Balancing Rods
You are given a set of N rods of lengths 1 to N. Each rod weighs a number
of ounces equal to its length (i.e. the rod of length 4 weighs 4 ounces.)
A small [weightless] loop is attached to the end of each rod, letting it
either support or hang from another rod.
A small loop is also suspended from the ceiling.
Build a mobile out of the rods, trying to maximize:
 the longest horizontal distance from the original loop.
 the horizontal distance from the furthest left to the furthest right
point on the mobile.
Solve for N ranging from 1 to 6.
What are the resulting distances in each case?
For example, I believe the following arrangement solves both questions above for
N=4. (I'll let you determine the distances.)

444444X44
1
333333
2
2
Source: Original.
I've limited N to 6 to keep the problem simple to approach,
but I'd be happy to accept and publish results for higher N.
Solution
Mail to Ken