GeekDad Puzzle of the Week Solution – Efficient Gardening

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Our most recent puzzle, as previously presented:

This past weekend, we decided that we would take part of our yard at home, and start a small garden. Here is how the front yard look so far:

Our first 6x6'  square of potential vegetables!
Our first 6×6′ square of potential vegetables!

Well, that’s what we decided at first, but now the current plans are to pretty much take over the front yard with as much gardening square footage as we can. This, of course, lead to a question that is leading to this week’s GeekDad Puzzle of the Week:

For our front yard, let’s assume the usable area is 50′ x 100′, and that for the purposes of this discussion, the walls of the raised beds are negligibly thin (or at least not counted.) If my wife and I can bend over to lean in and weed at most 3′ into a bed, and that the space between beds needs to be at least 2′ to fit a wheel barrow, what is the most efficient plan or diagram to fill our front yard with as much garden as possible?

Maximizing the growing space is all about minimizing the access paths.

Assuming that the edge beds could actually be tended from outside the growing area, the two contenders for optimal planting beds start with complete coverage and have either horizontal or vertical internal paths, as shown below:

horizontalGardenWith horizontal paths, 6 two-foot wide paths each 100′ long are needed, for 1200 ft2 of path. This leaves 50×100=5000-1200=3800 ft2 of gardening area.

verticalGardenWith vertical paths, 12 two-foot wide paths each 50′ long are needed, also for 1200 ft2 of path. This also leaves 3800 ft2 of gardening area.

Given that the beds could be tended from outside the growing area, horizontal and vertical paths provide the same potential vegetable yield.

However, if the beds could not be tended from outside the growing area, each plan would require one extra “path,” having the first path from either edge start 3′ into the garden instead of 6′. As the vertical paths are shorter, a garden plan using strictly vertical paths would enable a larger vegetable yield.

Congratulations to Keith Griffith for submitting a reasonably well reasoned garden plan! A fabulous prize in the form of a $50 ThinkGeek Gift Certificate will be on its way shortly.

Many thanks to everyone that sent in a response, and the ThinKGeek for being our faithful puzzle sponsor.

Happy puzzling!

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