re: My solution Reply with quote

keith wrote:
I get it to here:

Code:
+----------------+----------------+----------------+
| 1    9    27a  | 5    3    27b  | 4    6    8    |
| 27b  36   36   | 8    47   247  | 5    9    1    |
| 8    4    5    | 1    9    6    | 27   27   3    |
+----------------+----------------+----------------+
| 24   235  238  | 9    6    45   | 238  1    7    |
| 247a 2357 89   | 23   1    457c | 68   24   69   |
| 6    1    79   | 23   47   8    | 23   5    49   |
+----------------+----------------+----------------+
| 5    26   246  | 7    8    1    | 9    3    246  |
| 3    8    247  | 6    5    9    | 1    47   24   |
| 9    67   1    | 4    2    3    | 67   8    5    |
+----------------+----------------+----------------+


Note the hidden triple <689> in R5.

There is an interesting UR in R78C39. R8C9 cannot be <4>, it must be <2>, but this does not solve the puzzle.

Coloring on <7> (either "a" or "b" is <7>) eliminates <7> from R5C6 ("c") and the puzzle is solved.

Keith


I must've reached a similar, if not the same, position as you did Keith. I noticed that rectangle but didn't try anything with it because I was looking for other options first.

Now I have a very interesting observation. There is a strong link on "7" in cols. 1 and 6 ( what you might call a "fork"); I used that to eliminate the "7" from r2c5 (either r1c6 or r6c5 must be "7") and that broke the puzzle wide open.

So we each solved the puzzle by eliminating a "7" from c5, but from two different cells. Therefore, one of us has made an error or else this puzzle does not have a unique solution.
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Sat Jul 29, 2006 5:34 pm    Post subject: Unhidden triple Reply with quote

Marty,

One step back from what I posted, the situation is:

Code:
+----------------------+----------------------+----------------------+
| 1      9      27     | 5      3      27     | 4      6      8      |
| 27     36     36     | 8      47     247    | 5      9      1      |
| 8      4      5      | 1      9      6      | 27     27     3      |
+----------------------+----------------------+----------------------+
| 24     235    2348   | 9      6      45     | 238    1      7      |
| 247    2357   234789 | 23     1      457    | 2368   24     2469   |
| 6      1      479    | 23     47     8      | 23     5      49     |
+----------------------+----------------------+----------------------+
| 5      26     246    | 7      8      1      | 9      3      246    |
| 3      8      247    | 6      5      9      | 1      247    24     |
| 9      67     1      | 4      2      3      | 67     8      5      |
+----------------------+----------------------+----------------------+

The triple is hidden. I "unhid" it. It is quite difficult to spot, I think. The corresponding naked set in R5 is <23457>.

There is a UR on <23> in R56C47 which will help to partly reveal the triple.

Keith
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keith



Joined: 19 Sep 2005
Posts: 3136
Location: near Detroit, Michigan, USA

PostPosted: Sat Jul 29, 2006 5:51 pm    Post subject: The fork that I see Reply with quote

Marty,

The fork that I see is in C1 (ab) and C5 (cd):

Code:
+----------------+----------------+----------------+
| 1    9    27g  | 5    3    27h  | 4    6    8    |
| 27a  36   36   | 8    47c  247  | 5    9    1    |
| 8    4    5    | 1    9    6    | 27   27   3    |
+----------------+----------------+----------------+
| 24   235  238  | 9    6    45   | 238  1    7    |
| 247b 2357 89   | 23   1    457f | 68   24   69   |
| 6    1    79e  | 23   47d  8    | 23   5    49   |
+----------------+----------------+----------------+
| 5    26   246  | 7    8    1    | 9    3    246  |
| 3    8    247  | 6    5    9    | 1    47   24   |
| 9    67   1    | 4    2    3    | 67   8    5    |
+----------------+----------------+----------------+


One of b or d must be <7>; You can eliminate <7> from cells e and f. The last one is the same elimination I made with coloring.

edit: Now I see the other fork in R1 (gh) and R5 (ed). One of h or d must be <7>; You can eliminate <7> from cells f and c.

Keith
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David Bryant



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

PostPosted: Sat Jul 29, 2006 6:01 pm    Post subject: Rows or columns? Reply with quote

Marty R wrote:
... one of us has made an error or else this puzzle does not have a unique solution.

I don't see a "fork" in columns 1 and 6, Marty ... I see it in rows 1 & 6, instead. I think that might be a typo.

There's no conflict between your method and Keith's -- you eliminated "7" from r2c5, meaning that r2c5 = 4, and Keith eliminated a "7" from r5c6, leaving the {4, 5} pair in r45c6, and eliminating "4" from r2c6 (leaving r2c5 = 4, unique horizontal). Maybe we're all getting cross-eyed from staring at these things too long!

Oh -- I hit on the same basic structure, but I noticed the "fork" between row 1 and column 5 ({2, 7} pair in row 1 -- {4, 7} pair in column 5). That allows one to eliminate "7" from r6c3, and r6c3 = 9 also solves this puzzle. dcb
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Marty R.



Joined: 12 Feb 2006
Posts: 5064
Location: Rochester, NY, USA

PostPosted: Sat Jul 29, 2006 6:28 pm    Post subject: Reply with quote

Quote:
The triple is hidden. I "unhid" it. It is quite difficult to spot, I think. The corresponding naked set in R5 is <23457>.

There is a UR on <23> in R56C47 which will help to partly reveal the triple.


I did the same thing as you did Keith. It's just a difference what we call things. Rather than a hidden triple (which would be near-impossible for me to spot), I spotted the naked set which I would call a "quint", and that exposed the triple.

I also used that 23 rectangle, which I forgot to mention in my original post.

Quote:
I don't see a "fork" in columns 1 and 6, Marty ... I see it in rows 1 & 6, instead. I think that might be a typo.

There's no conflict between your method and Keith's -- you eliminated "7" from r2c5, meaning that r2c5 = 4, and Keith eliminated a "7" from r5c6,


Yes David, a typo. The fork is in rows, not columns.

As to no conflict between Keith's method and mine, again correct. Maybe I'm getting dyslexic in my dotage, as I saw his elimination of the "7" from r5c6 and I was thinking r6c5.

Sorry to start all this confusion and cause all the wasted keystrokes. Embarassed
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