My Math Forum Formula for this permutation?

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 January 12th, 2012, 03:07 PM #1 Newbie   Joined: Jan 2012 Posts: 1 Thanks: 0 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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