24 into 21 best min fragment found: 15/2
  Cut up 24 sticks of length 21 like this:
    6 x (21/2 + 21/2)
    6 x (9 + 12)
    12 x (15/2 + 27/2)
  Reassemble as 21 sticks of length 24 like this:
    3 x (12 + 12)
    12 x (21/2 + 27/2)
    6 x (15/2 + 15/2 + 9)