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Question
The question is not homework.  I have been out of school over 35 years and I am re-learning math/algebra on my own.  I was just needing some assistance.  Thank you.

Answer
There are n+1 equal spaces between the posts, so the distance between any two posts will be
d/(n+1)

Draw a few pictures to see why

Let "p" represent a post

If n=3

p  p  p  p  p

4 spaces


If n=7

p  p  p  p  p  p  p  p  p

8 spaces


there's a space in front of each post except the last one , so n+1 spaces  

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