Originally posted by Anthem
You have a bunch of sections of fence (however many you need), all the same length, all straight and impossible to bend. Your goal is to build two closed fences, one containing the other, such that the inner fence uses a greater number of sections than the outer one.
What is the minimum number of sections that you need to achieve your goal?
(note: a section of fence can have an arbitrarily small, but positive, thickness)
One thing you didn't specify is whether the fence sections have to be touching end-to-end. In other words can a fence section have a part that is dangling, not enclosing anything, while another section pokes it in its side. If so, I have constructed a toothpick example that I think is the minimum,
a rhombus of 4 enclosing a weird arrangement of 5
but it's hard to describe and impossible to really prove that I did it because of the olives or maybe it was the gin.