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Your neighbor's lawn may look nice, but if Armadillos are feasting there, it's an indication of an underlying problem - usually grubs, and Armadillo's favorite snack and the reason they dig the holes. They do not dig random holes, no profit in that, they can hear the little critters moving under the sod and go in after them. If your neighbor gets rid of the grubs, the Armadillos will wander through the yard in search of lunch, but they won't dig up the grass.