18 into 13 best min fragment found: 13/3
  Cut up 18 sticks of length 13 like this:
    3 x (19/3 + 20/3)
    3 x (56/9 + 61/9)
    3 x (6 + 7)
    3 x (17/3 + 22/3)
    3 x (50/9 + 67/9)
    3 x (13/3 + 13/3 + 13/3)
  Reassemble as 13 sticks of length 18 like this:
    1 x (6 + 6 + 6)
    3 x (50/9 + 17/3 + 61/9)
    3 x (13/3 + 20/3 + 7)
    3 x (13/3 + 19/3 + 22/3)
    3 x (13/3 + 56/9 + 67/9)