19 into 10 best min fragment found: 11/3
  Cut up 19 sticks of length 10 like this:
    2 x (13/3 + 17/3)
    2 x (4 + 6)
    15 x (11/3 + 19/3)
  Reassemble as 10 sticks of length 19 like this:
    5 x (19/3 + 19/3 + 19/3)
    2 x (11/3 + 11/3 + 17/3 + 6)
    1 x (11/3 + 11/3 + 11/3 + 4 + 4)
    2 x (11/3 + 11/3 + 11/3 + 11/3 + 13/3)