22 into 10 best min fragment found: 13/3
  Cut up 22 sticks of length 10 like this:
    2 x (5 + 5)
    4 x (14/3 + 16/3)
    16 x (13/3 + 17/3)
  Reassemble as 10 sticks of length 22 like this:
    2 x (16/3 + 16/3 + 17/3 + 17/3)
    4 x (5 + 17/3 + 17/3 + 17/3)
    4 x (13/3 + 13/3 + 13/3 + 13/3 + 14/3)