22 into 8 best min fragment found: 18/5
  Cut up 22 sticks of length 8 like this:
    2 x (4 + 4)
    20 x (18/5 + 22/5)
  Reassemble as 8 sticks of length 22 like this:
    4 x (22/5 + 22/5 + 22/5 + 22/5 + 22/5)
    4 x (18/5 + 18/5 + 18/5 + 18/5 + 18/5 + 4)