A Bell

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A Bell

Postby m_b_metcalf » Thu Dec 18, 2008 9:30 pm

It appears that a Christmas Bell cannot be produced as a standard sudoku, so here it is as an X-sudoku:

Code: Select all
 . . . . 1 . . . .
 . . . 9 4 7 . . .
 . . 9 . . . 5 . .
 . 7 . . . . . 3 .
 . 5 . . . . . 4 .
 . 6 . . . . . 8 .
 . 2 . . . . . 9 .
 5 3 4 2 9 1 6 7 8
 . . . . 7 . . . .           X-sudoku, non-trivial

Season's Greetings,

Mike Metcalf
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Postby udosuk » Fri Dec 19, 2008 11:53 pm

Okay, here is the first try for a (not so elegant) solving path:



After basic moves (singles, subsets, intersections):

Code: Select all
+----------------------+----------------------+----------------------+
| 236    48     2367   | 3568   1      23568  | 479    26     49     |
| 26     1      5      | 9      4      7      | 8      26     3      |
| 2367   48     9      | 368    2368   2368   | 5      1      47     |
+----------------------+----------------------+----------------------+
| 12489  7      128    | 4568   26     49     | 129    3      12569  |
| 12389  5      1238   | 17     268    2369   | 1279   4      12679  |
| 12349  6      123    | 17     23     2345   | 1279   8      12579  |
+----------------------+----------------------+----------------------+
| 1678   2      1678   | 3468   5      3468   | 34     9      14     |
| 5      3      4      | 2      9      1      | 6      7      8      |
| 168    9      168    | 3468   7      3468   | 1234   5      24     |
+----------------------+----------------------+----------------------+

1. r2c18={26}
=> r9c1, seeing r2c18, can't be 6

2. r6c4 from {17}
=> r7c3+r9c1 can't be [71]
=> r79c13 can't be [8716]
=> r7c1 can't be 8

3. Now 8 @ c1 locked @ r459c1, 8 @ b5 locked @ r4c4+r5c5
But r5c5 & r9c1 can't be both 8
=> either r45c1 have 8, or r4c4=8, or both
=> r4c3, seeing r45c1+r4c4, can't be 8

4. Now 4 @ r6 locked @ r6c16, 9 @ r6 locked @ r6c179
But r6c1 can't be 4 & 9 simultaneously
=> either r6c6=4, or r6c79 have 9, or both
=> r4c67 can't be [49]
=> r4c7 can't be 9

The rest can be solved with basic moves.:idea:



Now I challenge everyone to name the techniques I applied in these steps.:)
udosuk
 
Posts: 2698
Joined: 17 July 2005

Postby m_b_metcalf » Sun Dec 21, 2008 7:31 am

For those struggling with the first puzzle, here's a (somewhat) easier one:
Code: Select all
 . . . . 2 . . . .
 . . . 7 3 9 . . .
 . . 9 . . . 7 . .
 . 7 . . . . . 2 .
 . 4 . . . . . 3 .
 . 1 . . . . . 8 .
 . 5 . . . . . 9 .
 7 2 3 9 6 5 1 4 8
 . . . . 4 . . . .                              sudoku-X



Season's Greetings

Mike Metcalf
User avatar
m_b_metcalf
2017 Supporter
 
Posts: 8416
Joined: 15 May 2006
Location: Berlin


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