19 into 11 best min fragment found: 9/2
  Cut up 19 sticks of length 11 like this:
    1 x (11/2 + 11/2)
    6 x (5 + 6)
    12 x (9/2 + 13/2)
  Reassemble as 11 sticks of length 19 like this:
    6 x (6 + 13/2 + 13/2)
    3 x (9/2 + 9/2 + 5 + 5)
    2 x (9/2 + 9/2 + 9/2 + 11/2)