19 into 18 best min fragment found: 6
  Cut up 19 sticks of length 18 like this:
    3 x (9 + 9)
    6 x (8 + 10)
    6 x (7 + 11)
    4 x (6 + 6 + 6)
  Reassemble as 18 sticks of length 19 like this:
    6 x (9 + 10)
    6 x (8 + 11)
    6 x (6 + 6 + 7)