22 into 12 best min fragment found: 14/3
  Cut up 22 sticks of length 12 like this:
    2 x (124/21 + 128/21)
    2 x (38/7 + 46/7)
    2 x (110/21 + 142/21)
    4 x (100/21 + 152/21)
    12 x (14/3 + 22/3)
  Reassemble as 12 sticks of length 22 like this:
    4 x (22/3 + 22/3 + 22/3)
    2 x (100/21 + 100/21 + 110/21 + 152/21)
    2 x (14/3 + 14/3 + 128/21 + 46/7)
    2 x (14/3 + 14/3 + 124/21 + 142/21)
    2 x (14/3 + 14/3 + 38/7 + 152/21)