15 into 13 best min fragment found: 9/2
  Cut up 15 sticks of length 13 like this:
    3 x (13/2 + 13/2)
    2 x (6 + 7)
    2 x (11/2 + 15/2)
    2 x (5 + 8)
    6 x (9/2 + 17/2)
  Reassemble as 13 sticks of length 15 like this:
    1 x (15/2 + 15/2)
    2 x (7 + 8)
    6 x (13/2 + 17/2)
    2 x (9/2 + 5 + 11/2)
    2 x (9/2 + 9/2 + 6)