22 into 21 best min fragment found: 7
  Cut up 22 sticks of length 21 like this:
    6 x (10 + 11)
    6 x (9 + 12)
    6 x (8 + 13)
    4 x (7 + 7 + 7)
  Reassemble as 21 sticks of length 22 like this:
    3 x (11 + 11)
    6 x (10 + 12)
    6 x (9 + 13)
    6 x (7 + 7 + 8)