27 into 12 best min fragment found: 21/4
  Cut up 27 sticks of length 12 like this:
    3 x (6 + 6)
    24 x (21/4 + 27/4)
  Reassemble as 12 sticks of length 27 like this:
    6 x (27/4 + 27/4 + 27/4 + 27/4)
    6 x (21/4 + 21/4 + 21/4 + 21/4 + 6)