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January 12th, 2012, 03:07 PM   #1
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Formula for this permutation?

I wanted to figure out the formula for the following problem concerning crop rotation: If you have six plots with six different crops, and each year no crop may be on the same plot until the seventh year, nor may it be besides the same crop from the previous year, what are the possible permutation/combinations* for the six years? (*I came up with this problem myself, so I'm unsure if this is the correct math terms)

In a convoluted manner, I figured this out manually:
123456
241635
462513
654321
536142
315264
I noticed that you could take the outer most crops (in this case 1 and 6), and move them to the middle, while "pairing" every other number together (2 with 4, 3 with 5), and moving them to the left or right (again, very convoluted). Obviously, these are not the only combinations that work.
123456
246135
362514
654321
531642
415263

Am I on the right track? Is this a combinatorics question?
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