18 into 17 best min fragment found: 6
  Cut up 18 sticks of length 17 like this:
    6 x (8 + 9)
    6 x (7 + 10)
    6 x (6 + 11)
  Reassemble as 17 sticks of length 18 like this:
    3 x (9 + 9)
    6 x (8 + 10)
    6 x (7 + 11)
    2 x (6 + 6 + 6)