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An ant’s stroll within the Cartesian Plane

An ant lives within the origin of the Cartesian Plane. Every morning, at 6 am, it units out on a 16-hour stroll which will get her again residence exactly at 10 pm. In the primary hour the ant walks precisely one unit, two models within the second hour, three within the third, and so forth, till the sixteenth hour, throughout which she walks 16 models. During every hour she walks in a straight line, and on the finish of each hour´s stroll she should discover herself at a lattice level and, if not but residence, change instructions for the following hour’s stroll. No the place alongside her stroll should her path cross over itself, and her stroll on the final hour should be alongside a special axis than her stroll within the first hour. (Her stroll, thus, can have the form of a hexadecagon with sides 1, 2, 3, …, 16, and all vertices on lattice factors.)

If the ant complies with these guidelines:

  1. What is the furthest away she will get from the x-axis?
  2. What is the furthest away she will get from the origin?

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