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detailed solution

The maximum number of turbines that can be placed on this plot of land is 17, with a 6 + 5 + 6 arrangement (better than the alternative 5 + 6 + 5 arrangement, which is only 16 turbines).

Because there is some extra space available, top to bottom, we can shift groups of turbines up and down to cover as many windier areas as possible. Note how the interlocking nature of the wind turbine footprints force entire sections of turbines to move together.

Is it possible to remove turbines in order to create enough room to move others to windier areas, thus increasing the energy output? In short, no. Here are two examples of attempts to do just that. On the left, two turbines have to be removed in order to just move one turbine to a windier area, a net loss of 1.5 units of energy. On the right, three turbines have to be removed in order to move two turbines to windier areas, a net loss of 2 units of energy.

Basically, because of the interlocking nature of the turbine footprints, too many turbines have to be removed in order to disrupt the footprint pattern and move other turbines to windier areas. In other words, there just arenâ€™t enough windier areas to justify removing turbines.