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Jan 1 VH

 
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Clement



Joined: 24 Apr 2006
Posts: 638
Location: Dar es Salaam Tanzania

PostPosted: Mon Dec 31, 2012 10:58 pm    Post subject: Jan 1 VH Reply with quote

Code:

+--------------+-------------+---------+
| *18   6   *18  | 3   7    9  | 4  5 2  |
| 9    3   4   | 2   5    8  | 1  6 7  |
| 2    7   5   | 6   1    4  | 9  3 8  |
+--------------+-------------+---------+
| 78   1   2   | 478 34-8  5  | 6  9 34 |
| 3    45  67  | 9   46   2  | 57 8 1  |
| 5678 458 9   | 1   3468 37 | 57 2 34 |
+--------------+-------------+---------+
| *17-8  9   *17-8 | -78  2    6  | 3  4 5  |
| 5678 58  678 | 478 348  37 | 2  1 9  |
| 4    2   3   | 5   9    1  | 8  7 6  |
+--------------+-------------+---------+
Type 4 UR 18 in r17c13; r7c13<>8 opens an
xy-wing 47-37-34 pivoted in r6c6; r4c9<>4 which solves it.
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arkietech



Joined: 31 Jul 2008
Posts: 1686
Location: Northwest Arkansas USA

PostPosted: Tue Jan 01, 2013 12:42 am    Post subject: Reply with quote

Code:
 *-----------------------------------------------------------*
 | 18    6     18    | 3     7     9     | 4     5     2     |
 | 9     3     4     | 2     5     8     | 1     6     7     |
 | 2     7     5     | 6     1     4     | 9     3     8     |
 |-------------------+-------------------+-------------------|
 | 78    1     2     | 478   348   5     | 6     9     34    |
 | 3    b45    7-6   | 9    c46    2     | 57    8     1     |
 |a56    458   9     | 1     3468  37    | 57    2     34    |
 |-------------------+-------------------+-------------------|
 | 178   9     178   | 78    2     6     | 3     4     5     |
 | 56    58    678   | 478   348   37    | 2     1     9     |
 | 4     2     3     | 5     9     1     | 8     7     6     |
 *-----------------------------------------------------------*
xy-wing
(6=5)r6c1-(5=4)r5c2-(4=6)r5c5 => -6r5c5; stte
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hughwill



Joined: 05 Apr 2010
Posts: 141
Location: Birmingham UK

PostPosted: Tue Jan 01, 2013 11:03 am    Post subject: Jan 1 VH Reply with quote

Nice to start a new year with a classic VH.

The double 567 XY wing does it in one as well (pivot r4c3 or r5c1).
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Tue Jan 01, 2013 10:19 pm    Post subject: Reply with quote

As already posted, this puzzle has a Type 4 UR(18)r17c13. These same four cells also offer a Type 2 UR(18) that results in the identical deletions; neither completes the puzzle. However a one step solution is achievable from a third perspective: AUR(18)r17c13.

Looking at the external implications, we find that only two constraints are necessary to prevent the deadly pattern: r4c1=8 & r8c3=8.
1): If r4c1=8, then r4c1<>7, then r5c3=7, then r5c3<>6, then r5c5=6, then r5c5<>4, then r5c2=4;
2): If r8c3=8, then r8c2=5, then r8c1=6, then r6c1=5, then r5c2=4;
Thus, both conditions to prevent the DP provide the same result, r5c2=4, which completes the puzzle.

Ted
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hughwill



Joined: 05 Apr 2010
Posts: 141
Location: Birmingham UK

PostPosted: Wed Jan 02, 2013 10:37 am    Post subject: Reply with quote

Quote:
As already posted, this puzzle has a Type 4 UR (18)r17c13. These same four cells also offer a Type 2 UR (18 ) that results in the identical deletions; neither completes the puzzle. However a one step solution is achievable from a third perspective: AUR(18)r17c13.

Looking at the external implications, we find that only two constraints are necessary to prevent the deadly pattern: r4c1=8 & r8c3=8.
1): If r4c1=8, then r4c1<>7, then r5c3=7, then r5c3<>6, then r5c5=6, then r5c5<>4, then r5c2=4;
2): If r8c3=8, then r8c2=5, then r8c1=6, then r6c1=5, then r5c2=4;
Thus, both conditions to prevent the DP provide the same result, r5c2=4, which completes the puzzle.

Ted


Excellent!
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