IBM Ponder This #111 · July 2007

Given a square piece of property of unit side you wish to build fences so that it is impossible to see through the property, ie there is no sightline connecting two points outside the property and passing through the property that does not intersect a fence. The fences do not have to be connected and several fences can come together at a point. What is the minimum total length of fencing required and how is it arranged. For example you could place fencing along all four sides. This would have total length 4 but is not the best possible.

I do not have a proof that my answer is minimal. I will accept as correct any answer that does at least as well.

UPDATE, 7/12/07: The fences can be placed in the interior of the property, they aren't restricted to the boundary.

Solution

Best opened after a real attempt

To be added.