When it comes to how to mow a lawn most efficiently, the argument inevitably comes down to two main approaches: You either mow in rows or spirals. Which is the better technique? With the help of a famous puzzle maker, a few lawn-mowing experts and some simple mathematical calculations, we answer the question once and for all.

The first factor to consider is distance, and this one is easily ruled out by the first law of mowing a lawn: Don't go over the same patch twice. This given knocks out many well-meaning but clearly inefficient routes on an unimpeded patch of lawn.

Note: For argument's sake, we compared techniques on an empty square plot — fancy garden mazes, orchards or sheds may be part of the picture for most mowing, but in order to answer such a broad, important question as rows or spirals, we must make like the great philosophers and lay our argument down on a theoretically perfect plane.

Now that we're down to a fixed square footage of lawn to mow, we can focus on turns. If you have a push or zero-turn mower, you can skip straight to the next paragraph, but if you're using a riding mower, stick with us here and tackle the problem of turning distance. If you look at your everyday, run-of-the-mill John Deere riding mower, you have anywhere from 15 to 22 inches of travel before you can make a 180-degree turn. Assuming the same number of turns, the way that this play will affect your efficiency will depend on how tight your turns need to be. If your turn is as tight as the tractor is long, minus 15 to 22 inches, you're going to be left with patches — uncut grass that will force you to break the first rule of lawn mowing. In the battle between spirals and rows, this is a hindrance only for a spiral that is not perfectly plotted. For the careful mower, then, rows and spirals remain tied so far on any type of mower. (Bing: Find lawn-care services)

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Now, on to the big question: Which technique requires more turns? As it turns out, neither. The following illustrations by master puzzler Scott Kim shows that on a square 16-foot-by-16-foot lawn, both the spiral and row techniques take a total of 30 turns; 14 left and 16 right for the rows, and 30 right turns for the spiral. One could argue that to mow in rows, there are half as many turns — when you get to the end of a row you make two 90-degree turns, which you could also count as a single 180-degree turn. Still, the total number of angular degrees you turn is the same in either case.


Rows (© Scott Kim)

Left turns 14, right turns 16 = 30 total turns.

The most common pattern has about the same number of left and right turns, for a total of 30 right-angle turns. There's no pattern with fewer turns that mows every square.


Spiral (© Scott Kim)

Left turns zero, right turns 30 = 30 total turns.

The other common mowing pattern is a spiral. The total number of turns is also 30, the same as the grid. But this time all turns are in the same direction.

The nature of the turns with these two techniques varies. To turn to only one side for the course of a mow has two possible disadvantages — mechanical and horticultural. First, the mechanics of turning one way: According to Mark Waldvogel, product manager and spokesman for John Deere, there are "no data to indicate constant turning in the same direction would cause any long-term wear on a machine." This makes sense. Like all well-engineered vehicles, a quality lawnmower is going to be capable of handling more turns than you'll ever be able to throw its way. But although Mitchell says there are no data to indicate it would wear on the mower, he says, "Most lawn mowers discharge to the right, so the user is normally making left-hand turns on a regular basis." And this, he says, may wear on your lawn. Granted, there are no hard data to indicate whether the spiral would actually wear on your lawn. But if your mower discharges to the right and all your turns are to the left, you will not have an evenly mulched lawn. Our suggestion to those who choose the spiral is this: Bag it and spread it.

The bottom line: If you plot your turns well and are willing and able to spread bagged clippings, the battle between rows and spirals ends with a fizzle: It looks like it's a tie, folks.

Of course, the battle between spirals and rows is one for the most efficient route. These are techniques for those who have better things to do and just want to get through the mowing to work on real projects — like the Ducati in the garage, or that shed that's not building itself.

What if you want to make mowing your lawn into a project in itself? To find out how to make your mow the envy of the neighborhood, we went to puzzler Kim to devise seven brilliant, mathematically pleasing ways to mow lawns. We hope that you'll try one out. But be warned, these turn-intensive designs are not for the faint of mowing.