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A VH+ Menneske

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Tue Jul 28, 2009 11:09 pm    Post subject: A VH+ Menneske Reply with quote
I enjoyed doing this one with pencil and paper.
Code:
Puzzle: M4914746sh(10)
+-------+-------+-------+
| . 4 . | . . 2 | 8 6 . |
| . . 9 | . . . | . . . |
| . 7 . | . . 6 | . . 3 |
+-------+-------+-------+
| . . . | 2 . 4 | . 1 6 |
| . . 4 | 1 . 8 | 5 . . |
| 7 3 . | 5 . 9 | . . . |
+-------+-------+-------+
| 9 . . | . . 1 | . 2 . |
| . . . | . . . | 9 . . |
| . 1 6 | . . 7 | . 8 . |
+-------+-------+-------+
Hint: Fill in pencil marks only for cells that have two candidates, and look for patterns. Then, I did not need to go further than a few cells with three candidates.

Best wishes,

Keith
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Wed Jul 29, 2009 8:58 pm    Post subject: Reply with quote
Code:
.---------------------.---------------------.---------------------.
| 135    4    C3D5    | 379    159    2     | 8      6    A5B7    |
| 13568  568    9     | 3478   1458   35    | 14   B5A7     2     |
| 1258   7      258   | 48     1458   6     | 14     9      3     |
:---------------------+---------------------+---------------------:
| 58     9      58    | 2      3      4     | 7      1      6     |
| 26     26     4     | 1      7      8     | 5      3      9     |
| 7      3      1     | 5      6      9     | 2      4      8     |
:---------------------+---------------------+---------------------:
| 9      58   -35B78  | 348    458    1     | 6      2      457   |
| 23458  258   235A78 | 6      2458   35    | 9    A5B7     1     |
| 245    1      6     | 49     2459   7     | 3      8      45    |
'---------------------'---------------------'---------------------'

Medusa provides a quick route home. the above grid is after most if not all basics.

I started with the {5,7} cell and colored a medusa cluster A and B

then I saw that there was a bi-value cell {3,5} in r1c3, so I marked it C and D

the bridge to the chains is on the 5's. both 5's that are colored in row 1 can't both be true, in other words the A's and D's can't both be true.

this means that the B's and C's can't both be false.

looking at r7c3 we see that there is a trap. either the 7B is true in that cell or the 3C is true in r1c3. either way, the 3 in r7c3 can't exist and it solves the puzzle.

(3=5)r1c3 - (5=7)r1c9 - (7)r2c8 = (7)r8c8 - (7)r8c3 = (7)r7c7; r7c7 <> 3
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Thu Jul 30, 2009 2:58 am    Post subject: Reply with quote
After basics, showing only cells that have one or two candidates:
Code:
+----------+----------+----------+
| .  4  35 | .  .  2  | 8  6  57 |
| .  .  9  | .  .  35 | 14 57 2  |
| .  7  .  | 48 .  6  | 14 9  3  |
+----------+----------+----------+
| 58 9  58 | 2  3  4  | 7  1  6  |
| 26 26 4  | 1  7  8  | 5  3  9  |
| 7  3  1  | 5  6  9  | 2  4  8  |
+----------+----------+----------+
| 9  58 .  | .  .  1  | 6  2  .  |
| .  .  .  | 6  .  35 | 9  57 1  |
| .  1  6  | 49 .  7  | 3  8  45 |
+----------+----------+----------+
The <35> cells in R12 are a W-wing, excited by the <57> cells in the same rows.

There is a very obvious X-wing on <5> in C68, which is not needed.

Which brings us to here:
Code:
+----------------+----------------+----------------+
| 135  4    35   | 79a  159  2    | 8    6    57b  |
| 168  68   9    | 37   148  35   | 14   57   2    |
| 1258 7    258  | 48   1458 6    | 14   9    3    |
+----------------+----------------+----------------+
| 58   9    58   | 2    3    4    | 7    1    6    |
| 26   26   4    | 1    7    8    | 5    3    9    |
| 7    3    1    | 5    6    9    | 2    4    8    |
+----------------+----------------+----------------+
| 9    5    378  | 348  48   1    | 6    2    47   |
| 2348 28   2378 | 6    248  35   | 9    57   1    |
|2-4   1    6    | 49d 2-459 7    | 3    8    45c  |
+----------------+----------------+----------------+
abcd is a loop that eliminates <4> in R9 as shown. Solving the puzzle.

Sweet! (When I first found the loop, I had not completed basics. Note that it eliminates <7> in R1, <4> in R9, <9> in C4, and <5> in C9.

All you need is the W-wing and the loop.

Best wishes,

Keith
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Earl



Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
PostPosted: Thu Jul 30, 2009 3:41 am    Post subject: VH+ Reply with quote
x-wing (5)
w-wing (35)
xy-chain eliminates 4 in R9C1 and solves the puzzle.

Earl
of the chain gang
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