8 into 7 best min fragment found: 5/2
  Cut up 8 sticks of length 7 like this:
    2 x (7/2 + 7/2)
    2 x (3 + 4)
    4 x (5/2 + 9/2)
  Reassemble as 7 sticks of length 8 like this:
    1 x (4 + 4)
    4 x (7/2 + 9/2)
    2 x (5/2 + 5/2 + 3)