19 into 7 best min fragment found: 25/8
  Cut up 19 sticks of length 7 like this:
    1 x (7/2 + 7/2)
    2 x (27/8 + 29/8)
    2 x (13/4 + 15/4)
    14 x (25/8 + 31/8)
  Reassemble as 7 sticks of length 19 like this:
    2 x (29/8 + 15/4 + 31/8 + 31/8 + 31/8)
    2 x (7/2 + 31/8 + 31/8 + 31/8 + 31/8)
    1 x (25/8 + 25/8 + 25/8 + 25/8 + 13/4 + 13/4)
    2 x (25/8 + 25/8 + 25/8 + 25/8 + 25/8 + 27/8)