27 into 16 best min fragment found: 13/2
  Cut up 27 sticks of length 16 like this:
    3 x (8 + 8)
    4 x (15/2 + 17/2)
    4 x (7 + 9)
    16 x (13/2 + 19/2)
  Reassemble as 16 sticks of length 27 like this:
    4 x (17/2 + 9 + 19/2)
    6 x (8 + 19/2 + 19/2)
    2 x (13/2 + 13/2 + 7 + 7)
    4 x (13/2 + 13/2 + 13/2 + 15/2)