Solution

The resistance between two points on a conducting plate depends on how far the current has to travel. If you place the contacts facing each other at the center of each face, the path the current takes is the shortest possible: it simply goes straight through the thickness of the plate.

Therefore, the resistance is minimal when the contacts are located exactly at the center of each face. This way, the current flows radially and along the shortest possible path through the thickness of the plate.

$\boxed{\text{The contacts must be placed at the center of the plate from opposite sides.}}$