22 into 20 best min fragment found: 7
  Cut up 22 sticks of length 20 like this:
    2 x (10 + 10)
    8 x (9 + 11)
    4 x (8 + 12)
    8 x (7 + 13)
  Reassemble as 20 sticks of length 22 like this:
    4 x (11 + 11)
    4 x (10 + 12)
    8 x (9 + 13)
    4 x (7 + 7 + 8)