## Problem of the Day #115: Picture Hanging
*July 12, 2011*

*Posted by Albert in : potd , 5 comments*

There are $n$ evenly spaced nails on a wall, parallel to the floor. Saketh wants to hang a picture on the nails so that when all the nails are in place, the picture doesn’t fall, but when Sreenath removes *any* one nail, the picture *does* fall. The infinitely strong, infinitely thin, weightless wire of arbitrarily long length is already attached to the picture frame. Let $f(n)$ be the minimum number of times Saketh can do clockwise and counterclockwise wraps around the nails to set up this system (note: $f(1) = 1$). Find: $$\sum\limits_{i=1}^{32} f(i)$$