21 into 9 best min fragment found: 15/4
  Cut up 21 sticks of length 9 like this:
    3 x (9/2 + 9/2)
    18 x (15/4 + 21/4)
  Reassemble as 9 sticks of length 21 like this:
    3 x (21/4 + 21/4 + 21/4 + 21/4)
    6 x (15/4 + 15/4 + 15/4 + 9/2 + 21/4)