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From a book

 
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keith



Joined: 19 Sep 2005
Posts: 3182
Location: near Detroit, Michigan, USA

PostPosted: Sat Aug 09, 2014 1:14 pm    Post subject: From a book Reply with quote

This puzzle is from a book of puzzles bought at the local dollar store. Surprisingly difficult, I have not found a nice solution.
Code:
Puzzle: 290Puzzle70
+-------+-------+-------+
| . 5 3 | . . . | . 1 . |
| . . . | . 2 . | . 9 . |
| 1 . . | 9 . . | . . 6 |
+-------+-------+-------+
| . . 1 | . 3 . | . . 8 |
| . . 8 | 1 . 5 | 7 . . |
| 3 . . | . 7 . | 1 . . |
+-------+-------+-------+
| 6 . . | . . 8 | . . 5 |
| . 2 . | . 4 . | . . . |
| . 3 . | . . . | 4 6 . |
+-------+-------+-------+

Keith
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JC Van Hay



Joined: 13 Jun 2010
Posts: 372
Location: Charleroi, Belgium

PostPosted: Sat Aug 09, 2014 3:10 pm    Post subject: Reply with quote

What is a nice solution? ...

Here is my "path" :

Analysis of the puzzle : Red Green Transport from R79 : r7c4=2or7 => r6c6=9, r7c4=2; singles to the end.
Interpretation :
Code:
+------------+--------------+--------------+
| 9   5    3 | 467   8  467 | 2  1     47  |
| 47  8    6 | 347   2  1   | 5  9     347 |
| 1   47   2 | 9     5  347 | 8  347   6   |
+------------+--------------+--------------+
| 47  479  1 | (24)  3  249 | 6  5     8   |
| 2   49   8 | 1     6  5   | 7  34    349 |
| 3   6    5 | 8     7  9-4 | 1  (24)  249 |
+------------+--------------+--------------+
| 6   1    4 | 7(2)  9  8   | 3  7(2)  5   |
| 5   2    7 | 36    4  36  | 9  8     1   |
| 8   3    9 | 5     1  27  | 4  6     27  |
+------------+--------------+--------------+
WWing(2-4)r4c4,r6c8,2r7c48-(4=9)r6c6; singles to the end.
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keith



Joined: 19 Sep 2005
Posts: 3182
Location: near Detroit, Michigan, USA

PostPosted: Sat Aug 09, 2014 3:43 pm    Post subject: Reply with quote

To me, a "nice" solution is one that does not require a succession of chains to chip away one digit at a time.
Code:
+----------------+----------------+----------------+
| 9    5    3    | 467  8    467  | 2    1    47   |
| 47   8    6    | 347  2    1    | 5    9    347  |
| 1    47   2    | 9    5    347  | 8    347  6    |
+----------------+----------------+----------------+
| 247  479  1    | 24   3    249  | 6    5    8    |
| 24   49   8    | 1    6    5    | 7    234  2349 |
| 3    6    5    | 8    7    249  | 1    24   249  |
+----------------+----------------+----------------+
| 6    1    4    | 27   9    8    | 3    27   5    |
| 5    2    7    | 36   4    36   | 9    8    1    |
| 8    3    9    | 5    1    27   | 4    6    27   |
+----------------+----------------+----------------+
A W-wing (24) takes out 4 in R6C6.

An extended XY-wing 24 27 27 27 47takes out 4 in R1C4.

An XY-wing 47 27 24 takes out 4 in R2C4.

Keith
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JC Van Hay



Joined: 13 Jun 2010
Posts: 372
Location: Charleroi, Belgium

PostPosted: Sat Aug 09, 2014 5:17 pm    Post subject: Reply with quote

Oops, I forgot an intermediate step assigning 2r5c1 justified by
Code:
+-----------------+----------------+-----------------+
| 9       5     3 | 467   8  467   | 2  1      47    |
| (47)    8     6 | 347   2  1     | 5  9      347   |
| 1       4(7)  2 | 9     5  34(7) | 8  34(7)  6     |
+-----------------+----------------+-----------------+
| 47(-2)  479   1 | 4(2)  3  249   | 6  5      8     |
| (+2-4)  49    8 | 1     6  5     | 7  34-2   349-2 |
| 3       6     5 | 8     7  249   | 1  24     249   |
+-----------------+----------------+-----------------+
| 6       1     4 | (27)  9  8     | 3  2(7)   5     |
| 5       2     7 | 36    4  36    | 9  8      1     |
| 8       3     9 | 5     1  2(7)  | 4  6      27    |
+-----------------+----------------+-----------------+
r7c2=7 -> r4c4=2=r5c1
or
r7c2=2 -> r7c8=7=r9c6=r3c2, r2c1=4, r5c1=2

A "nice solution" : r6c6=2or4or9 => r7c4=2
Code:
+---------------+------------------+----------------+
| 9    5      3 | 467     8  467   | 2  1      47   |
| 47   8      6 | 347     2  1     | 5  9      347  |
| 1    4(7)   2 | 9       5  347   | 8  34(7)  6    |
+---------------+------------------+----------------+
| 247  4(79)  1 | 4(-2)   3  24(9) | 6  5      8    |
| 24   49     8 | 1       6  5     | 7  234    2349 |
| 3    6      5 | 8       7  (249) | 1  (24)   249  |
+---------------+------------------+----------------+
| 6    1      4 | -7(+2)  9  8     | 3  (7-2)  5    |
| 5    2      7 | 36      4  36    | 9  8      1    |
| 8    3      9 | 5       1  7-2   | 4  6      27   |
+---------------+------------------+----------------+
r6c6=2 -> r7c4=2
or
r6c6=4 -> r6c8=2=r7c4
or
r6c6=9 -> r4c2=9, r3c2=7=r7c8, r7c4=2
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