You need to make it so that all the numbers from 1 to 6 appear once in every row and column. You can only do that by "pushing" the rows down and the columns left. Each time you "push" a row or a column all the numbers in it move 1 block to the direction you have pushed it.
| | | 1 | | 3 | | 6 | | 2 | | 5 | | |
| | | | | | | | | | | | | |
| | | 4 | | 6 | | 4 | | 1 | | 5 | | 1 |
| | | | | | | | | | | | | |
| | | 3 | | 2 | | 5 | | 2 | | 6 | | 3 |
| | | | | | | | | | | | | |
| | | 5 | | 2 | | 6 | | 1 | | 4 | | 4 |
| | | | | | | | | | | | | |
| | | 4 | | 6 | | 3 | | 4 | | 3 | | 2 |
| | | | | | | | | | | | | |
| | | 1 | | 5 | | 2 | | 6 | | 5 | | 1 |
| | | | | | | | | | | | | |
| 3 | | | | | | | | | | | | |
| | | | | | | | | | | | | |
Can you complete the grid?
If there is just ONE solution, it must be either RCRCRCRCRC or CRCRCRCRCR (R means push a row, C means push a column) for if you had two R's or two C's in a row, you could interchange them an find a second solution.
Instead of trying 10! possibilities, you need test 2x5!²
Edited on February 12, 2007, 2:26 pm
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Posted by e.g.
on 2007-02-12 14:25:13 |
How many cases?
