27 into 10 best min fragment found: 9/2
  Cut up 27 sticks of length 10 like this:
    3 x (5 + 5)
    24 x (9/2 + 11/2)
  Reassemble as 10 sticks of length 27 like this:
    6 x (5 + 11/2 + 11/2 + 11/2 + 11/2)
    4 x (9/2 + 9/2 + 9/2 + 9/2 + 9/2 + 9/2)