Question

what if another style of rail fencing has 6 rails between each pair of post. how many rails are needed for 27 posts?

Answer 1

Here we have 6 rails between each pair of posts.

If the extremes are not conected, and we have 27 posts, then we must have 27 - 2 pairs of posts. Because the posts at the ends do not have any other post to form a pair, then we have 25 pairs.

and for each pair we have 6 rails, so we have 25*6 = 150 rails

If the ends are conected, like in a square, then the first post and the 27th post does make a pair, so in this case we have a pair more than in the previous case, so we have:

27 - 1 = 26 pairs, and the number of rails is:

26*6 = 156 rails