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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

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 re: heuristic computer solution | Comment 3 of 9 |
(In reply to heuristic computer solution by Charlie)

The picture with separation might show that geometrical fact is missing, but it's hard to tell because of pixelation.

I was able to derive a formula for these paths and then the outer edge.  It took some help from Wolfram|Alpha.

 Posted by Jer on 2018-08-24 22:47:49

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