27 into 21 best min fragment found: 15/2
  Cut up 27 sticks of length 21 like this:
    9 x (9 + 12)
    18 x (15/2 + 27/2)
  Reassemble as 21 sticks of length 27 like this:
    9 x (27/2 + 27/2)
    3 x (9 + 9 + 9)
    9 x (15/2 + 15/2 + 12)