27 into 22 best min fragment found: 8
  Cut up 27 sticks of length 22 like this:
    3 x (11 + 11)
    12 x (9 + 13)
    12 x (8 + 14)
  Reassemble as 22 sticks of length 27 like this:
    12 x (13 + 14)
    4 x (9 + 9 + 9)
    6 x (8 + 8 + 11)