Here is the first part of Pushing Numbers.
You need to make it so that all the numbers from 1 to 8 appear once in every row and column. You can only do that by "pushing" the columns down and the rows left. Each time you "push" a row or a column all the numbers in it move one block in the direction you have pushed it.
| | | | | 6 | | 4 | | 8 | | 6 | | 8 | | 7 | | | | |
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| | | | | 1 | | 3 | | 1 | | 2 | | 5 | | 6 | | | | |
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| | | | | 7 | | 4 | | 2 | | 8 | | 5 | | 4 | | 2 | | 2 |
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| | | | | 7 | | 5 | | 3 | | 7 | | 5 | | 3 | | 1 | | 3 |
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| | | | | 3 | | 8 | | 4 | | 7 | | 5 | | 6 | | 2 | | 1 |
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| | | | | 6 | | 3 | | 1 | | 6 | | 1 | | 4 | | 7 | | 8 |
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| | | | | 2 | | 5 | | 4 | | 3 | | 4 | | 5 | | 2 | | 1 |
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| | | | | 7 | | 2 | | 1 | | 3 | | 6 | | 4 | | 8 | | 7 |
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| 8 | | 6 | | | | | | | | | | | | | | | | |
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| 5 | | 8 | | | | | | | | | | | | | | | | |
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Can you do it?
(In reply to
No Subject by Ken Haley)
I'm not sure the formula for eliminating all the permutations of a series of vertical or horizontal moves in a row, but the major consideration, the numerator of the fraction would be 24!, as each pushing advances the strip by only one digit position, so a total of 24 pushes must be done.
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Posted by Charlie
on 2007-05-27 22:04:59 |