8 into 3 best min fragment found: 4/3
  Cut up 8 sticks of length 3 like this:
    2 x (3)
    6 x (4/3 + 5/3)
  Reassemble as 3 sticks of length 8 like this:
    2 x (5/3 + 5/3 + 5/3 + 3)
    1 x (4/3 + 4/3 + 4/3 + 4/3 + 4/3 + 4/3)