SWEET SIXTEEN: North & South Regions

NORTH:
Game E:
H:  4I24E11 O3E1I12 3O4E 13O1E A34IE4E2 I1 1OU11A3E11 31A4 1E11 1U3 O4 I11 1I1E 4A1UE1 2U1I12 2A3E 4O1 44I34 3O83I3 4A1 O44I3IA1 4U3O1 3A2A10I1E
L: X = the product of the coordinates of the circumcenter of the triangle whose vertices are A) the population rank of State N on the x-axis, B) the rank according to entry in the union of State N on the y-axis, and C) at the point ( half the number of the letters in State N’s name , number of state owned universities in State N ) ; where State N is the state with the longest name that doesn’t have the same initial letter as another state.

Game F:
H:  Number most prominently displayed on the large colourful object to the left (as we face them) of the large colourful object on the right on the stamp issued 48 years after song A made it to #1 on the Billboard charts in the US and whose singer's original last name, when doubled and joined by the first name of a children's song writer (mentioned later), evokes the large colourful object on the right of the stamp, and whose name (song A's) is mentioned as a world location in the lyrics of song B, written by the children's song writer mentioned previously and released 23 years after song A, which (song B) lists over 60 world locations, all of which are actual world locations except for song A's title, according to the Times World Atlas, and whose lyrics (song B's) includes another location that was involved in a milestone (or first) involving a Locomobile Steamer 100 years before the issue of the stamp.
L:  gekubeerde la raíz cuadrada de la racine carrée de duecento cinquanta sei

SOUTH:
Game E:
H: By taking the most direct route via state highways between two towns whose names are synonymous with a clothing storage device and a large group of trees in the state that produces the most cranberries, the sum of your route.
L: All fifth powers end in the same digit as the root.  What is the smallest two-digit number for which neither digit appears in its square, cube, or fourth power?

Game F:
H:  Value of Bob's initials, quotient in this substitution problem:

              B L
       ----------
B O B / L O D G E
        E Z E Z
        -------
          H E H E
          H E H E

L:  Number that is shared by highways that go through Waco, Lincoln and Charlotte.