A rancher plans to add a post between every two posts of an open-ended (straight) fence. If he currently has 10 posts in the fence, how many does he need to insert?

Assuming he intends to do it once only for each existing pair of posts, he will need 9.
If existing posts are represented by E and new posts are represented by n, the modified fence can be represented by
  E  n  E  n  E  n  E  n  E  n  E  n  E  n  E  n  E  n  E