21 into 8 best min fragment found: 7/2
  Cut up 21 sticks of length 8 like this:
    3 x (4 + 4)
    18 x (7/2 + 9/2)
  Reassemble as 8 sticks of length 21 like this:
    6 x (7/2 + 4 + 9/2 + 9/2 + 9/2)
    2 x (7/2 + 7/2 + 7/2 + 7/2 + 7/2 + 7/2)