Ken's Puzzle of the Week

Rods in a Box

  1. Place 3 length=1 rods together into a configuration which maximizes the volume of the smallest box (rectangular prism) which contains the rods.  What is the configuration and resulting volume of the box?  The rods do not necessarily have to touch the box along their length; the entire structure must simply fit within the box's volume.
  2. What are the dimensions of the smallest box which can hold 3 rods regardless of their configuration?
Extension: Solve for 4 and 5 rods.

Source: Original.
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