Brain Teaser

Question

An ant named Honey is kept outside a solid cube on a leash, which extends to twice the side length of the cube.

The leash can be attached

  • on the center of a face, or
  • on the midpoint of an edge, or
  • on a vertex.

Answer

Below are 2D nets of the cube. On the left the leash is attached to the center of a face, in the middle it’s on the midpoint of an edge and on the right it’s on a vertex.

All of the points inside of the circle can be reached.

When the leash is attached on the center of a face, the entire cube can be reached. This might sound strange, because a section of the overview above is outside the circle. These points can still be reached by either traveling to the left, up or down.

When the leash is attached to either the midpoint of an edge or a vertex, there are a few red segment in the overviews that can’t get reached. Trying to approach the points from a different angle, as described above, can reduce the amount of unreachable segments more, but it won’t become 0.

The leash attach point that gives the greatest area to roam is the center of a face.

  • Problem by Jeremy Galvagni
  • Solution by Stefan van der Waal
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