10 into 7 best min fragment found: 7/3
  Cut up 10 sticks of length 7 like this:
    2 x (10/3 + 11/3)
    2 x (3 + 4)
    2 x (8/3 + 13/3)
    4 x (7/3 + 7/3 + 7/3)
  Reassemble as 7 sticks of length 10 like this:
    2 x (7/3 + 11/3 + 4)
    2 x (7/3 + 10/3 + 13/3)
    1 x (7/3 + 7/3 + 8/3 + 8/3)
    2 x (7/3 + 7/3 + 7/3 + 3)