27 into 19 best min fragment found: 19/3
  Cut up 27 sticks of length 19 like this:
    2 x (28/3 + 29/3)
    2 x (9 + 10)
    2 x (26/3 + 31/3)
    2 x (25/3 + 32/3)
    2 x (8 + 11)
    2 x (23/3 + 34/3)
    2 x (22/3 + 35/3)
    2 x (7 + 12)
    2 x (20/3 + 37/3)
    9 x (19/3 + 19/3 + 19/3)
  Reassemble as 19 sticks of length 27 like this:
    1 x (19/3 + 31/3 + 31/3)
    2 x (19/3 + 10 + 32/3)
    2 x (19/3 + 29/3 + 11)
    2 x (19/3 + 28/3 + 34/3)
    2 x (19/3 + 9 + 35/3)
    2 x (19/3 + 26/3 + 12)
    2 x (19/3 + 25/3 + 37/3)
    2 x (19/3 + 19/3 + 7 + 22/3)
    2 x (19/3 + 19/3 + 20/3 + 23/3)
    2 x (19/3 + 19/3 + 19/3 + 8)