11 into 7 best min fragment found: 11/4
  Cut up 11 sticks of length 7 like this:
    1 x (7/2 + 7/2)
    2 x (13/4 + 15/4)
    2 x (3 + 4)
    6 x (11/4 + 17/4)
  Reassemble as 7 sticks of length 11 like this:
    2 x (13/4 + 7/2 + 17/4)
    2 x (3 + 15/4 + 17/4)
    2 x (11/4 + 4 + 17/4)
    1 x (11/4 + 11/4 + 11/4 + 11/4)