22 into 13 best min fragment found: 21/4
  Cut up 22 sticks of length 13 like this:
    2 x (13/2 + 13/2)
    2 x (25/4 + 27/4)
    2 x (6 + 7)
    2 x (23/4 + 29/4)
    2 x (11/2 + 15/2)
    12 x (21/4 + 31/4)
  Reassemble as 13 sticks of length 22 like this:
    2 x (7 + 29/4 + 31/4)
    2 x (27/4 + 15/2 + 31/4)
    4 x (13/2 + 31/4 + 31/4)
    1 x (21/4 + 21/4 + 23/4 + 23/4)
    2 x (21/4 + 21/4 + 11/2 + 6)
    2 x (21/4 + 21/4 + 21/4 + 25/4)