13 into 8 best min fragment found: 13/4
  Cut up 13 sticks of length 8 like this:
    2 x (15/4 + 17/4)
    3 x (7/2 + 9/2)
    8 x (13/4 + 19/4)
  Reassemble as 8 sticks of length 13 like this:
    1 x (17/4 + 17/4 + 9/2)
    2 x (15/4 + 9/2 + 19/4)
    3 x (7/2 + 19/4 + 19/4)
    2 x (13/4 + 13/4 + 13/4 + 13/4)