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DB Saturday Puzzle - May 6, 2006

 
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keith



Joined: 19 Sep 2005
Posts: 3178
Location: near Detroit, Michigan, USA

PostPosted: Sat May 06, 2006 1:19 pm    Post subject: DB Saturday Puzzle - May 6, 2006 Reply with quote

This one looks interesting - I haven't solved it yet.
Code:


Puzzle: DB050606  ******
+-------+-------+-------+
| 7 . . | 3 . . | 6 . 2 |
| . . . | 5 . . | 7 . . |
| 4 . 9 | . 8 . | . 5 . |
+-------+-------+-------+
| . . . | . . . | 5 . 7 |
| 8 . 3 | 6 . 4 | 1 . 9 |
| 1 . 7 | . . . | . . . |
+-------+-------+-------+
| . 3 . | . 6 . | 9 . 5 |
| . . 8 | . . 5 | . . . |
| 5 . 4 | . . 1 | . . 3 |
+-------+-------+-------+



Here is the starting point with all the possibilities:

Code:



+-------------------+-------------------+-------------------+
| 7     158   15    | 3     149   9     | 6     1489  2     |
| 236   1268  126   | 5     1249  269   | 7     13489 148   |
| 4     126   9     | 127   8     267   | 3     5     1     |
+-------------------+-------------------+-------------------+
| 269   2469  26    | 1289  1239  2389  | 5     23468 7     |
| 8     25    3     | 6     257   4     | 1     2     9     |
| 1     24569 7     | 289   2359  2389  | 2348  23468 468   |
+-------------------+-------------------+-------------------+
| 2     3     12    | 2478  6     278   | 9     12478 5     |
| 269   12679 8     | 2479  23479 5     | 24    12467 146   |
| 5     2679  4     | 2789  279   1     | 28    2678  3     |
+-------------------+-------------------+-------------------+



Keith
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TKiel



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

PostPosted: Sat May 06, 2006 1:31 pm    Post subject: Reply with quote

Keith,

You aught to like it since it's solvable by your discovery.
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keith



Joined: 19 Sep 2005
Posts: 3178
Location: near Detroit, Michigan, USA

PostPosted: Sat May 06, 2006 3:09 pm    Post subject: Really? Reply with quote

Tracy,

I saw the UR, but not a conjugate pair or link. I'll have to look again.

By the way, to crack the puzzle I used coloring, which you introduced to me!

Keith
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keith



Joined: 19 Sep 2005
Posts: 3178
Location: near Detroit, Michigan, USA

PostPosted: Sat May 06, 2006 4:36 pm    Post subject: A way to the solution Reply with quote

Using standard techniques, you get to here:

Code:


+----------------+----------------+----------------+
| 7    18   5    | 3    14   9    | 6    48   2    |
| 3    18   26b  | 5    14   26a  | 7    9    48   |
| 4    26a  9    | 27   8    267  | 3    5    1    |
+----------------+----------------+----------------+
| 69   4    26   | 1    29   38   | 5    38   7    |
| 8    5    3    | 6    7    4    | 1    2    9    |
| 1    29b  7    | 289  5    238  | 48   3468 468  |
+----------------+----------------+----------------+
| 2    3    1    | 478  6    78   | 9    478  5    |
| 69   679  8    | 2479 3    5    | 24   1    46   |
| 5    679  4    | 2789 29   1    | 28   678  3    |
+----------------+----------------+----------------+

The unique rectangle on <38> is in R46C68. Since the only possibilities for <3> in R6 are the corners of the rectangle, neither R6C6 or R6C8 can be <8>.

But, you don't need the UR. Look at the coloring chain on <2>, labeled "a-b". So, R6C6 cannot be <2>. This solves the puzzle.

Keith
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