23 into 21 best min fragment found: 29/4
  Cut up 23 sticks of length 21 like this:
    1 x (21/2 + 21/2)
    4 x (39/4 + 45/4)
    2 x (19/2 + 23/2)
    4 x (37/4 + 47/4)
    2 x (17/2 + 25/2)
    4 x (31/4 + 53/4)
    2 x (15/2 + 27/2)
    4 x (29/4 + 55/4)
  Reassemble as 21 sticks of length 23 like this:
    1 x (23/2 + 23/2)
    4 x (45/4 + 47/4)
    2 x (21/2 + 25/2)
    4 x (39/4 + 53/4)
    2 x (19/2 + 27/2)
    4 x (37/4 + 55/4)
    2 x (15/2 + 31/4 + 31/4)
    2 x (29/4 + 29/4 + 17/2)