Hole in the Wall

hole in wall

A man is lost in a desert and comes upon a wall. The wall has a miniature of a picture of the wall and an arrow pointing at the very middle saying “you are here”. It also states that that, at some location, the wall is broken, opening up a passageway to a garden of fruit and water.

The man, hoping to survive, wants to minimize his time finding this hole in the wall.

What should the man’s strategy be if he assumes:

  1. The hole’s location is randomly distributed across the entire wall
  2. The hole’s location is distributed with a symmetrical triangular distribution with the peak probability at the center.