Pure Nerd Fun: The Grasshopper Problem

illustration of grasshopper.[image: awesomedude.com]


It’s a sunny afternoon in July and a grasshopper lands on your lawn. The lawn has an area of a square meter. The grasshopper lands at a random place and then jumps 30 centimeters. Which shape must the lawn have so that the grasshopper is most likely to land on the lawn again after jumping?


I know, sounds like one of these contrived but