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 Ant highway with energy loss (Posted on 2018-08-24)
An ant starts at the origin of the coordinate plane. The ant only has enough energy to walk for 10 units along either the x- or y-axis before stopping. These lines are the two ant highways.

However, if it goes off the highway, more energy is needed for the same distance. That is, the further the ant deviates, the greater the energy consumption, as represented by the factor 1+0.4d, where d is the distance to the nearest highway. For example, if the ant is 1 unit away from the nearest highway, it uses 1.4 times the energy on the highway to walk 1 meter.

What is the area of the set of points the ant can reach before getting tired and stopping?

 No Solution Yet Submitted by Jer No Rating

 Subject Author Date re(2): possible analytical approach (thoughts) Steven Lord 2018-08-26 18:46:08 re: possible analytical approach (thoughts) Charlie 2018-08-26 12:49:47 re(3): heuristic computer solution Charlie 2018-08-26 12:44:59 possible analytical approach (thoughts) Steven Lord 2018-08-26 10:48:16 re(2): heuristic computer solution Charlie 2018-08-25 12:07:58 larger paths Steven Lord 2018-08-24 23:53:02 re: heuristic computer solution Jer 2018-08-24 22:47:49 heuristic computer solution Charlie 2018-08-24 18:42:13 attempt.... Steven Lord 2018-08-24 18:32:33

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