Horizontal Force

You want to slowly push a stiff board across a 20 cm gap between two tabletops that are at the same height.

If you apply only a horizontal force, how long must the board be so that it doesn’t tilt down into the gap before reaching the other side?

This is a conceptual problem. The board needs to go over it’s center of gravity in order for it to fall. If it is a 20 cm gap the board needs to be double that length to maintain it’s equilibrium at the center.