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DB Saturday Puzzle - August 5, 2006

 
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keith



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

PostPosted: Sat Aug 05, 2006 9:12 am    Post subject: DB Saturday Puzzle - August 5, 2006 Reply with quote

Here is today's puzzle. I have not yet looked at it.

Code:
Puzzle: DB080506  ******
+-------+-------+-------+
| 7 . 3 | 5 . . | . . 9 |
| . . . | . 7 . | 4 5 . |
| . . . | . 6 . | . 8 . |
+-------+-------+-------+
| . . . | . . 7 | 8 . 5 |
| . 1 . | . . . | . 6 . |
| 5 . 8 | 4 . . | . . . |
+-------+-------+-------+
| . 7 . | . 9 . | . . . |
| . 2 5 | . 1 . | . . . |
| 9 . . | . . 3 | 1 . 7 |
+-------+-------+-------+


Keith
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Marty R.



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

PostPosted: Sat Aug 05, 2006 3:18 pm    Post subject: Reply with quote

For me, three strong links and a Type 4 opened it up.
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David Bryant



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

PostPosted: Sun Aug 06, 2006 12:57 am    Post subject: This one is fun Reply with quote

I had a great deal of fun with this one. Lately I've been searching for unusual paths to sudoku solutions, and this puzzle didn't disappoint me.

After making the obvious moves I arrived at this position.
Code:
  7     68    3     5     4    128+   26    12-   9
 1268  689   1269  1238   7    1289   4     5    1236
 124    5    1249  123    6    129    7     8    123
 246   3469  2469   16-   23    7     8    1249+  5
  24    1     7     9     8     5     3     6     24
  5    369    8     4     23    16+   29    7     12-
13468   7    146   268    9    2468   5    234   2468
 3468   2     5     7     1    468    69   349   468
  9    468    46   268    5     3     1     24    7

Here there's an inconsistent color chain on the digit "1":

r6c9 --> r6c6 --> r4c4 --> r4c8 --> r1c8 --> r1c6

Inspection of the parity (+/-) leads us to conclude that
r4c4 = 1; r6c9 = 1; r1c8 = 1

This is probably the set of "strong links" that Marty R. found. After making a couple of obvious moves we reach this position.
Code:
  7     68    3     5     4     28a   26    1     9
 1268a 689   1269  238    7    1289   4     5    236
 124    5    1249   23    6    129    7     8     23
 246   3469  2469   1     23    7     8    249    5
  24    1     7     9     8     5     3     6     24
  5     39    8     4     23    6     29    7     1
13468   7    146   268a   9    248    5    234   2468
 3468   2     5     7     1     48    69   349   468a
  9    468a   46   268b   5     3     1     24    7

Now an analysis of the possible positions for the digit "8" breaks the puzzle wide open.

A. r9c2 = 8 ==> r2c1 = 8 ==> r1c6 = 8 ==> r7c4 = 8 ==> r8c9 = 8
B. r9c2 <> 8 ==> r9c4 = 8

We conclude that the "8" in the bottom center 3x3 box must lie in column 4, and after eliminating "8" from r2c4, r7c6, and r8c6, the rest is a piece of cake. dcb
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Mon Aug 07, 2006 10:07 am    Post subject: Reply with quote

The "usual" way to solve it is with two turbot fishes in 1 and 8:
Code:
  7     68    3     5     4   -128    26   #12    9
 1268  689   1269  1238   7    1289   4     5    1236
 124    5    1249  123    6    129    7     8    123
 246   3469  2469   16    23    7     8   #1249   5
  24    1     7     9     8     5     3     6     24
  5    369    8     4     23   #16    29    7    #12
13468   7    146   268    9    2468   5    234   2468
 3468   2     5     7     1    468    69   349   468
  9    468    46   268    5     3     1     24    7

Leads there (note the hidden pair 19 in r23c6):
Code:
  7    -68    3     5     4    #28    26    1     9
 1268  689   1269 #238    7     19    4     5    236
 124    5    1249   23    6     19    7     8     23
 246   3469  2469   1     23    7     8    249    5
  24    1     7     9     8     5     3     6     24
  5     39    8     4     23    6     29    7     1
13468   7    146   268    9    248    5    234   2468
 3468   2     5     7     1     48    69   349   468
  9   #468    46  #268    5     3     1     24    7
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