Ken's Puzzle of the Week

Rods in a Mobile

The diagram is not drawn to scale.  Every horizontal length is an integer.  If all three horizontal rods are the same length, what is that length when:

  1. The weights from left to right are 1,2,3,4,5?
  2. The weights from left to right are 5,4,3,2,1?
What configuration of the weights 1,2,3,4,5 leads to the longest/shortest rod-length?

Extension: What is the lightest configuration of unique weights for a rod length of 3?  4?  5?

Source: Original.

Solution
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