Set Multiplicity analyzing

Advanced methods and approaches for solving Sudoku puzzles

Set Multiplicity analyzing

Postby bennys » Sun Jan 01, 2006 1:38 am

Code: Select all
+-------+-------+-------+
| 8 . 6 | 2 3 . | . . 1 |
| . . 5 | 8 4 1 | 6 . . |
| . . . | 7 6 . | 8 . . |
+-------+-------+-------+
| . 8 . | . 7 . | 2 . 9 |
| 6 . . | 9 5 8 | . . 4 |
| 9 . 7 | . 2 . | . 8 . |
+-------+-------+-------+
| . . 8 | 5 9 2 | . . . |
| . . 9 | 4 1 7 | 3 . 8 |
| 1 . . | 6 8 3 | . . 5 |
+-------+-------+-------+

+-------------------+-------------------+-------------------+
| 8     479   6     | 2     3     59    | 4579  4579  1     |
| 237   239   5     | 8     4     1     | 6     39    237   |
| 234   12349 1234  | 7     6     59    | 8     3459  23    |
+-------------------+-------------------+-------------------+
| 345   8    *134   |*13    7     46    | 2    *1356  9     |
| 6     123   123   | 9     5     8     | 17    137   4     |
| 9     1345  7     | 13    2     46    | 15    8     36    |
+-------------------+-------------------+-------------------+
| 347   346   8     | 5     9     2     | 14    146   67    |
|*25    256   9     | 4     1     7     | 3    *26    8     |
| 1     247  *24    | 6     8     3     | 479   2479  5     |
+-------------------+-------------------+-------------------+

A={R4C3,R4C4,R4C8,R8C1,R9C3,R8C8}
|A|=6           
V(A)={123456} |V(A)|=6
The only values that can appear more then once are 2,5 but in the only way that 2 appear twice
R8C1 is still 5.
the conclusion is that 5 must appear in A.
and we get that r4c1<>5 that solve the puzzle.
bennys
 
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Joined: 28 September 2005

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