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Vanhegan extreme

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Thu Aug 30, 2012 4:45 pm    Post subject: Vanhegan extreme Reply with quote
Another one that I'm stuck on. This is puzzle #6-1645514, rated 2.2.0.1.1.

Code:

+------------------+------------+-----------------+
| 4     27  2679   | 17 69   3  | 2789  5    1289 |
| 369   37  1      | 5  8    2  | 379   3467 349  |
| 23569 8   235679 | 17 69   4  | 2379  2367 1239 |
+------------------+------------+-----------------+
| 7     6   234    | 8  245  9  | 1     234  2345 |
| 129   5   29     | 3  124  7  | 6     8    24   |
| 123   234 8      | 6  1245 15 | 235   9    7    |
+------------------+------------+-----------------+
| 358   347 3457   | 2  57   6  | 35789 1    3589 |
| 256   1   2567   | 9  3    8  | 4     27   25   |
| 2358  9   2357   | 4  157  15 | 23578 237  6    |
+------------------+------------+-----------------+

Play this puzzle online at the Daily Sudoku site
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
PostPosted: Fri Aug 31, 2012 5:20 pm    Post subject: Reply with quote
Couldn't break this one. Sad I was hoping someone else could.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Fri Aug 31, 2012 6:27 pm    Post subject: Reply with quote
Dan, did you by any chance do something to check if the grid is valid?
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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
PostPosted: Fri Aug 31, 2012 6:45 pm    Post subject: Reply with quote
Looking at the set of bivalues and bilocals, the candidates for the digits 4 and 1 are the "strongest" (see why !).
Furthermore they are "coupled" in r5c5.
Therefore, I suggest, as a hint, to investigate the consequences of assuming either 1r5c5 or 2r5c5 or 4r5c5 to be true.
If you do so, you will save much time in the solving of this puzzle !

Regards, JC.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Fri Aug 31, 2012 7:18 pm    Post subject: Reply with quote
I don't know if that is what JC had in mind, but looking at the 124 possibilities in r5c5, I found 4 to be invalid, and that was all that was needed.
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JC Van Hay



Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
PostPosted: Sat Sep 01, 2012 7:37 am    Post subject: Reply with quote
Yes Marty.

With the bilocals on 4s and 1s, one can make 2 chains of length 4 and 2, a "Jellyfish" and a "Kite", respectively.
As they are weakly coupled in r5c5, it is natural to begin the analysis of the puzzle from the cell r5c5 before investigating any other "weaker" patterns.

r5c5=1->solution
Or
r5c5=2->contradiction after a cascade of singles
or
r5c5=4->contradiction after a cascade of singles while r5c9=4->solution

It remains to find one chain to explain -4r5c5. The length of that chain should be the shortest, but this is not necessary.

Example:

Code:
+--------------------------+------------------+---------------------+
| 4        27     2679     | 17  69      3    | 2789     5     1289 |
| 69(3)    7(3)   1        | 5   8       2    | 379      3467  349  |
| 2569(3)  8      2679(35) | 17  69      4    | 2379     2367  1239 |
+--------------------------+------------------+---------------------+
| 7        6      23(4)    | 8   245     9    | 1        234   2345 |
| 129      5      29       | 3   12-4    7    | 6        8     (24) |
| 12(3)    2(34)  8        | 6   125(4)  1(5) | 2(35)    9     7    |
+--------------------------+------------------+---------------------+
| 358      (347)  37(45)   | 2   (57)    6    | 3789(5)  1     3589 |
| 256      1      267(5)   | 9   3       8    | 4        27    (25) |
| 2358     9      237(5)   | 4   157     1(5) | 2378(5)  237   6    |
+--------------------------+------------------+---------------------+

Chain[11] : If r5c5=4, then [r5c9=2,r8c9=5=r6c7=r9c6,r7c5=7] and r6c2=4=r7c3;r6c1=3=r7c2,r3c3=5;no 3 in B1 => -4r5c5


I hope that this way of writing the chain will seem easier to read than the corresponding "forbidding matrix", where no assumption is done, proving the derived SL 4r5c9=4r6c5 :=> -4r5c5.

Note : the rating of this puzzle is SER=8.4, while the puzzles proposed on this site rarely exceed SER=7.1 !

Regards, JC.
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