30 into 18 best min fragment found: 15/2
  Cut up 30 sticks of length 18 like this:
    6 x (9 + 9)
    24 x (15/2 + 21/2)
  Reassemble as 18 sticks of length 30 like this:
    12 x (9 + 21/2 + 21/2)
    6 x (15/2 + 15/2 + 15/2 + 15/2)