Please help me with a fencepost problem
My name is Alex, I'm new to the forum.
I'm not sure if I'm posting my question in the right thread but it is about a very specific case of a fencepost problem, so it must be geometry...
Here is the picture:
1) 2 long sides, 100 units each, with 20 square posts 1 unit each
2) 2 short sides, 50 units each, with 10 square posts 1 unit each
3) Fence is located at the outter perimeter of the posts.
4) 2 long pieces of the fence are 100 units each, in 5 units sections between centers of the posts.
5) 2 short pieces of the fence are 50 units each, in 5 units sections between centers of the posts.
6) Just to be clear, length\width\perimeter of the fence equals that of a space that is enclosed by the fence.
So my question is:
Is it possible to mathematically arrive to such locations of the posts and length(5 units) of the equal pieces of the fence?
I think that it is not possible, because:
1) Posts can be any width between 0 <= W <= 5\3 units, and still have 5 units of fence between their centers.
2) Since centers of the posts are not located ON the perimieter of the fence, there had to be 61 posts total, as per standard fencepost formula for the perimeter.
3) Such locations of the posts are only true for a line of fence with the lengh of 100+100+50+50=300 units and 60 posts, but not for the rectangular fence of 100x50 units.
If you need more details, I would be glad to provide them.