20 into 6 best min fragment found: 8/3
  Cut up 20 sticks of length 6 like this:
    8 x (6)
    12 x (8/3 + 10/3)
  Reassemble as 6 sticks of length 20 like this:
    2 x (10/3 + 10/3 + 10/3 + 10/3 + 10/3 + 10/3)
    4 x (8/3 + 8/3 + 8/3 + 6 + 6)