22 into 18 best min fragment found: 13/2
  Cut up 22 sticks of length 18 like this:
    2 x (9 + 9)
    8 x (15/2 + 21/2)
    4 x (7 + 11)
    8 x (13/2 + 23/2)
  Reassemble as 18 sticks of length 22 like this:
    2 x (11 + 11)
    8 x (21/2 + 23/2)
    4 x (7 + 15/2 + 15/2)
    4 x (13/2 + 13/2 + 9)